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Statistics LibreTexts

1: Introduction to Statistics

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  • Page ID 258

  • Rice University

This first chapter begins by discussing what statistics are and why the study of statistics is important. Subsequent sections cover a variety of topics all basic to the study of statistics. One theme common to all of these sections is that they cover concepts and ideas important for other chapters in the book.

  • 1.1: What are Statistics? Statistics include numerical facts and figures, but also involves math and relies upon calculations of numbers. It also relies heavily on how the numbers are chosen and how the statistics are interpreted.
  • 1.2: Importance of Statistics It is important to properly evaluate data and claims that bombard us every day. If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest. Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, statistics is one of the most important things that you can study.
  • 1.3: Descriptive Statistics Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics.
  • 1.4: Inferential Statistics In statistics, we often rely on a sample --- that is, a small subset of a larger set of data --- to draw inferences about the larger set. The larger set is known as the population from which the sample is drawn.
  • 1.5: Sampling Demonstration This demonstration is used to teach students how to distinguish between simple random sampling and stratified sampling and how often random and stratified sampling give exactly the same result.
  • 1.6: Variables Variables are properties or characteristics of some event, object, or person that can take on different values or amounts (as opposed to constants such as π that do not vary). When conducting research, experimenters often manipulate variables. When a variable is manipulated by an experimenter, it is called an independent variable. The experiment seeks to determine the effect of the independent variable on a dependent variable.
  • 1.7: Percentiles A test score in and of itself is usually difficult to interpret. For example, if you learned that your score on a measure of shyness was 35 out of a possible 50, you would have little idea how shy you are compared to other people. More relevant is the percentage of people with lower shyness scores than yours. This percentage is called a percentile.
  • 1.8: Levels of Measurement Before we can conduct a statistical analysis, we need to measure our dependent variable. Exactly how the measurement is carried out depends on the type of variable involved in the analysis. Different types are measured differently. To measure the time taken to respond to a stimulus, you might use a stop watch. Stop watches are of no use, of course, when it comes to measuring someone's attitude towards a political candidate.
  • 1.9: Measurements This is a demonstration of a very complex issue. Experts in the field disagree on how to interpret differences on an ordinal scale, so do not be discouraged if it takes you a while to catch on. In this demonstration you will explore the relationship between interval and ordinal scales. The demonstration is based on two brands of baked goods.
  • 1.10: Distributions Define "distribution" Interpret a frequency distribution Distinguish between a frequency distribution and a probability distribution Construct a grouped frequency distribution for a continuous variable
  • 1.11: Summation Notation Many statistical formulas involve summing numbers. Fortunately there is a convenient notation for expressing summation. This section covers the basics of this summation notation.
  • 1.12: Linear Transformations Often it is necessary to transform data from one measurement scale to another. For example, you might want to convert height measured in feet to height measured in inches.
  • 1.13: Logarithms The log transformation reduces positive skew. This can be valuable both for making the data more interpretable and for helping to meet the assumptions of inferential statistics.
  • 1.14: Statistical Literacy
  • 1.E: Introduction to Statistics (Exercises)

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Statistics and probability

Unit 1: analyzing categorical data, unit 2: displaying and comparing quantitative data, unit 3: summarizing quantitative data, unit 4: modeling data distributions, unit 5: exploring bivariate numerical data, unit 6: study design, unit 7: probability, unit 8: counting, permutations, and combinations, unit 9: random variables, unit 10: sampling distributions, unit 11: confidence intervals, unit 12: significance tests (hypothesis testing), unit 13: two-sample inference for the difference between groups, unit 14: inference for categorical data (chi-square tests), unit 15: advanced regression (inference and transforming), unit 16: analysis of variance (anova).

  • Math Article

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. However, there are two important and basic ideas involved in statistics; they are  uncertainty and variation.  The uncertainty and variation in different fields can be determined only through statistical analysis. These uncertainties are basically determined by the probability that plays an important role in statistics. 

What is Statistics?

Statistics is simply defined as the study and manipulation of data. As we have already discussed in the introduction that statistics deals with the analysis and computation of numerical data. Let us see more definitions of statistics given by different authors here.

According to Merriam-Webster dictionary , statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.

According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.

Statistics – Download PDF

Statistics examples.

Some of the real-life examples of statistics are:

  • To find the mean of the marks obtained by each student in the class whose strength is 50. The average value here is the statistics of the marks obtained.
  • Suppose you need to find how many members are employed in a city. Since the city is populated with 15 lakh people, hence we will take a survey here for 1000 people (sample). Based on that, we will create the data, which is the statistic.

Basics of Statistics

The basics of statistics include the measure of central tendency and  the measure of dispersion. The central tendencies are  mean, median and mode  and dispersions comprise variance and standard deviation. 

Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set.

Variation is the measure of spread out of the collection of data. Standard deviation is the measure of the dispersion of data from the mean. The square of standard deviation is equal to the variance.

Mathematical Statistics

Mathematical statistics is the application of Mathematics to Statistics, which was initially conceived as the science of the state — the collection and analysis of facts about a country: its economy, and, military, population, and so forth.

Mathematical techniques used for different analytics include mathematical analysis, linear algebra, stochastic analysis, differential equation and measure-theoretic probability theory.

Types of Statistics

Basically, there are two types of statistics.

Descriptive Statistics

Inferential Statistics

In the case of descriptive statistics, the data or collection of data is described in summary. But in the case of inferential stats, it is used to explain the descriptive one. Both these types have been used on large scale.

The data is summarised and explained in descriptive statistics. The summarization is done from a population sample utilising several factors such as mean and standard deviation. Descriptive statistics is a way of organising, representing, and explaining a set of data using charts, graphs, and summary measures. Histograms, pie charts, bars, and scatter plots are common ways to summarise data and present it in tables or graphs. Descriptive statistics are just that: descriptive. They don’t need to be normalised beyond the data they collect.

We attempt to interpret the meaning of descriptive statistics using inferential statistics. We utilise inferential statistics to convey the meaning of the collected data after it has been collected, evaluated, and summarised. The probability principle is used in inferential statistics to determine if patterns found in a study sample may be extrapolated to the wider population from which the sample was drawn. Inferential statistics are used to test hypotheses and study correlations between variables, and they can also be used to predict population sizes. Inferential statistics are used to derive conclusions and inferences from samples, i.e. to create accurate generalisations.

Statistics Formulas

The formulas that are commonly used in statistical analysis are given in the table below.

Summary Statistics

In Statistics, summary statistics are a part of descriptive statistics (Which is one of the types of statistics), which gives the list of information about sample data. We know that statistics deals with the presentation of data visually and quantitatively. Thus, summary statistics deals with summarizing the statistical information. Summary statistics generally deal with condensing the data in a simpler form, so that the observer can understand the information at a glance.  Generally, statisticians try to describe the observations by finding:

  • The measure of central tendency or mean of the locations, such as arithmetic mean.
  • The measure of distribution shapes like skewness or kurtosis.
  • The measure of dispersion such as the standard mean absolute deviation.
  • The measure of statistical dependence such as correlation coefficient.

Summary Statistics Table

The summary statistics table is the visual representation of summarized statistical information about the data in tabular form.

For example, the blood group of 20 students in the class are O, A, B, AB, B, B, AB, O, A, B, B, AB, AB, O, O, B, A, AB, B, A.

Thus, the summary statistics table shows that 4 students in the class have O blood group, 4 students have A blood group, 7 students in the class have B blood group and 5 students in the class have AB blood group.  The summary statistics table is generally used to represent the big data related to population, unemployment, and the economy to be summarized systematically to interpret the accurate result.

Scope of Statistics

Statistics is used in many sectors such as psychology, geology, sociology, weather forecasting, probability and much more. The goal of statistics is to gain understanding from the data, it focuses on applications, and hence, it is distinctively considered as a mathematical science.

Methods in Statistics

The methods involve collecting, summarizing, analyzing, and interpreting variable numerical data. Here some of the methods are provided below.

  • Data collection
  • Data summarization
  • Statistical analysis

What is Data in Statistics?

Data is a collection of facts, such as numbers, words, measurements, observations etc.

Types of Data

  • Example- She can run fast, He is thin.
  • Example- An Octopus is an Eight legged creature.

Types of quantitative data

  • Discrete data- has a particular fixed value. It can be counted
  • Continuous data- is not fixed but has a range of data. It can be measured.

Representation of Data

There are different ways to represent data such as through graphs, charts or tables. The general representation of statistical data are:

  • Frequency Distribution

Measures of Central Tendency

In Mathematics, statistics are used to describe the central tendencies of the grouped and ungrouped data. The three measures of central tendency are:

All three measures of central tendency are used to find the central value of the set of data.

Measures of Dispersion

In statistics, the dispersion measures help interpret data variability, i.e. to understand how homogenous or heterogeneous the data is. In simple words, it indicates how squeezed or scattered the variable is. However, there are two types of dispersion measures, absolute and relative. They are tabulated as below:

Skewness in Statistics

Skewness, in statistics, is a measure of the asymmetry in a probability distribution. It measures the deviation of the curve of the normal distribution for a given set of data. 

The value of skewed distribution could be positive or negative or zero. Usually, the bell curve of normal distribution has zero skewness.

ANOVA Statistics

ANOVA Stands for Analysis of Variance. It is a collection of statistical models, used to measure the mean difference for the given set of data.

Degrees of freedom

In statistical analysis, the degree of freedom is used for the values that are free to change. The independent data or information that can be moved while estimating a parameter is the degree of freedom of information. 

Applications of Statistics

Statistics have huge applications across various fields in Mathematics as well as in real life. Some of the applications of statistics are given below:

  • Applied statistics, theoretical statistics and mathematical statistics
  • Machine learning and data mining
  • Statistics in society
  • Statistical computing
  • Statistics applied to the mathematics of the arts

Video Lesson

Grade 11 statistics.

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Statistics Related Articles

Hope this detailed discussion and formulas on statistics will help you to solve problems quickly and efficiently. Learn more Maths concepts at BYJU’S with the help of interactive videos.

Frequently Asked Questions on Statistics

What exactly is statistics.

Statistics is a branch that deals with the study of the collection, analysis, interpretation, organisation, and presentation of data. Mathematically, statistics is defined as the set of equations, which are used to analyse things.

What are the two types of statistics?

The two different types of statistics used for analyzing the data are:

  • Descriptive Statistics: It summarizes the data from the sample using indexes
  • Inferential Statistics: It concludes from the data which are subjected to the random variation

What is Summary Statistics?

How is statistics applicable in maths.

Statistics is a part of Applied Mathematics that uses probability theory to generalize the collected sample data. It helps to characterize the likelihood where the generalizations of data are accurate. This is known as statistical inference.

What is the purpose of statistics?

What is the importance of statistics in real life.

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  • Prof. Philippe Rigollet

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  • Mathematics

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  • Probability and Statistics

Learning Resource Types

Statistics for applications, lecture 1: introduction to statistics.

*NOTE: This video was recorded in Fall 2017. The rest of the lectures were recorded in Fall 2016, but video of Lecture 1 was not available.

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MIT Open Learning

MA121: Introduction to Statistics

Course introduction.

  • Time: 32 hours
  • College Credit Recommended ($25 Proctor Fee) -->
  • Free Certificate

The purpose of this course is to introduce you to the subject of statistics as a science of data. There is data abound in this information age; how to extract useful knowledge and gain a sound understanding of complex data sets has been more of a challenge. In this course, we will focus on the fundamentals of statistics, which may be broadly described as the techniques to collect, clarify, summarize, organize, analyze, and interpret numerical information.

This course will begin with a brief overview of the discipline of statistics and will then quickly focus on descriptive statistics, introducing graphical methods of describing data. You will learn about combinatorial probability and random distributions, the latter of which serves as the foundation for statistical inference. On the side of inference, we will focus on both estimation and hypothesis testing issues. We will also examine the techniques to study the relationship between two or more variables; this is known as regression.

By the end of this course, you should gain a sound understanding of what statistics represent, how to use statistics to organize and display data, and how to draw valid inferences based on data by using appropriate statistical tools.

Course Syllabus

First, read the course syllabus. Then, enroll in the course by clicking "Enroll me". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.

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Unit 1: Statistics and Data

In today's technologically advanced world, we have access to large volumes of data. The first step of data analysis is to accurately summarize all of this data, both graphically and numerically, so that we can understand what the data reveals. To be able to use and interpret the data correctly is essential to making informed decisions. For instance, when you see a survey of opinion about a certain TV program, you may be interested in the proportion of those people who indeed like the program. 

In this unit, you will learn about descriptive statistics, which are used to summarize and display data. After completing this unit, you will know how to present your findings once you have collected data. For example, suppose you want to buy a new mobile phone with a particular type of a camera. Suppose you are not sure about the prices of any of the phones with this feature, so you access a website that provides you with a sample data set of prices, given your desired features. Looking at all of the prices in a sample can sometimes be confusing. A better way to compare this data might be to look at the median price and the variation of prices. The median and variation are two ways out of several ways that you can describe data. You can also graph the data so that it is easier to see what the price distribution looks like. 

In this unit, you will study precisely this; namely, you will learn both numerical and graphical ways to describe and display your data. You will understand the essentials of calculating common descriptive statistics for measuring center, variability, and skewness in data. You will learn to calculate and interpret these measurements and graphs.

Descriptive statistics are, as their name suggests, descriptive. They do not generalize beyond the data considered. Descriptive statistics illustrate what the data shows. Numerical descriptive measures computed from data are called statistics. Numerical descriptive measures of the population are called parameters. Inferential statistics can be used to generalize the findings from sample data to a broader population.

Completing this unit should take you approximately 7 hours.

Unit 2: Elements of Probability and Random Variables

Probabilities affect our everyday lives. In this unit, you will learn about probability and its properties, how probability behaves, and how to calculate and use it. You will study the fundamentals of probability and will work through examples that cover different types of probability questions. These basic probability concepts will provide a foundation for understanding more statistical concepts, for example, interpreting polling results. Though you may have already encountered concepts of probability, after this unit, you will be able to formally and precisely predict the likelihood of an event occurring given certain constraints. 

Probability theory is a discipline that was created to deal with chance phenomena. For instance, before getting a surgery, a patient wants to know the chances that the surgery might fail; before taking medication, you want to know the chances that there will be side effects; before leaving your house, you want to know the chance that it will rain today. Probability is a measure of likelihood that takes on values between 0 and 1, inclusive, with 0 representing impossible events and 1 representing certainty. The chances of events occurring fall between these two values. 

The skill of calculating probability allows us to make better decisions. Whether you are evaluating how likely it is to get more than 50% of the questions correct on a quiz if you guess randomly; predicting the chance that the next storm will arrive by the end of the week; or exploring the relationship between the number of hours students spend at the gym and their performance on an exam, an understanding of the fundamentals of probability is crucial.  

We will also talk about random variables. A random variable describes the outcomes of a random experiment. A statistical distribution describes the numbers of times each possible outcome occurs in a sample. The values of a random variable can vary with each repetition of an experiment. Intuitively, a random variable, summarizing certain chance phenomenon, takes on values with certain probabilities. A random variable can be classified as being either discrete or continuous, depending on the values it assumes. Suppose you count the number of people who go to a coffee shop between 4 p.m. and 5 p.m. and the amount of waiting time that they spend in that hour. In this case, the number of people is an example of a discrete random variable and the amount of waiting time they spend is an example of a continuous random variable.

Completing this unit should take you approximately 8 hours.

Unit 3: Sampling Distributions

The concept of sampling distribution lies at the very foundation of statistical inference. It is best to introduce sampling distribution using an example here. Suppose you want to estimate a parameter of a population, say the population mean. There are two natural estimators: 1. sample mean, which is the average value of the data set; and 2. median, which is the middle number when the measurements are arranged in ascending (or descending) order. In particular, for a sample of even size n, the median is the mean of the middle two numbers. But which one is better, and in what sense? This involves repeated sampling, and you want to choose the estimator that would do better on average. It is clear that different samples may give different sample means and medians; some of them may be closer to the truth than the others. Consequently, we cannot compare these two sample statistics or, in general, any two sample statistics on the basis of their performance with a single sample. Instead, you should recognize that sample statistics are themselves random variables; therefore, sample statistics should have frequency distributions by taking into account all possible samples. In this unit, you will study the sampling distribution of several sample statistics. This unit will show you how the central limit theorem can help to approximate sampling distributions in general.

Completing this unit should take you approximately 5 hours.

Unit 4: Estimation with Confidence Intervals

In this unit, you will learn how to use the central limit theorem and confidence intervals, the latter of which enables you to estimate unknown population parameters. The central limit theorem provides us with a way to make inferences from samples of non-normal populations. This theorem states that given any population, as the sample size increases, the sampling distribution of the means approaches a normal distribution. This powerful theorem allows us to assume that given a large enough sample, the sampling distribution will be normally distributed. 

You will also learn about confidence intervals, which provide you with a way to estimate a population parameter. Instead of giving just a one-number estimate of a variable, a confidence interval gives a range of likely values for it. This is useful, because point estimates will vary from sample to sample, so an interval with certain confidence level is better than a single point estimate. After completing this unit, you will know how to construct such confidence intervals and the level of confidence. 

Completing this unit should take you approximately 4 hours.

Unit 5: Hypothesis Test

A hypothesis test involves collecting and evaluating data from a sample. The data gathered and evaluated is then used to make a decision as to whether or not the data supports the claim that is made about the population. This unit will teach you how to conduct hypothesis tests and how to identify and differentiate between the errors associated with them.  

Many times, you need answers to questions in order to make efficient decisions. For example, a restaurant owner might claim that his restaurant's food costs 30% less than other restaurants in the area, or a phone company might claim that its phones last at least one year more than phones from other companies. In order to decide whether it would be more affordable to eat at the restaurant that "costs 30% less" or another restaurant in the area, or in order to decide which phone company to choose based on the durability of the phone, you will have to collect data to justify these claims. The process of hypothesis testing is a way of decision-making. In this unit, you will learn to establish your assumptions through null and alternative hypotheses. The null hypothesis is the hypothesis that is assumed to be true and the hypothesis you hope to nullify, while the alternative hypothesis is the research hypothesis that you claim to be true. This means that you need to conduct the correct tests to be able to accept or reject the null hypothesis. You will learn how to compare sample characteristics to see whether there is enough data to accept or reject the null hypothesis.

Unit 6: Linear Regression

In this unit, we will discuss situations in which the mean of a population, treated as a variable, depends on the value of another variable. One of the main reasons why we conduct such analyses is to understand how two variables are related to each other. The most common type of relationship is a linear relationship. For example, you may want to know what happens to one variable when you increase or decrease the other variable. You want to answer questions such as, "Does one variable increase as the other increases, or does the variable decrease?” For example, you may want to determine how the mean reaction time of rats depends on the amount of drug in bloodstream.

In this unit, you will also learn to measure the degree of a relationship between two or more variables. Both correlation and regression are measures for comparing variables. Correlation quantifies the strength of a relationship between two variables and is a measure of existing data. On the other hand, regression is the study of the strength of a linear relationship between an independent and dependent variable and can be used to predict the value of the dependent variable when the value of the independent variable is known.

Study Guide

This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary terms. It is not meant to replace the course materials!

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Please take a few minutes to give us feedback about this course. We appreciate your feedback, whether you completed the whole course or even just a few resources. Your feedback will help us make our courses better, and we use your feedback each time we make updates to our courses.

If you come across any urgent problems, email [email protected].

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Take this exam if you want to earn a free Course Completion Certificate.

To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt.

Once you pass this final exam, you will be awarded a free Course Completion Certificate .

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Take this exam if you want to earn college credit for this course . This course is eligible for college credit through Saylor Academy's Saylor Direct Credit Program .

The Saylor Direct Credit Final Exam requires a proctoring fee of $5 . To pass this course and earn a Credly Badge and official transcript , you will need to earn a grade of 70% or higher on the Saylor Direct Credit Final Exam. Your grade for this exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again a maximum of 3 times , with a 14-day waiting period between each attempt.

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Introductory Statistics

(34 reviews)

www introduction to statistics

Barbara Illowsky, Cupertino, California

Susan Dean, Cupertino, California

Laurel Chiappetta, Pittsburgh, Pennsylvania

Copyright Year: 2013

ISBN 13: 9781938168208

Publisher: OpenStax

Language: English

Formats Available

Conditions of use.

Attribution

Learn more about reviews.

Reviewed by Amish Mishra, Assistant Professor, Taylor University on 1/3/24

The text provides the necessary details of the most important topics in an introductory statistics course without going too deep into details or calculations. read more

Comprehensiveness rating: 5 see less

The text provides the necessary details of the most important topics in an introductory statistics course without going too deep into details or calculations.

Content Accuracy rating: 5

Formula 10 in Appendix F has the bounds flipped on the gamma function’s integral. It should go from 0 to infinity.

Relevance/Longevity rating: 3

Perhaps using the TI calculators is now a thing of the past. I can understand if the authors would like to keep the statistical concepts in the focus rather than the tool, but today statistics can hardly be done in the workplace or academia without software like R or SPSS.

Clarity rating: 5

I like the dotplot introduction to give students an easy visualization and invitation to statistics

Consistency rating: 5

I found the section at the end listing the mathematical notation to be quite a helpful reference

Modularity rating: 5

It has a similar format to most statistics textbooks I’ve seen. Perhaps the chapter on descriptive statistics could be broken down further into a graphical chapter and a numerical chapter.

Organization/Structure/Flow rating: 5

The text has clear organization and supplements new concepts with good examples

Interface rating: 5

I found it quite nice to have the book in pdf or online format. The various formats are helpful for different students’ learning styles

Grammatical Errors rating: 5

I did not see any

Cultural Relevance rating: 5

examples were great

- In the descriptive statistics section, it could also include examples of heatmaps and pictographs because those have become very popular - In the section about exponential distributions, some more justification can be provided for the memoryless property. For example, this sentence made me question the utility of the distribution: “In this case it means that an old part is not any more likely to break down at any particular time than a brand new part.” It is unintuitive for students to think this so some justification is needed for why thinking like this makes sense. - Introduction of Chapter 6: In reference to the normal distribution, the authors said, “The probability density function is a rather complicated function.” I would rather say it is surprisingly elegant so students also gain an appreciation for its formulation 😊 - Key terms section at the end of Chapter 7: not sure why there’s a paragraph for exponential distributions again when they were already discussed in 5.3 - In chapter 11, it may be worth commenting briefly on how the chi-squared test of independence is related to the chi-squared test of association - Overall, a fantastic resource that is open and free for anyone who wants to self-study statistics well. Thank you!

Reviewed by Daniel McGough, Graduate Student Instructor, Purdue University on 10/26/23

This book covers a broad category of statistics and statistical techniques, some of which I just ended up skipping. read more

Comprehensiveness rating: 4 see less

This book covers a broad category of statistics and statistical techniques, some of which I just ended up skipping.

This book is very accurate.

As an instructor in a psychology department, there were a lot of things in this text that I didn't end up needing or using.

Clarity rating: 4

I think some of the terminology, while accurate, was difficult for some of my students to understand.

Good internal consistency in terminology and formulas.

Modularity rating: 4

Pretty good modularity, as i only assigned part of each chapter for readings.

I think the organization is great. It starts off with the background things one needs, such as what a random variable is and what distributions are, then advances through more complex information regarding inferential statistics. I might change the order of a few of the chapters towards the end of the book, but that would be all.

Interface rating: 4

There are a lot of "Box"es that almost seem necessary for students to read/interact with to get the knowledge in them. I would just make those part of the plain text.

No grammar errors that I caught.

I don't think it referred to race at all.

This book is a great resource for teaching intro stats. However, I do think that the next time I teach this material, I will be switching to Learning Statistics with R or one of its variants. That is not because I think this textbook is bad by any means, but it actually is just too general in its approach. I want an open text book that is more geared towards psychology students, rather than general statistical use.

www introduction to statistics

Reviewed by Kim Proctor, Lecturer, California State University, Dominguez Hills on 12/8/22

The text covers multiple areas that are necessary for students to grasp a basic knowledge of statistics. However, I would have liked to see the inclusion of information for some kind of computer-assisted analysis of descriptive statistics,... read more

The text covers multiple areas that are necessary for students to grasp a basic knowledge of statistics. However, I would have liked to see the inclusion of information for some kind of computer-assisted analysis of descriptive statistics, contingency tables, z-test, t-tests, ANOVA, linear regression, and chi-square. Whether these analyses were conducted via excel, SPSS, some free online calculator, or R, these would have been helpful as I end up using other resources in order to include computer-assisted analyses to familiarize my students with these processes. The index is comprehensive. However, some information included in both the main sections and glossary is somewhat confusing, e.g., the data set(s), of which there are only two, are not fully explained and are somewhat unuseful for multiple forms of analysis practice.

I did not notice any errors in the accuracy of the book. However, the supplemental materials--in particular the lecture slides had a few slight errors.

While I do believe the book has excellent longevity, I maintain that adding support information on computer-aided analyses for each of the sections using Excel, SPSS, R, or some free online calculator would make the book much more relevant and more attractive to instructors who would prefer a book that includes such information. I do believe the way the book is arranged and formatted aids in ease of updating. With that stated, some questions discuss elections, polling or other issues that do not account for the current influence and uses of social media, the internet, and smart phones.

Clarity rating: 2

The text is somewhat accessible. I do not believe the way the different areas of text, examples, and explanations are set up within the book are as accessible, clear, and readable as they could be. In fact, the format of the text and examples at times makes the book difficult to follow. As stated in a previous section, some information included in both the main sections and glossary is somewhat confusing, e.g., formulas, concepts, and the data set(s)(of which there are only two) are not fully explained and are somewhat unuseful or confusing without further explanation from the instructor and examples from other texts, this is particularly relevant to the "try this, and "let's practice" examples.

The text is extremely consistent in terms of terminology and framework. Although, in my opinion, the terminology and framework are not as accessible to college-level intro stats students as it could be.

I believe the modularity of the reading sections and the inclusion of a course pack that can be uploaded to Canvas or Blackboard is extremely helpful. I can assign students to read only one or two sections of a chapter, and I can mix and match sections from different chapters. I absolutely love the Modularity of this book.

Organization/Structure/Flow rating: 3

The topics are presented in a logical and clear fashion. However, I believe the ordering of topics could be improved. For example, ANOVA should be presented after the chapter on 2-sample t-tests, and Normal Distribution should be presented after the chapter on probability.

The text is free from navigation issues and distortion of images. However, the images and other display features are not that aesthetically pleasing: most are presented as grey tables, etc.

I noted no grammatical errors in the text.

Cultural Relevance rating: 2

The text is not culturally offensive. However, the text is extremely insensitive. It does not account for alternative options for male/ female, and is not inclusive towards varied cultures and beliefs. Racial "minorities" are rarely mentioned in the text, and are not reflected in visuals.

1. I suggest alterations/ additions to the information in the text: in the form of some kind of computer-assisted analysis of descriptive statistics, contingency tables, z-test, t-tests, ANOVA, linear regression, and chi-square. 2. I do not believe the way the different areas of text, examples, and explanations are set up within the book are as accessible, clear, and readable as they could be. In fact, the format of the text and examples at times makes the book difficult to follow. 3. With regard to relevance, some questions discuss elections, polling, or other issues that do not account for the current influence and uses of social media, the internet, and smartphones. 4. The text is not culturally offensive, but it is extremely insensitive. It does not account for alternative options for male/ female, and is not inclusive towards varied cultures and beliefs. Racial "minorities" are rarely mentioned in the text and are not reflected in visuals.

Reviewed by Lauren Farr, Instructor of Mathematics, Spartanburg Community College on 9/22/22

In reviewing this material, it appears as though the text meets or exceeds the standards set for traditional textbooks for an Introductory Statistics course. The content appears to be comprehensive, accurate, and up to date. This text could be... read more

In reviewing this material, it appears as though the text meets or exceeds the standards set for traditional textbooks for an Introductory Statistics course. The content appears to be comprehensive, accurate, and up to date. This text could be used to teach an Elementary Statistics class and covers enough topics that it could be used for an additional course in Intermediate Statistics.

I have yet to find an error in any of the material.

Relevance/Longevity rating: 5

The problems in the book are made in such a way that the text will not become obsolete. For example, they use general topics such as heights of people on a sport’s team instead of naming a specific team or year. This is good because the book can be used for a longer period of time.

The book gives the formal definitions and applicable theorems. For clarity, it then gives problems and examples to illustrate what these definitions and theorems actually mean so students can better understand them. The examples are provide students with a reasoning behind why we "need" the theorems to begin with and how Statistics can apply to their life.

Material is presented in an orderly way. It gives the definition and applicable theorems. It then gives problems and examples to illustrate what these definitions and theorems actually mean so students can better understand them.

The glossary and the table of contents are especially important aspects of online learning tools. This text makes it extremely easy to switch between different topics and navigate around the book. The book is broken up into sections that cover a specific topic, so it is easy to find material. This divides the material into smaller sections which helps students better learn the material and to not become overwhelmed.

The glossary and the table of contents are especially important aspects of online learning tools. This text makes it extremely easy to switch between different topics and navigate around the book. The book does go in a logical fashion from basic Statistics concepts/definitions to more complex ones.

Many students do not want to write in a physical textbook. This online book allows you to highlight sections and make notes while you are reading that you can easy access later without having to flip through the book to look for where you wrote notes. I have yet to find any interface issues.

I have yet to find any grammatical errors.

Cultural Relevance rating: 3

The text is not culturally insensitive as most problems are about “people” or “doctors” or “neighbors”. There is no reference to race, ethnicities, or backgrounds.

This appears to be a fabulous textbook. I look forward to investigating it further. I am also excited to apply some of the ideas, such as the group project problems, to my classes.

Reviewed by Nels Grevstad, Professor of Statistics, Metropolitan State University of Denver on 8/18/22

The book covers all the topics typically covered in an introductory statistics class, but the depth of the coverage is sometimes less than adequate. As an example, self-selected samples are described as "unreliable", but there's no mention of... read more

Comprehensiveness rating: 3 see less

The book covers all the topics typically covered in an introductory statistics class, but the depth of the coverage is sometimes less than adequate. As an example, self-selected samples are described as "unreliable", but there's no mention of WHY. As another example, there book provides almost no intuition behind the (probability) Multiplication Rule and Addition Rule.

Content Accuracy rating: 3

The content is generally accurate, but in a few places it's just plain wrong. For example, Figs. 8.2 and 8.3 attempt to explain confidence intervals using a graph of a normal curve centered on X-bar (the SAMPLE mean) and with the CONFIDENCE INTERVAL endpoints marked on the horizontal axis capturing the middle 90% of the normal distribution. What variable is this the distribution of?

Some of the data sets will become outdated with time, but I think that's true of any statistics textbook.

Clarity rating: 3

The clarity of the book is generally adequate, but explanations are often lacking, and there are numerous places where clarity could be improved upon. An example of this is using the same symbol to represent different things -- in Try It 3.13 (a probability problem), the letter S is used to represent an event, but everywhere else in the chapter, S is used to represent the sample space.

Consistency rating: 3

The text is generally internally consistent, but there are several inconsistencies. For example, in Chapter 2, sometimes the symbol used for the sample standard deviation is Sx (S with subscript x), other times it's just S (no subscript). As another example, sometimes the right side of the (probability) Multiplication Rule is written as P(B)P(A|B) and other times as P(A|B)P(B).

There are not any major problems with the modularity of the book that I could see.

Organization/Structure/Flow rating: 2

The organization/structure/flow of the book is NOT well-thought-out.

There are numerous places where a term is used before it has been defined. For example, in Example 1.3 the term "simple random sample" is used before that term has even been defined. In Try It 1.10, a histogram is used before histograms have even been covered.

Furthermore, there are several instances where NEW ideas are introduced in the Chapter Review section. An example of this is describing the relative advantages and disadvantages of stem-and-leaf plots versus histograms in the Chapter 2 Review, but this isn't mentioned at all in the main body of the chapter. Another example of this (also in the Chapter 2 Review) is the introduction of grouped bar charts and stacked bar charts, neither of which is discussed in the main body of the chapter.

There are many other organizational deficiencies, too numerous to mention here.

I only saw only a few minor issues with the interface of the book, and they shouldn't distract or confuse the reader.

Grammatical Errors rating: 2

There are grammatical errors and typos, and in some cases, they can cause confusion. For example, the term "statistic of a sampling distribution" appears in multiple places (it's supposed to be "sampling distribution of a statistic"), including in a section header.

Cultural Relevance rating: 4

The text is not culturally insensitive or offensive, but it does not appear to me that the authors went out of their way to find examples that are particularly inclusive.

I do not plan on using this book for my classes in future semesters.

Reviewed by Aaron Zerhusen, Assistant Professor, Dominican University on 5/9/22

Most of the typical topics covered in an Introduction to Statistics class are all covered in reasonable detail. Basic descriptive statistics, constructing and reading various types of graphs and charts, an introduction to relevant concepts of... read more

Most of the typical topics covered in an Introduction to Statistics class are all covered in reasonable detail. Basic descriptive statistics, constructing and reading various types of graphs and charts, an introduction to relevant concepts of probability, and hypotheses testing. Notably, Bayes’ Rule is absent. Instructions for use of a TI-83/84 calculator are included, but no other technology is used. The data sets used in the text (including within the homework) do not seem to be provided anywhere in a format that would allow for easy use of technology such as Excel, Minitab, or R. The inclusion of a section on ethics in statistics and experimental design in the first chapter is a welcome feature.

The content is accurate.

Relevance/Longevity rating: 4

Material is presented with some examples drawn from real-world data, but there could be more. Again, examples and homework problems utilizing data sets that are provided in a format (such as csv files) that could be read by a variety of statistics software would help greatly.

The clarity of the exposition within the sections is lacking. Explanations are terse, relying on the examples to illustrate the concepts. Definitions and theorems are not clearly indicated, but rather are often hidden within a paragraph. The key terms, chapter review, and formula review sections at the end of each chapter are helpful.

The notation and techniques introduces are consistent.

The modularity by chapter is typical of a book of this type. A flowchart of dependencies would help instructors, and is not provided.

The organization is typical of an introduction to statistics text.

The interface is standard and clear. The web version of the book takes advantage of HTML to show/hide solutions as appropriate in exercises for students to work through.

Grammatical Errors rating: 3

There are a number of errors in the mathematical typesetting which detract from the clarity of the book.

Examples are pulled from data for a range of subjects. The language used in the text is rather neutral.

If the instructor is careful to address the places where the book is not clear I think this will be a fine textbook. The inclass activities and lab assignments are very nice.

Reviewed by Lance Kruse, Adjunct Assistant Professor, Bowling Green State University on 4/17/22

The textbook addresses the foundational concepts for statistics, including a robust discussion of sampling and descriptive statistics. Even for students who may not frequently utilize inferential statistics, the beginning chapters provide a wealth... read more

The textbook addresses the foundational concepts for statistics, including a robust discussion of sampling and descriptive statistics. Even for students who may not frequently utilize inferential statistics, the beginning chapters provide a wealth of knowledge about descriptive statistics and introductory probability concepts. The inferential statistics are quite comprehensive and organized logically based on the samples and means being compared. The concepts align with the several introductory educational statistics courses I have taught.

No errors or biases were identified.

The topics used in the examples span a diverse range of topics including higher education enrollment, high school sports, technology, research projects, business, politics, health care, and many everyday life examples (e.g., pizza delivery). Some of the dates mentioned in the scenarios are a bit dated (e.g., year 2008, iPhone 4s), but these do not impact the purpose of the example. Statistics do not become out of date, so there is not a concern about the relevancy of the content moving forward. The textbook does provide support for using a TI-83/84 calculator, which is quite nice to improve accessibility to the calculations required.

The writing is clear, accessible, and approachable to any reader regardless of their prior statistics knowledge and/or experience.

Terminology is clear and consistent. There are helpful glossaries at the end of each chapter to define the key terms used. Parenthetical clarifications are provided to ensure ideas are clear.

Each section has several subheadings to more clearly identify specific sections of the reading. Those sections are accessible as separate standalone readings that do not require readings of previous sections to understand them. The text uses several examples to clarify the concepts and does not overly refer to previous sections of the text.

The flow of topics is logical and appropriate for an introductory statistics course.

The PDF download is neat and clear. There is a digital table of contents that shows all of the chapters and subsections in the chapters that automatically navigate you to those sections. This makes it very easy to jump around to various parts of text with ease.

No grammatical errors were noticed.

Gender is presented as a binary (male/female) and is not inclusive of the full spectrum of gender identity. However, this issue is not relegated to only this text and is commonly present in most statistics textbooks. I believe a standalone discussion of inclusivity in research and statistics should be presented by the instructor to discuss the importance of inclusivity in research, but yet the practical issues this may cause for statistics (e.g., having inclusive categories for self-identification that may result in very small sample sizes that violate the statistical assumptions required for an inferential test). These discussions should be happening in the classroom to ensure students are engaging in ethical and culturally responsive research while also understanding the implications of such decisions.

Reviewed by Matthew van den Berg, Professorial lecturer, American University on 1/14/22

Provides coverage of all the usual topics for an introductory statistics course along with extra topics that many courses will likely skip due to time constraints. read more

Provides coverage of all the usual topics for an introductory statistics course along with extra topics that many courses will likely skip due to time constraints.

I came across no errors or accuracy issues, and did not perceive any biases.

The text is relevant and up-to-date. It's introductory statistics, so I can't really imagine a text being "out-of-date" in this field. The one issue here may be that this text provides additional instruction for using a TI-83+ and/or TI-84 calculator. This may still be the preferred calculator for many students, but students many students may only rely on computer based analysis so the calculator instructions are less valuable.

The text is well written and comparable to the clarity of any other statistics textbook. This may be subject to students' preferred learning methods however, as this text heavily emphasizes examples to explain new concepts. Often rather than introducing the theory behind a new concept, then providing an example, the text often goes straight into an example and uses that example to show the theory.

The formulas and language are consistent throughout.

I skipped several sections within the text, and the flow of the material and explanations did not suffer from it.

Organization/Structure/Flow rating: 4

Sometimes, the text over-uses examples as an introductory tool for new concepts. This may be helpful for some students, while other students may prefer an organization structure the first provides theory and formulas, and then offers an example. I think the heavy use of examples in the text is generally a good thing, however it can lead to formulas and theoretical concepts getting somewhat lost in those examples.

I experienced no interface issues with the text.

The text was well-written and free of grammatical errors.

I noticed no cultural biases or insensitivity issues.

I was happy with the textbook for an introductory statistics course that covered: descriptive statistics, probability, hypothesis testing, and simple linear regression. Stylistically, the text relies heavily on examples to explain the concepts. This provides a lot of chances for students to read applied examples, but can sometimes obscure the core concepts, theories, and formulas.

Reviewed by Emily Breit, Professor, Fort Hays State University on 10/13/21

The textbook covers the chapters you would generally find in a one semester statistics course. It provides general coverage of the content areas including: descriptive statistics, probability, CLT, confidence intervals, hypothesis testing, and... read more

The textbook covers the chapters you would generally find in a one semester statistics course. It provides general coverage of the content areas including: descriptive statistics, probability, CLT, confidence intervals, hypothesis testing, and linear regression.

Content appears to be error-free and unbiased.

The content is up-to-date and, as with most statistics textbook, the material should remain relevant for an extended period of time.

The textbook provided simple, easy to follow examples.

Consistency rating: 4

Terminology and variables were consistent throughout the text.

The authors did a good job of providing both written and visual examples of the content.

The chapters followed from descriptive statistics and probability into more application based examples.

Charts and graphs were clear and provided additional insight into the problems presented.

Grammatical errors were not detected.

The examples were easy to follow and were based on content that is inclusive to students with diverse backgrounds.

Reviewed by Stanley Elias, Adjunct Professor, Massasoit Community College on 6/24/21

Quite comprehensive as an introductory text for non-technical students. It touches on topics not usually seen in an introductory text (hypergeometric and Poisson distributions, e.g.) The index is an effective search tool for finding specific... read more

Quite comprehensive as an introductory text for non-technical students. It touches on topics not usually seen in an introductory text (hypergeometric and Poisson distributions, e.g.) The index is an effective search tool for finding specific topics. New terms are generally introduced at the beginnings of the chapters.

Content Accuracy rating: 4

I noticed a very few minor inconsistencies in the tables, but on the whole the text is accurate and unbiased.

Content is in keeping with current society and technology and can be easily updated when the need arises. The modularity of the text allows for the easy rearrangement of the order of presentation.

It is easy for mathematics texts to lapse into jargon. That is not the case here. Topics are explained carefully and logically in a way that is easy to follow. The conclusions thus reached are abundantly clear.

The terminology used in the text is consistent from one chapter to the next. Especially appealing are the "Try It" problems that follow example problems, enabling the student to apply what was illustrated in the example

Each chapter follows from the one before and leads to the next, but if desired they can be rearranged without any loss in continuity. For example, I prefer to teach correlation and regression earlier in the course than it usually occurs, so I present Chapter 12 (Linear Regression and Correlation) between Chapter 3 (Probability Topics) and Chapter 4 (Discrete Random Variables). This change is mentioned in the preface as a possible rearrangement.

Topics are presented in the logical order one would expect. I especially appreciated the different problem sets (Practice, Homework and Bringing It Together) that present problems of increasing difficulty.

There are no interface issues. The charts and tables are appropriately sized and colored and easy to read.

I found no grammatical errors.

The text is apolitical. Some of the names mentioned in the problems appear to be the only cultural or ethnic references.

I have used this text the last three times I have taught the course, and I intend to use it again. I especially appreciate the inclusion of Texas Instruments calculators when appropriate. The guidelines and step-by-step procedures are a great help. Another help is the set of practice tests and finals in Appendix B. The text is not as slickly produced as those from the major publishers, but it is still complete and very accessible to students. And as an Open Source text, there is never any excuse not to have a copy!

Reviewed by Tingting Fang, Associate Professor, North Shore Community College on 6/23/21

This OER book covers all the required topics as an introductory statistics text. The content is well presented using examples, lots of exercises problems. After examples, there are Try it questions provided. This gives the students chance to check... read more

This OER book covers all the required topics as an introductory statistics text. The content is well presented using examples, lots of exercises problems. After examples, there are Try it questions provided. This gives the students chance to check their understandings of the topics immediately. TI calculators are widely used in this text, so some formulas or complicated mathematical theories are not introduced. For Non-math majors, I would say this is good and give the students chance to focus on the application part of the theory. TI-calculator command descriptions are included within examples. Students can easily follow what is taught.

Most of the contents are accurate and presented very well.

Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement.

It is easy for me as an instructor to read the book since I already know the fundamental concepts for probabilities and statistics. However, there are some symbols that are not commonly used in the other same level statistics book. For example, chapter 10 presents how to calculate confidence interval. EBM is used to represent” margin of error”. This 3-word symbol is not user friendly in the formulas. It is better to use a single letter E to denote it as in the other books

It is very consistent. The language of the contents is easy to follow.

In general, each model of the book is well designed. Different sections could be rearranged easily depending on the topics covered by the instructors. One thing that can be improved is in chapter 2: Descriptive Statistics. Measures of the Location (2.3) is introduced before Measures of the center (2.5). However, the concept of mean (average) is used when Percentile is calculated in sec 2.3. I would suggest to move sec 2.5 before sec 2.3.

This book is well organized. The part I like most is that each chapter includes contents part, Key terms, Chapter review, homework problems and solution keys. Students can easily find what they need. It is easy to use.

It is very easy to find the right contents.

It is well written. It is easy to understand what the book is trying to present.

The text is not culturally insensitive or offensive in any way.

As an OER book, this text is a good choice with no cost. For those who heavily rely on TI-calculators, this book is even better.

Reviewed by Isaias Sarmiento, Assistant Professor, Bunker Hill Community College on 6/7/20

This textbook is a bit different from other textbooks in its coverage of topics. Here are some observations: 1. The topic on ethics is addressed early in the textbook. (Most textbooks I have found don't pay much attention to ethics.) 2. While... read more

This textbook is a bit different from other textbooks in its coverage of topics. Here are some observations: 1. The topic on ethics is addressed early in the textbook. (Most textbooks I have found don't pay much attention to ethics.) 2. While there is mention of experiments, I could not find any mention of observational studies. 3. Percentiles are mentioned, but there is no discussion on how to find percentiles methodically. 4. There is strong presence of the use of tree diagrams and Venn diagrams in calculating probabilities. 5. There is strong emphasis on the TI-83/84 to calculate probabilities.

I did not notice any math computation errors. I did notice some typos. In Section 1.2, there is a math example about the demographics of two colleges in the Spring 2010 quarter, but then there are references to Fall 2007.

I'm reviewing the 2018 edition of the textbook. Some of the contexts seem a little outdated. (In Chapter 8, there is an example about smartphones, and the phones listed date back to the early 2010s.) With that said, I don't think the outdated contexts detract too much from the content. At least they are still within the same decade!

The textbook sufficiently defined vocabulary terms and, where appropriate, provided examples of those terms.

In Chapter 3, there is mention of the P(A and B) probability. But I think we have to be careful about this notation. If the problem involves a single selection, then P(A and B) is really just a joint probability -- one fraction, that's it. But if the problem involves two selections (with or without replacement), now we're talking about the multiplication rule. The book mentions the multiplication rule early on in 3.2, but I just couldn't find any examples of how with/without replacement is applied within the multiplication rule.

The discussion on conditional probability could have included the intuitive approach.

It seemed that the terminology used was consistent throughout the textbook. The one time where I felt that there was an inconsistency is in the construction of histograms. In some histograms, the classes overlapped (e.g. 59.95 - 61.95, 61.95 - 63.95). In other histograms, the classes did not overlap. Also, some histograms used class boundaries (Example 2.8), while other histograms did not (Example 2.9). On page 82, the authors state that there is more than one way to create a histogram. However, I feel that the authors should stick with just one way for consistency.

The textbook does a good job in breaking down each section through Examples, a Try It! feature, Collaborative Exercises, and a Statistics Lab. Some sections discuss how to use a TI-83/84 calculator to obtain answers. At the end of each chapter, there is a Key Terms list, a Chapter Review, and a list of math exercises followed by the solution key.

Overall, the topics are presented logically. There were some instances in which I felt that specific vocabulary terms were introduced a little early. For example, the term "probability" was defined in Chapter 1, but only in Chapter 3 was the term fully addressed. The concept of sampling with or without replacement was described in Section 1.2, when its relevance was really in Chapter 3. The term "median" was mentioned in Section 2.3 as part of the larger discussion of the percentiles, but then it was formally defined in Section 2.5 as an example of a measure of central tendency. I felt that the discussion on box plots in 2.4 should have been integrated with the discussion on quartiles in 2.3. The linear regression equation was mentioned before the linear correlation coefficient, which I found unusual.

One recommendation would be to place vocabulary terms in boxes. The terms were bold-faced, but the text can sometimes be so dense that vocabulary boxes would have been helpful in breaking up the text.

The page breaks in some places seem strange. On page 138, halfway through the page, there is an instruction to find the standard deviation, but the rest of the page is blank. On page 141, there is only one line of text.

The interface was sufficiently clear. I noticed that, in the online version of the textbook, the exercises that referenced tables and figures included a hyperlink to the table/figure so that the student can easily refer to it. Also, the online version allows you to highlight text and make comments, as though you were writing notes within the book.

Grammatical Errors rating: 4

In a couple of instances did I find a grammar or spelling error. In the 1.10 Try It!, the graph should say "per Student", not "per Students". On page 181, the word "rolls", as in "rolls of a fair die", was misspelled as "roles".

The textbook was culturally sensitive. The book made an effort to use names that imply different racial/ethnic backgrounds (e.g. Rosa, Binh). The textbook was also willing to include applications that may be deemed controversial (e.g. AIDS). I did notice that, at least in the first chapter, there seemed to be a focus on California-related contexts, though I don't recall the entire textbook being that way.

If you are accustomed to using a author like Triola, this textbook might take some getting used to. You will be hard pressed to find any mention of the counting methods (factorial, permutation, combination), and this may help explain why the binomial probability distribution formula is not mentioned. Regarding hypothesis testing, the null hypothesis is not restricted to the "equal" case, as it considers the cases "less than or equal to" and "greater than or equal to". With its focus on the TI-83/84, the textbook effectively avoids other accessible tools like Excel and even normal probability tables. If you have students who do not have access to a TI-83/84, then you will need to provide extra instruction.

Reviewed by Elaine Petrocelli, Adjunct Instructor, North Shore Community College on 5/27/20

This text is comprehensive for an Elementary Statistics course that is not geared toward math or engineering majors. It covers all the typical topics found in an Intro to Statistics book. The text includes an introduction and chapter... read more

This text is comprehensive for an Elementary Statistics course that is not geared toward math or engineering majors. It covers all the typical topics found in an Intro to Statistics book. The text includes an introduction and chapter objectives at the beginning of each chapter. There are examples as well as Try It problems. At the end of each chapter included are key terms, chapter review, formula review, practice and homework problems and a StatsLab exercise. Answers to odd questions are available as well. It includes a nice glossary and index that are easy to use.

The text is complete and the formulas and key terms are accurate as well as unbiased. I did not find any errors in the calculations.

The content is up to date and will not become obsolete any time soon. The examples used are classic and ageless. Because of the structure of the book, any updates would be relatively easy to incorporate.

The text is written very clearly in a manner that students can understand. The examples and try it problems allow the student to apply what they've learned to test their understanding. The end of the chapter review, key terms and formula review are also very helpful. The instructions for the problems are clearly written and easy to follow.

The text is consistent throughout in format and in usage of industry standard terms and formulas. The framework and terminology is consistent with that of other published statistics text books.

The text can easily be divided into sections that can be taught at different times during the course. In the preface of the book it even lists alternate sequencing. There are several sections that could be left out or used as stand alone.

The topics in the book are presented in a clear logical order. The text includes an introduction and chapter objectives at the beginning of each chapter. There are examples as well as try it problems. At the end of each chapter included are key terms, chapter review, formula review, practice and homework problems and a StatsLab exercise. Answers to odd questions are available as well. The different color highlighting and bolding also help to transition from topic to topic or to the next chapter. The organization also allows for skipping sections or teaching out of order.

The interface was easy to use and had no navigation issues. The images and charts were clear and easy to understand. The highlighting and bolding made it easy to know when a new section began and easy to find what you were searching for. I didn't encounter any distortion of images or charts.

I did not find any grammatical errors.

The text appeared to be neutral regarding culture. There were no offensive or insensitive references. Examples were inclusive and diverse.

I liked the StatsLab and Try It sections. I also liked the collaborative exercises and Bringing it Together Homework. This text offers much opportunity to apply what is learned which is really important in statistics.

Reviewed by Rachel Keller, Adjunct Instructor, Radford University on 1/21/20

This book is quite comprehensive for an introductory course. Many topics that are not typically covered in a survey course are included (e.g., the geometric, hypergeometric, and exponential distributions are included in addition to the ubiquitous... read more

This book is quite comprehensive for an introductory course. Many topics that are not typically covered in a survey course are included (e.g., the geometric, hypergeometric, and exponential distributions are included in addition to the ubiquitous binomial, poisson, and normal distributions). Furthermore, there is an extensive collection of supplemental resources for both the student (e.g., calculator guide, formula sheets, descriptions of mathematical phrases and symbols) as well as the instructor (e.g., data sets, practice exams, projects).

The content of this text is adequately accurate and unbiased.

The fundamental concepts covered in this text are classic and likely to withstand the test of time. What distinguishes statistics textbooks from various decades is not the tests, distributions, or even necessarily terminology, but rather the technology and the datasets. This text illustrates data analysis with the current technological standard of the TI calculator series, which has all expectation of remaining current for some time. A majority of the provided data for examples is based on demographic/social/educational data (e.g. heights, pizza delivery times, test scores) that are unlikely to become problematically dated so as to obfuscate the underlying statistical process. When specific dates and data are provided, they seem to be largely representative of the most recent decade and updates would be straightforward to implement if desired.

The prose of the text is lucid and accessible. Key terms and formulas are offset in bold text and subsequently defined/listed (in end-of-chapter resources) in that familiar presentation that students have come to expect. The one disadvantage is that the explanations are quite succinct, but border on terse sometimes in a manner that might leave weaker students wanting more detailed descriptions in layman's terms to accompany the math jargon. On the other hand, what the text lacks in depth of prose, it makes up for in breadth of example problems which allows the author to "show" the reader how the concepts works rather than "tell" him so.

There were no issues with consistency.

Like most statistics textbooks, the topics are presented in such a manner that individual sections or chapters can be omitted freely at the instructor's discretion. There are occasional references to preceding material (with hyperlinks to another section of the text) which might direct the student to a section the instructor did not cover, but these are infrequent enough as not to be problematic. One nice feature of this text is that the practice problems and exams are subdivided by section/chapter for easy problem identification which facilitates test construction when sections/chapters have been omitted - this is in contrast to those textbook publishers who simply publish chapter reviews with a jumble of problems the instructor has to sift through when not covering all topics.

This textbook is arranged in the typical ordering/grouping of topics as most introductory texts. Most instructors will find no need to reorder, but this can be easily accomplished if desired.

Interface rating: 3

The interface of this textbook is reasonably user-friendly. Navigation within the textbook sections and supplemental resources is quite straightforward. The only issue I see here is that the there are no physical copies of statistical tables provided; rather, the reader is directed to "links to government site tables used in statistics" - which is a link to a SUNY Polytechnic Institute website with an online textbook (Engineering Statistics Handbook). The individual 'tables' present at first glance like they might be online distribution calculators, but they are not, and the table values are listed after the content in a form that is not readily conducive to printing. Arguably, a student could learn to find appropriate values within this page, but scrolling would make this needlessly annoying and the instructor could not provide exam copies of these tables from this site and would need to look elsewhere. My suggestion is that the book could be improved by directing the students to links to online distributional calculators (for use on HW and in-class) and by providing printer-ready pages (for exams) in the appendices so that both formats were available.

No obvious issues with grammatical errors.

No reason that any reasonable person would find legitimate claim that this book is culturally insensitive. Statistics is a subject that is universally relevant and the problem sets, descriptions, and examples show no intentional cultural bias or insensitivity.

Reviewed by Jamie McGill, Assistant Professor, East Tennessee State University on 10/31/19

The text is comprehensive for an Introduction to Statistics course. The topics include what is typically taught in a freshman level Probability and Statistics course. I compared the topics with those taught from our current textbook and there is... read more

The text is comprehensive for an Introduction to Statistics course. The topics include what is typically taught in a freshman level Probability and Statistics course. I compared the topics with those taught from our current textbook and there is no difference in coverage.

The book is accurate and complete in examples and information. No errors or bias noted. A good attribute of online textbooks is that if an error is noticed, it can be fixed quickly.

The text presents the topics in a way that will not become obsolete. Because no statistical software is included in the textbook, the instructor always has the option to introduce the software preferred at the time. Various calculators are mentioned, again because there isn't only one, the textbook will withstand time.

Definitions and summaries are included in each chapter. The text is written in a clear manner and is easy to understand.

The book follows the same basic structure for all chapters, making it consistent and easy to follow within each chapter.

The chapters could easily be reorganized while still making sense. This allows the instructor some flexibility in covering the material.

The arrangement of topics is presented in a logical manner. The topics are organized for an easy flow from chapter to chapter. Within each chapter, there is the same structure and arrangement. Again, this helps with the transition from chapter to chapter.

Overall, the interface is adequate. Slight distortions of images/tables are not significant nor confusing when reading through the chapters.

I did not see any grammatical errors.

Examples are culturally inclusive. I noted no offensive or insensitive wording or examples.

Being an OER textbook, it is a much better deal for the students than the traditionally published text that is often used. This text covers the same topics and links to an online homework platform if that is desired. It appears to be comprehensive as a textbook for a non-calculus based statistics course.

Reviewed by Meryem Abouali, Adjunct lectruer, LAGCC on 5/10/19

This book does contain a table of contents and the main components necessary to cover the average course in statistics. It provides an effective index. read more

This book does contain a table of contents and the main components necessary to cover the average course in statistics. It provides an effective index.

The content is accurate. Formulas and definitions are accurate . There isn't any obvious numerical error

The book is very relevant. the context is up to date. The text is written and arranged in such a way that necessary updates will be relatively easy and straight forward to implement. An instructor can supplement this with hands-on activities. Many of the examples are universal in nature and will still remain relevant for some time to come.

The text is clear and provides adequate context for any technical terminology used. It is clearly defined in terms of the notation and symbol used.

The text is consistent in terms of terminology and framework. The layout of each chapter is consistent . The reader quickly can become familiar with how each chapter is presented and knows what to expect.

It is nicely laid out and can be no problem modularize it depending on an instructor's preference. . The text is readily divisible into smaller reading sections that can be assigned at different points within the course. On a larger scale, the chapters are organized logically and in a manner consistent with other similar texts.

The topics in the text are presented in a logical , clear fashion. The statistical concepts are presented inn a clear and logical order and the flow is logical too.

The interface is base on PDF format which is convenient for students and allows them to download the text to their laptops, tablets, ...etc

The text contains no grammatical errors.

The text is not culturally insensitive or offensive in any way . It should make use of examples that are inclusive of different races , ethnicity of different background.

Overall, the text does the job for which is written for and covering most of thee necessary topics needed for introductory statistics course.

Reviewed by Thomas Blamey, Math Faculty, University of Hawaii Maui College on 5/8/19

I felt the textbook was as good as an publishers text in this introductory field. read more

I felt the textbook was as good as an publishers text in this introductory field.

I did not see any glaring errors...and for the most part I felt is used common language an introductory text would use... Accept when the authors were introducing "Confidence Intervals". They used uncommon language such as: EBM (this is not common and they should use a more common item such as "E" or "ME") error bound (this is not common and they should uses "margin of error" as the vast majority of intro texts do) P′ =X/n (they bounce back and forth on a "cap" X or not x...it should be non cap). This would make it much easier for the majority of students who will be migrating on to the next course in this area of study.

This area of study has changed little in recent times...and the text displays a "standard" delivery of the content. I would have love to see them include multiple technologies (not just the TI calculator). I use Excel as it is the gold standard for desk-stations around the globe (although I understand many classrooms are not equipped with computing so the TI is the standard technology for "Ed").

The text is written well and has an average communication level when delivering this material.

The authors have done well to keep a consistent tone - difficulty when more than 1 author is involved.

The text does a good job of following the market and breaking the topics into chapters that can be taken or re-arranged to suit most introductory courses.

The organization is typical of this level of course - there is disagreement as to where "correlation/regression" should be placed (but the majority of texts at this level place it in the end - I would split this into "descriptive" and "inferential"). The "descriptive" could be included in Ch2 as a section.

The interface is fine - it is a "free" text so one would not expect the top shelf pictures and images.

Again...the only issues I saw here (minor) were the "cap" X or not when discussing sample proportion.

The text seemed culturally neutral...

I want to thank the authors for their work...I am actually using it in my University courses with MyOpen Math... And I am currently reworking the standard to fit my thoughts above and using data local to my community.

Reviewed by Kim Spayd, Assistant Professor, Gettysburg College on 3/11/19

The very basic topics are included and a surprisingly large number of specific probability distributions. However, inferential topics are lacking. Sampling distributions are glossed over in a very unsatisfactory manner and their connection to... read more

The very basic topics are included and a surprisingly large number of specific probability distributions. However, inferential topics are lacking. Sampling distributions are glossed over in a very unsatisfactory manner and their connection to inferential techniques is not made clear enough. Additionally, the coverage of confidence intervals is inadequate; only three intervals are discussed. In contrast, hypothesis tests are adequately covered.

I found no factual errors.

The content is standard and updates would be infrequent, if necessary at all. However, many of the examples are disappointingly banal. It is understandable that the authors would not want to include examples or references that might need frequent updating. But there are so many options for examples that are more interesting and appealing to college students.

The prose and examples are very accessible but maybe too much so. The level of exposition is very low, leaving out many details that could explain choices made later. Such information would not necessarily be lost on an introductory statistics student; rather, I think it would make for a richer understanding of the mechanics of inferential statistics, which is the most useful part of the text.

Vocabulary is repeatedly introduced but in different contexts; this could be confusing or helpful, depending on the person reading.

Sections are short and easily divisible for reading assignments.

The organization of the material is the biggest weakness of this text. A multitude of topics are introduced quickly within the same chapter or section, one right after the other, with little connection between them. Terminology is often reintroduced. For example, the median of a data set is described in the context of quartiles and the interquartile range, then later reintroduced in the section about measures of center. The interquartile range is not addressed in the section about measures of spread. Another example is the inclusion of Type I and Type II errors before finishing the mechanics of a hypothesis test. No adequate discussion of the probabilities of these errors can take place until much later in the text. Unfortunately, there are many more examples of the seemingly haphazard organization of the material.

Overall the interface is adequate. There are some tables that are split between pages (for example, moderately sized frequency tables) and some notation that is spaced oddly (for example, sample mean and standard deviation as well as z-scores for confidence intervals). Every so often, there is a page that is mostly blank for no clear reason.

The examples generally avoid topics that could be considered even close to topical or controversial. The one caveat I have noticed, not limited to this text, is the repeated mention of gender binaries (boys and girls, men and women). Recognizing and including a category for people who identify as non-binary would be a step towards increased inclusivity.

Reviewed by Patricia Swails, Professor of Education, Oakland City University on 2/25/19

The text presents a comprehensive course in basic statistics. There is an index as well as a glossary and reference list after each chapter. Chapter sections are congruent across chapters, including collaborative exercises for group work,... read more

The text presents a comprehensive course in basic statistics. There is an index as well as a glossary and reference list after each chapter. Chapter sections are congruent across chapters, including collaborative exercises for group work, guiding questions a Statistics Lab, Try It guided practice, extensive practice problems based on real-world experiences, and homework. Problem solutions are also provided. Ancillary materials include an instructor manual, Get Start guide, and PowerPoint. Instruction includes key terms, statistical formulas, graphing, and calculator information. There is, however, no discussion of validity or reliability, nor is there any discussion of post hoc testing in the ANOVA chapter.

The text is predominantly error free and unbiased. There is a typo on page 456, listing both Goset and Gossett as the statistician’s name. It makes a clear distinction between data and datum, which is commendable considering the current tendency to use data as a singular term. The null and alternate hypothesis formats are a bit unusual, stating the null as less than and the alternate as more than, rather than the usual no difference or relationship for the null and increase/decrease or there is a difference or relationship leading to a two- or one-tailed discussion.

The text is a traditional presentation of statistics that strongly supports its longevity. The text is appropriate for advanced high school and bachelor levels as well as a graduate-level survey or resource for an advanced statistics course. Information is also presented on IRB and ethics, not always found in statistics instruction. Each chapter is thorough, including TI programming calculator instructions, but there is only a vague reference to statistical software with no direct mention of Excel or other statistical software such as SPSS. The instructor can easily add computer software to the Collaborative Exercises.

The instructional narrative is presented in a conversational style that helps those students intimidated by statistics. The text thorough fulfills its purpose to help students design, implement, and analyze basic statistical concepts. Key terms are presented in bold font. Each chapter states specific objectives and learner outcomes. Most importantly, the text explains the why as well as the how, much more than the basic, Do This. Further, the text includes traditional formula notation, a feature often omitted in many statistics texts.

The text is most consistent in the presentation of terminology. There are some variations, however, such as the introduction of the Independent variable but no reference to the dependent variable. Rather, the terms explanatory and response variables are used. There is no mention of control, moderator, or intervening variables and uses the term, lurking variable rather than the traditional term, extraneous variable. Skewness is presented as right or left skew with no mention of positive or negative skew except in a table. Further, the term, symmetric, is used early in the text then the term, normal, is used later in the text to describe distributions. Different terms are used in place of measures of dispersion and central tendency.

The congruency of chapter components allows instructors and students to easily organize the learning environment. Using the same sections in all chapters assures the instructor of a thorough coverage of any topic presented. Each chapter includes objectives and learning outcomes to assist the instructor in identifying specific readings for a course or for ordering the chapters in a specific sequence.

There is a logical sequence of chapters, but some instructors may find the Chi Square instruction out of place. The chapter can easily be positioned between descriptive and inferential chapters without any loss in accuracy and clarity. Chapters can be rearranged or omitted, depending on the course’s purpose. Each chapter builds in complexity of narrative, formulas, problems, etc.

The congruent structure of each chapter helps students anticipate the scope of instruction, practice, and other supports provided for each topic. This ease of navigation also serves to decrease the anxiety level of statistics-phobic students. This text would be an excellent main text or ancillary text for online course delivery formats.

The text does refer to GPA’s rather than the preferred GPAs. The balance of information is error free.

The instruction is inclusive, sensitive, and inoffensive. The example scenarios are based on diverse, authentic studies. Culturally-diverse populations, both genders, etc. are used in examples and problems throughout all chapters.

Introductory Statistics is worthy of instructor review for a variety of secondary and post-secondary course work. I am using the text for my basic statistics survey course.

Reviewed by Kay Graves, Assistant Professor, Fontbonne University on 6/19/18

This Introductory Statistics book covers all the introductory areas/concepts very thoroughly with the exception of Counting methods such as permutations and combinations. These counting methods are not covered at all in the book and thus I must... read more

This Introductory Statistics book covers all the introductory areas/concepts very thoroughly with the exception of Counting methods such as permutations and combinations. These counting methods are not covered at all in the book and thus I must supplement this information into my course.

Per my review and use, I have found no errors.

This book could be used for many ears without any updates. The examples are current and would continue to remain current for several more years

Overall the text/concepts are written in a very clear manner. The only concern I have is that several times when calculations are used, the formulas are not always given in the text but the reader must find the formulas at the end of the chapter.

Text is consistent.

Each section of each chapter is well organized. While many sections of this (and other) intro stats books need to be followed in a order, there are several sections that could stand alone or be left out if time is short.

The topics are presented in a typical, logical order for an introductory statistics course.

The online interactive version of the book allows the students to work example problems and then click on the link to see if their work is correct. But the biggest hang-up that I have with this book is that the homework or review problems are numbered in the truly online interactive version; the homework or review problems are only numbered in the PDF or book version. This is a bit frustrating for the student to have to go back and forth between the two versions and for the instructor to assign work.

Grammar is fine.

This book has many examples and assignments that cover many different and diverse topics without being offensive or heavy in one area.

Reviewed by Peter Orgas, Adjunct Lecturer , LaGuardia Community College on 5/21/18

Introductory Statistics is comprehensive and includes all the topics needed for an introductory course in statistics. In the preface, you are given options on how to strategical present the topics during the semester rather than follow chapter by... read more

Introductory Statistics is comprehensive and includes all the topics needed for an introductory course in statistics. In the preface, you are given options on how to strategical present the topics during the semester rather than follow chapter by chapter. The section on using the calculator is useful for the students, however, adding the probability tables instead of a link would be beneficial.

I found no inconsistencies, errors or bias throughout the textbook’s content.

The examples and data sets would appeal to a variety of students regardless of their major. It shows that statistical analysis is present in all areas of study. There were sections within chapters that focused too much on the use of the calculator.

The text was very clear. Students can read each section and get a good understanding of the topic due to the use of highlighted definitions and breakdown of problems. There are various examples for students to work out and get a better understanding. Chapter reviews and formulas help to sum out all the topics’ main ideas and terms before the exercises.

I found all the chapters to be consistent in both layout and breakdown.

The chapters are separated into smaller topics which makes it easy to use all parts of the chapter if necessary. Also, the preface also gives you an option to use the chapters out of order to design your class differently than just chapter 1 then 2.etc., thus the textbook is structured to use the chapters you only need without losing the concepts.

The topics are presented in an order consistent with any high priced introductory statistics textbook I have used.

I found the interface to be very consistent and there were no images distorted.

In the various chapters I reviewed. I found no grammar errors.

I found the textbook to be neutral with no insensitive or offensive materials. It appears very inclusive.

I found the textbook very useful and better than some high priced textbooks and plan on using it in upcoming semesters.

Reviewed by Jill Jamison Beals, Assistant Professor, George Fox University on 3/27/18

Introductory Statistics includes all the topics critical to a first course in college statistics designed for a wide range of majors and programs. It is complete in its coverage of the entire statistical process from sampling to application of... read more

Introductory Statistics includes all the topics critical to a first course in college statistics designed for a wide range of majors and programs. It is complete in its coverage of the entire statistical process from sampling to application of inferential statistics to generalizing and/or making a decision about a population of interest. For a semester long course, which does not allow covering all the of chapters, the comprehensiveness allows for picking and choosing the most relevant topics for the course. One aspect that is less complete is the sole focus on using the TI-83, 83+, 84, 84+ Calculator for computations. While complete in itself, applications of spreadsheets and probability tables are missing.

I have not found anything that is inaccurate, in error or biased.

The examples and exercises are such that they will not be out of date. There many references to specific colleges and locations that may seem irrelevant to students, but the examples themselves are lasting. The text includes examples and exercises that could be considered “triggers” and instructors should be aware of these, but they are not so intense to be considered inappropriate. Overall the text includes wide ranging subjects, issues, fields, and interests to be meaningful to a wide cross section of students.

The textbook introduces new terminology, notation and formulas and concepts in each chapter while limiting excessive wordiness. This is enhanced by the key terms, chapter review and formula reviews provided at the end of each chapter. In some cases, extra notation is avoided without loss of conceptual completeness, such as using OR and AND for probability statements rather than set notation for union and intersection. The verbal descriptions are concise and dense with many examples to fill out a reader’s understanding of an idea or concept.

The text is consistent in layout and approach to topics. Terminology is used in a consistent way throughout the chapters.

Each chapter has a clear introduction with distinct objectives. And while sections and chapters are ordered in a progressive manner, the text is self-contained enough so that sections and chapters can be presented in an order (or skipped) to serve overall course objectives. Exercises within chapters are also broken out by section, facilitating the assigning of only those exercises that practice desired topics.

The text is organized such that concepts build on each other in a logical fashion. Within chapters, sections move back and forth between explanation and examples, also in a logical manner, addressing key points as appropriate to the flow of the text.

The interface is sufficient, navigating around the text with table of contents is convenient. At times page breaks chop up examples. The font choice and the layout of the online version makes for a more readable text than the PDF version and a better overall appearance.

I have not found any significant grammatical errors in the text book.

For use in the United States the text is relevant. While exercises and examples reference many different cultures (countries) most that have a culture specific reference are about US specific topics such as baseball, the US senate, presidential elections, income, etc. This enhances relevance for American students.

I have used many statistics textbooks for an introductory stats class and find this textbook to be just as good as ones with high price tags, so being free to students makes it a good choice. One of the best feature is the Stats Lab activities/assignments included for each chapter. As is, or adapted, they make for in depth exploration into the given topic.

Reviewed by Cathleen Battiste Presutti, Lecturer, Ohio University Lancaster on 2/1/18

This text covers almost all of the concepts required in an introductory or sophomore level statistics course. However, there is one topic omission that I feel should be included in a future edition is combinatorics. The inclusion of general... read more

This text covers almost all of the concepts required in an introductory or sophomore level statistics course. However, there is one topic omission that I feel should be included in a future edition is combinatorics. The inclusion of general counting techniques would be beneficial to students and could easily be included in the chapter on probability. In the current edition of the text, it seems as though the authors either assume that students already know the combination formula used in the section on binomial distributions or will be relying so heavily on their calculators that explaining the formula is not necessary.

Beyond the authors' errata which is available separately on textbook's webpage, I have found the textbook to be error-free and accurate.

For the most part, I find that the subject matter in the examples and exercises to be up-to-date. There are a couple of current "hot button" social/political topics and references to current technology that are incorporated into the exercises that I feel will be less relevant in a few years. However, they are few in number. Much of the subject matter used in the examples and exercises is timeless and would not need to be revised in order to make the text feel current.

The concepts throughout the text are explained appropriately and clearly. There is a nice balance between the clarity of the theory and the readability of the text. The prose format of definitions and theorems makes theoretical concepts more accessible to non-math major students without watering down the material.

The text is consistent in its terminology and framework.

There are a few sections in chapters one and two that didn't need to stand alone and could have been combined with other sections due to the relationship of the topics in them. These were sections on data displays. And there was no individual section that would have been improved by separating into two sections. Overall, having the topics separated into smaller sections promotes synthesis of the material.

In chapter three, it seems more appropriate to cover section five (Venn diagrams and factor trees) along with counting techniques before starting probability theory. I also believe that the topics in chapter twelve (linear regression and correlation) would be better suited to introduced before the chapters on probability distributions. Otherwise the remaining chapters of the text are appropriately and logically organized based on the material covered in an introduction to statistics course.

The text is free of any issues. There are no navigation problems nor any display issues.

There are no grammatical errors.

I found the text to be culturally respectful and inclusive with regard to gender, ethic background, etc.

This text is a good introduction to statistical methods. It presents formulas and techniques in a clear way with detailed examples. The theoretical depth of the material is at a level allowing students with a basic knowledge of algebra to understand the concepts while motivating deeper investigation for more mathematically advanced students.

Reviewed by Caitlin Finlayson, Assistant Professor, University of Mary Washington on 4/11/17

The text covers all of the major concepts students would be expected to learn in an introductory statistics course including sampling and data, descriptive statistics, and inferential statistics. While the text might be overly comprehensive for a... read more

The text covers all of the major concepts students would be expected to learn in an introductory statistics course including sampling and data, descriptive statistics, and inferential statistics. While the text might be overly comprehensive for a one semester statistics course, instructors could easily pick and choose which chapters and concepts to include or extend the course over two semesters. Each chapter includes a list of key terms alongside definitions. The text also includes an index as well as multiple appendices such as data sets and review exercises, which would be beneficial for students. The end-of-chapter reviews are also quite comprehensive and include a review of each section, reviews of formulas, and practice questions.

The book appears to be accurate, error-free, and unbiased. It includes numerous examples and sample problems throughout the chapters, whose answers appear to be correct. The text also discusses common biases in statistical research, such as assumptions, sampling methods, and research ethics.

The examples and data sets presented in the book help to make statistics relevant for students. Many of the examples reference university students and all are situated within real-world problems or issues. Most of the data sets are from several years ago (such as carbon dioxide emissions from 2009 and earlier), and it would be helpful if these were updated. However, the variety of examples and data sets provided make this book relevant and applicable to a variety of disciplines.

This text emphasizes examples and sample problems over extensive narratives. The introductory text in each chapter is helpful and clear, but the descriptive text in the various sections of the chapter are often quite brief. It would be helpful if the chapter's narrative flowed a bit more cohesively from one topic to the next. That said, the emphasis on practice questions and examples would pair well with an instructor who could clearly present the concepts in class and then assign the textbook reading following the class meeting.

The book's consistency is excellent and it follows a similar structure across all of the chapters. Each chapter includes numerous examples, and students would particularly find the examples with solutions followed by the "Try It" exercises without a solution immediately listed a helpful way to learn the material, practice it with guidance, and then try it on their own.

This text includes a variety of core concepts in statistics that could easily be rearranged depending on instructor preference. As with any mathematical course, some concepts need to be introduced before others (the normal distribution, for example, is fairly critical in understanding hypothesis testing), but later concepts especially could be reorganized. In addition, less essential core concepts could be eliminated or reduced depending on the course objectives with little disruption to the reader.

The text presents topics in a clear and organized way. Each chapter is similarly structured and presents core statistical concepts in a logical way, first introducing the concept, then providing examples, and finally offering sample problems for students to complete on their own in order to test their understanding.

The text is well-presented with clear, simple diagrams and a consistent visual framework. The tables and figures enhance the concepts discussed and would aid in the reader's understanding.

The text contains no grammatical errors and is well-written.

The text contains a variety of culturally relevant examples, including many data sets and sample problems related to college students. At times, the examples could be adjusted so they are less culturally insensitive. A sample problem in Chapter 10, for example, refers to iPhones being more popular with "whites" than with "African Americans," though some people prefer the label "black," and this example overlooks or oversimplifies broader issues with income distribution. (iPhone purchases are not simply based on cultural preferences, though it's likely a contributing factor.) Perhaps instead of using different races in the example, the text could be revised to compare age groups. Otherwise, the examples include a variety of women and men as well as varying ethnicities and the issues discussed would be relevant for students of a variety of ages and life experiences.

Overall, the text is highly comprehensive, covering a wide array of statistical concepts and including numerous examples and sample problems.

Reviewed by Jonathan Bayer, Associate Professor, Virginia Western Community College on 4/11/17

This book is sufficiently comprehensive for a non-majors introductory statistics course. In terms of content, it offers an adequate number of topics and adequate explanations. However, the book offers very little regarding sampling distributions... read more

This book is sufficiently comprehensive for a non-majors introductory statistics course. In terms of content, it offers an adequate number of topics and adequate explanations. However, the book offers very little regarding sampling distributions and the relationship to the normal distribution. There are enough example and homework problems to support the content. The index and glossary were also sufficiently comprehensive.

I did not find any obvious errors in the calculations or formulas.

I found the text contained an over reliance on the use of the graphing calculator. The textbook more or less requires the use of a graphing calculator. I think including a more substantial use of statistical software would have made the text more relevant. Students will find the use of data sets in the textbook and the citation of where to obtain them both relevant and helpful.

The material is presented clearly. Some of the sections are a little bit “wordy” but this does not take away from the overall clarity.

In the sections I reviewed, the notation and terminology was consistent.

The organization and chunking of material in each section is appropriate for an introductory statistics student.

The text is well organized. Each section I reviewed was presented in the same way. It begins with the objectives at the beginning of each chapter, proceeds through vocabulary and examples, and then ends with practice problems. It is organized similar to other statistics textbooks.

The interface of the online version of the textbook works very well. Working through the contents tab you can access any section of the text quickly. The show solution/hide solution option makes it easy for students to attempt examples without looking at the solution. I did have problems when I attempted to visit one of the links to an external website.

The text is “wordy”. I noticed the authors referenced certain ideas imprecisely. When referencing the outcomes of an experiment they failed to use the idea of a sample point and often used experiment interchangeably with event or in place of event when event was closer to the point. These mistakes did not take much away from the text and perhaps I am being a little too critical considering it is written for an introductory student.

The text did not seem to be particularly culturally relevant. I did not find any evidence of it being culturally offensive.

Reviewed by Sandra Porter, Math Instructor, Central Lakes College on 4/11/17

The text covers all of the topics that are included in the Minnesota Transfer Curriculum for an introductory statistics course. Calculator instructions for the TI- graphing calculator family are included in each section. The confidence interval... read more

The text covers all of the topics that are included in the Minnesota Transfer Curriculum for an introductory statistics course. Calculator instructions for the TI- graphing calculator family are included in each section. The confidence interval chapter [Chapter 8] does not include finding confidence intervals based on standard deviations and variances. The hypothesis testing chapter [Chapter 9] also does not mention testing for standard deviations or variances. This chapter does spend a significant amount of time giving a good background on the concept of hypothesis testing which will improve student understanding for the rest of the topics. Type I and Type II errors are given good coverage with the introductory hypothesis testing. Table F1 includes an overview of typical English phrases that are often misinterpreted when trying to devise hypothesis statements. Phrases such as, “x is no more than 4”, is illustrated to be equivalent to x = 4. Table F2 includes a chart showing the symbols used throughout a statistics course and gives its meaning and the associated topic for its use.

The content is generally accurate. There are some minor typos which might lead to confusion for students. A few noted below: Example 5.8 P(x < 5) = 1 – e(-0.25)(5) = 0.7135 should read P(x < 5) = 1 – e^(-0.25)(5) = 0.7135 In the paragraph following Figure 12.12, “the last two items at the bottom are r2 = 0.43969” should read “the last two items at the bottom are r^2 = 0.43969” Example 12.8 Figure 12-15 r = - 0.624-0.532, therefore r is significant, should read Figure 12-15 r = - 0.624 < - 0.532, therefore r is significant.

Statistics books that utilize actual studies are meaningful and demonstrate relevance to students. This book does make use of studies and indicates where the information originates. There are some problems that are included in Chapter 9 that are contributed by students of the author and are poetic in nature. The relevance of these problems can be assessed by individual instructors. Necessary updates should be relatively easy to implement.

Overall, the text does well in explanations of the technical procedures. Terminology is defined within context of the topic being addressed and is also included in a glossary at the end of the book. The writing is at an appropriate level for this course.

There did not appear to be any issues with consistency in terminology or framework.

Modularity rating: 2

The organization of this book allows for smaller reading sections to be easily assigned. Realignment of subunits should not provide disruption to the reader.

The topics are arranged in an order that follows natural progression in a statistics course. They are addressed logically and given adequate coverage.

images/charts, and any other display features that may distract or confuse the reader. The mean of a sample, x ¯, in most of the text is written as x, with a bar written a substantial distance above it as demonstrated by the snip from the text at right. [unable to paste the snip to this document] In other places, it is written as x ¯. This makes for inconsistent spacing in the paragraph structure.

Listing the probability of A and B as P(AANDB) is not very readable. [3.1 Terminology]

I did not notice any grammatical errors, although better use of punctuation within sentences could improve readability. Example: “you do not think Jeffrey swims the 25-yard freestyle in 16.43 seconds but faster with the new goggles.” Possible revision: “you do not think Jeffrey swims the 25-yard freestyle in 16.43 seconds, but faster with the new goggles.” [Example 9.14]

Cultural Relevance rating: 1

This text refers to many different cultures and ethnic backgrounds. The examples are respectful of differences in our society.

This textbook covers all of the required topics for transfer in the MNSCU [Minnesota State College and University] system. It would work best for a lecture course, where it could be used primarily as a resource. An online student might have difficulty with the readability of the text in the absence of instructor guidance. The margins are small to maximize the information that can be contained on each page. The amount of information contained in a small space might prove intimidating for some students, especially those that are not comfortable with math as a subject matter. I would consider this text for adoption, but not without exploring other options that are available.

Reviewed by Wendy Lightheart, Mathematics Faculty, Lane Community College on 8/21/16

This textbook covers all of the usual topics you would expect to cover in an introductory statistics course for non-math majors. There is a glossary available at the end of each chapter, which is very helpful. A comprehensive index is available in... read more

This textbook covers all of the usual topics you would expect to cover in an introductory statistics course for non-math majors. There is a glossary available at the end of each chapter, which is very helpful. A comprehensive index is available in this textbook at the end of the book, as you would expect. In addition, it's nice that a student may use the search option when using the pdf version of the textbook to search for specific terms.

I've went through most of the textbook, but didn't thoroughly check the Try It or homework exercises. In the content and examples, I have found several errors, most of which are minor. I will be submitting those errors to add to the errata.

The content is very relevant as it includes current studies and refers to today's modern technology and current events. It shouldn't be too difficult to update it with new studies and/or new technology and more current events in future versions.

The textbook is very clear and concise, for the most part.

Overall the book is fairly consistent in terms of terminology and framework. However, there are times when examples do not reflect the content exactly. For example, the histogram given in the solution to Example 2.9 does not follow the steps for making a histogram described previously in the content.

The text is split up into subsections and smaller reading sections quite well. The blocks of text are appropriately small and manageable and most sections could be reordered without much difficulty to the reader.

The topics are given in a very logical order. I particularly like how confidence intervals are covered for both a population mean (including t-intervals) and a population proportion before hypotheses tests for these parameters are explained. But if someone wants to cover both confidence intervals and hypotheses for a particular parameter together, then this can be easily done as well.

Most images and display features are very good. However, there are some formatting issues that should be resolved. For example, each x-bar in the text has the bar located a significant distance above the x. Also, many times what should be subscripts are not displayed that way, which can be confusing for students who are trying to learn the massive amount of notation used in a statistics course.

Of the errors I've found in this text, none of them were grammatical errors.

I haven't found any issues with cultural insensitivity or offensive material in this textbook. The examples tend to include people from various ethnic backgrounds and people of different gender and races as well.

Overall, I'm very happy with this textbook.

Reviewed by Rudolf Lublinsky, Instructor, Portland Community College, Oregon on 8/21/16

This textbook covers all of the standard topics usually covered in ? descriptive and inferential statistics textbooks for non- mathematicians. The sequence is the same used in almost every such book. All subject areas addressed in the Table of... read more

This textbook covers all of the standard topics usually covered in ? descriptive and inferential statistics textbooks for non- mathematicians. The sequence is the same used in almost every such book. All subject areas addressed in the Table of Contents are covered thoroughly.

The computational technology in this textbook is based on a specific brand of calculator (TI-83, TI-84) only. For using the textbook a student has almost evitable to purchase a calculator of this brand. Forcing students to buy a specific brand of calculator contradicts the very idea of saving money using OER. The technologies offered in the text especially do not make sense for online class students who use the computer technologies and don’t need to purchase and use a calculator at all. I think some instructions for using of the Excel statistical functions have to be added in the book.

The book is mathematically accurate, as far as I can see, but there are some minor errors. For example, in the formula of the confidence interval on page 417 there are the extra parenthesis in the wrong places. It gives wrong boundaries of the confidence interval. In headlines of Ch. 9 on pages 482, 484, 503, 507, 510, and 518 words “Full hypothesis test” are misleading. I suggest that it should be “Null hypothesis test”. The definition of mutually exclusive events on page 172 is correct but it makes sense to clarify it for the case when events A and B are exhaustive events of a phenomenon.

The introductory statistics doesn’t change quickly. In general, the content is as up-to-date as any introductory probability textbook can reasonably be. Main change is in technology used for computation. The calculator references will be out of date rather quickly. For non- mathematician students a statistics course is a prerequisite and computing in this course should be supplemented by at least some simple computer technologies, Excel for example, to connect this course with using the statistics in the students’ next disciplines

The clarity in the book is very good. The language in the book is simple and clear. The instructions in the book are detailed and easy to follow.

The text is consistent in its terminology and framework. Despite a difference of topics in statistics and multiple authors of the textbook, notation, vocabulary, organization, structure and flow don’t vary widely in the chapters of the book.

Chapters of the text are rather autonomous and each contains the explanation of key terms, notation, and some information from the previous chapters. I don't see any problems to divide the textbook into the weekly modules both in descriptive and inferential statistics.

The organization is fine. The text book presents all the topics in an appropriate sequence. The structure of each chapter is done in the same fashion. This makes reading much easier. Due to the autonomy of chapters instructors can easily adjust the flow.

I like the textbook interface. It is not monotonous; headlines of the different parts of the text are highlighted, bold or have a different color. The table of contents is allows direct access to the section but not vice versa.

I’ve not found any grammatical errors in this textbook (but English is not my native language). It is well written.

There are some examples that are inclusive of a variety of races, ethnicities and back grounds. No portion of this text appeared to me to be culturally insensitive or offensive in any way, shape, or form.

The textbook is a good book for introduction to statistics. Its Stats Lab fosters active learning in the class room. There are great number of examples, exercises in “Try it” and “Practice”. The language of the book is simple and clear. The graphing calculator is well integrated into curriculum. On the other hand sometimes the main stress is done not on conceptual understanding of statistics but on details of computational procedures for the specific brand of calculator and looks like a content of a calculator manual. The ignoring of the computer technologies is a weakness of the textbook.

The textbook available to students for free and with addition of the computational computer technologies can be recommended for a community college basic statistics courses.

Reviewed by Jaejin Jang, Associate Professor, University of Wisconsin, Milwaukee on 1/7/16

A Statistics textbook mostly have a standard structure. This bookk covers major subjects of the course. Central limit theorem is given a whole chapter, which is good because of its importance. However, I would like to see these more. No... read more

A Statistics textbook mostly have a standard structure. This bookk covers major subjects of the course. Central limit theorem is given a whole chapter, which is good because of its importance. However, I would like to see these more.

No explanation for Normal and other table use. I understand we now mostly use computers for the table values; however, I believe, students still get benefit from the use of tables although it is an additional material to cover. Normality test would be needed. No Goodness-of-fit test or probability plot is explained. Normality test is important for the inference statistics. It would be good to explain mean and variance of linear combination of variables, such as E[5X+2Y]= 5E[X]+2E[Y]. It will be better to give a form of PDF (or PMF) of discrete random variables. Confidence Interval formula of F-distrbution would be better.

This book is accurate.

Elementary Statitics theory is not changed quickly. Although the application examples can be more or less current, this book is uptodated.

This book is clear in its contents. This book is actually carefully written for better understandinig of the materials.

Yes. No problem.

This book follows standard chapter layout of Statistics books (except that F-distribution is explained and used at the last part of the book). Good concise sections with many problems helps understanding the materials.

Yes. Again, the standard structure of Statistics textbooks. Explanantions are simple and clear.

No interface problems.

Looks good.

No problem.

(1) The competition of Statistics textbooks in the market is very high, and there are many good books available (at high prices). One of the important aspects of the textbooks is the presentation, such as font, page layout and color. To choose a book to review for my possible use in the near future, I selected this book because it caught my eyes among a few candidate books. For example, this book has better use of colors, colorful boxes, and arrangement of tables to better guide the reading and understanding of the materials. This book has good details of the editing and has a very competitive presentation compared with other commercial Statistics textbooks. This book is well written. This book proves “a free textbook is not necessarily worse than more expensive books.”

(2) It is hard for a Statistics textbook to be better than others due to the large number of books available. The most successful aspect of this book to me is the exercises. They are carefully made to make students easily understand the lecture materials and get feeling of real statistical analysis. The book also has very nice in-class exercises (Stats Lab) in all chapters. While this is very good for student learning, I wonder if an instructor can find time for this when covering the materials of the course. This book has many good features – such as key word summary and chapter review at the end of a chapter.

(3) This book provides instructor resources such as syllabus, assignments, quizzes, exams, lecture videos and others. Although these are popular with commercial textbooks, these features are certainly helpful. Especially, it provides nice assignments (or projects). The lecture video, which is helpful, is partially based on hand writing. I would prefer the video to be completely based on PPT. No PowerPoint lecture note is provided. This will make the preparation of lecture note time taking.

(4) The book explains the use of TI calculators; however, use of Excel will be more helpful for the students, both for descriptive Statistics and inferential Statistics. Although one book cannot have all possible contents, explanation of Minitab or Matlab will be helpful.

(5) Editing The numbers in tables can be centered for a better appearance. The “bar” notation of some variables (e.g., x_bar for sample mean) is away from the variable (e.g. x), which makes some equations less neat appearance. Solution of homework of each chapter is given in the chapter, which is nice.

Reviewed by Undupitiya Wijesiri, Professor, Southwest Minnesota State University on 6/10/15

This book covers all necessary content areas for an introduction to Statistics course for non-math majors. The text book provides an effective index, plenty of exercises, review questions, and practice tests. read more

This book covers all necessary content areas for an introduction to Statistics course for non-math majors. The text book provides an effective index, plenty of exercises, review questions, and practice tests.

An overwhelming majority of the content is accurate. I found only couple of errors. The formula for finding the variance using grouped data is not consistent with the definition used. Assumptions for chi-squared tests were not mentioned.

Content is up to date. It would have been better if computer software such as MINITAB or SPSS was used for the computations. This would help students learn how to interpret standard statistical outputs in practice.

The textbook is written with adequate clarity. Discussion on sampling distributions would have helped the flow of the content. Central limit theorem for a sample proportions is not included. I think the authors rely too much on the graphing calculator for simple algebraic calculations. Should have used the normal and t-tables to find probabilities.

The notation used is consistent with standard notations used in the field throughout the text. However the formula used for finding variance of grouped data is not consistent with the definition. Poor notation is used in chapter 13 in discussion of ANOVA. Students may confuse the sum of the values in each group as the standard deviation in the group since the letter s is used for the sum.

The text is divided into easily readable sections. Content is well organized and presented in a manner so that reading sections can be assigned throughout the course. Different sections could be reorganized easily without presenting too much interruption to the reader.

The material is presented with a flow consistent with a standard statistic text. Sample percentiles should have been discussed before discussing the median and quartiles. Overall content is organized and structured well.

I do not see any significant interface issues. Some of the formulas were hard to read because of distortion but it will not post any confusion for a careful reader.

I did not see any culturally insensitive material or exercises in the text.

Overall a good text for non-math majors. Basic ideas such as experimental units, sampling distributions are not discussed. Relies too much on graphing calculators for simple algebraic calculations and finding probabilities. It is better to discuss percentiles before discussing the median and quartiles since they were defined later in the chapter. Could have used statistical software for hypothesis testing, chi-squared tests, ANOVA, and regression. Plenty of examples, exercises, review questions, and practice tests were given in the textbook. Good lab assignments.

Reviewed by Vance Revennaugh, Associate Professor, University of Northwestern - Saint Paul on 6/10/15

The text covers most of the areas and ideas of an introductory statistics course, The topics are covered at an appropriate depth. I did not find any work on confidence intervals for the population variance or standard deviation, although there... read more

The text covers most of the areas and ideas of an introductory statistics course, The topics are covered at an appropriate depth. I did not find any work on confidence intervals for the population variance or standard deviation, although there was a section on hypothesis teaching for a single population variance or standard deviation. Also, I did not find any discussion on non-parametic statistics. The authors do cover geometric, hypergeometric, and Poisson distributions in detail. The probability chapter did not cover Baye's Theorem or counting. Overall, the coverage and depth are satisfactory. Also, I am able to find topics using the index and Table of Contents adequately.

I could not find any typos. I feel the text was accurate, error-free, and unbiased.

Content is up-to-date. However I did notice an example using data from 1915 to 1964. I feel the authors encourage the use of a graphing calculator and do not mention any other statistical software. I feel the text is arranged in such a way that necessary updates will be relatively easy and straight forward to implement.

I believe the text is very clear and understandable for students. The authors explain and define statistic terms and concepts thoroughly. There are also a sufficient number of examples to help explain the material. The solutions to odd-numbered practice problems and homework problems are also provided at the end of each chapter

The text is consistent in terms of terminology and framework.

The text is easily and readily divisible into smaller reading sections. I noted that the authors did place a hypothesis test for a single population variance or standard deviation in the Chi-Square chapter instead of the Hypothesis Testing with One Sample chapter. The text should be easily reorganized and realigned without presenting much disruption to the reader.

The organization of the text is very similar to other introductory statistics texts. The topics are presented in a logical, clear fashion.

I reviewed with a hard-copy of the text, so I cannot comment on this item. I do plan to use the videos for the text in my online course.

I did not notice any grammatical errors.

I did not think that the text was culturally insensitive or offensive in any way. Any names of people used in the examples are inclusive of a variety of ethnicities, races, and backgrounds.

I plan to use this online text for an online course in the fall of 2015. I am planning to use the online text for day school stats classes in the spring of 2016.

Reviewed by Jacqueline Joslyn, Instructor/Teaching Assistant, University of Arizona on 6/10/15

The most important topics are covered. There are some concepts, like stem-and-leaf plots, that may be less critical for students in the social sciences to learn. Instructors can choose whether or not to skip the superfluous concepts. read more

The most important topics are covered. There are some concepts, like stem-and-leaf plots, that may be less critical for students in the social sciences to learn. Instructors can choose whether or not to skip the superfluous concepts.

I did not notice any glaring errors. There are some awkward word choices, which I discuss under "grammar".

The content is up-to-date. There are references to studies conducted from 2009 to 2013. Several questions discuss smartphones and other modern technologies. These questions can be easily updated, but they may lose relevance within a short period of time.

This textbook is ideal for students who learn by reading. The instructions are a bit wordy, which might be confusing for some students. It would be an excellent choice for instructors who tend to deliver concise, visual lectures. Since mathematical symbols and equations are often verbalized and instructions are reading intensive, classroom time can be used to engage students in hands-on practice (e.g. showing them how to use the graphing calculator) and to break down the concepts and exercises into visual and mathematical models (e.g. writing down the equation and explaining how to interpret the notation). The instructor can spend less time explaining concepts and more time helping students to work on their quantitative and logical thinking skills.

I appreciate that the textbook attempts to introduce students to various types of probability distribution functions in Chapter 4, but students may have trouble with some of these concepts because the information is not summarized or compared. Some chapters are written better than others. For instance, Chapter 11 is much more organized and readable. Different chi-square tests are explained separately, and then succinctly compared.

Consistency rating: 2

Examples, questions, and chapter sections are organized consistently. The “Formula Review” sections are especially useful. Important rules of thumb are usually typed in bold. There are well-organized appendices at the end of the book. However, as a reference book, it does not fulfill my expectations. The writing style is inconsistent. Sometimes formulas are stated plainly, sometimes not. Mathematical jargon is introduced with varying degrees of precision and elaboration from chapter to chapter.

It is very easy, and perhaps ideal, to pick specific chapters of this textbook to use in combination with other materials. Since the writing is inconsistent, it is not the best choice for instructors who prefer to teach from a single textbook.

The book is organized in the same way as other statistics textbooks.

Interface issues are minimal. Occasionally, there are large spaces between items (for example, page 72). This can be a little distracting.

The definitions of terms are satisfactory for the most part. However, there are segments of the book that are worded vaguely or oddly. For instance, the word “experiment” is often used to define words in the earlier chapters, which can be awkward. At one point, the authors state the tree diagrams are “used to determine the outcomes of the experiment” (188), but “event” might have been a better word to use than “experiment”. An advantage of this emphasis on statistical experiments is that it encourages the instructor to engage students in hands-on learning exercises, which introduces students to the rigors of collecting data.

The questions are culturally relevant to most U.S. students. Data on California is used fairly often. Chapter 9 includes some cute review questions written by students (sometimes in the form poems).

Reviewed by Edward Dillon, Instructor, Minneapolis Community and Technical College on 6/10/15

This textbook covers all of the standard topics usually covered in an undergradate introductory text including hyhothresis testing and ANOVA. The sequence is the same used in almost every such textbook. The index clearing describes the toppics... read more

This textbook covers all of the standard topics usually covered in an undergradate introductory text including hyhothresis testing and ANOVA. The sequence is the same used in almost every such textbook. The index clearing describes the toppics covered. Each chapter ends with a glossary for that particular chapter.

I randomly selected one example from each of the 13 chapters and worked through these finding no errors. The book includes extensive problem sets, "Try It" problems within the text after examples to give students practice, Review sets (Appendix A, for CH 3-13), practice tests and practice final exams (Appendix B). I did not spot any errors in the answer keys, though the real only way to vet so much content is to use the text. I did not spot any particula bias.

This text is full of relavant data sets providing believeable real life examples for students. Many of the data sets are cited so that students can follow up at the original source, if they are interested. Many timely topics like wifi performance and West Nile virus are included.

The text is indeed writeen clearly, if not a little dry (as are most stats books). Key words are highlighted in bold to alert the reading to thei importance. The text is nicely chunked with examples and graphics to make it readable. The page spacing is ocassionally odd, for example there will be a title for a new sub-topic within a section and then a page break (example: p. 43 has the sub-topic title "Simple Random Sample", then the text to explain the idea is on the next page). I think they could clean this flow by simply using page breaks.

The authors do not deviate from terminology and framework that is used in any of the popular intro stats textbooks put out by mainsteam publishers. The glossaries included could be used in any undergrad stats class that I have taught.

As mentioned earlier in this review I think they do a really good job of organizing the sequence of topics and then chunking each section in a way that flows nicely so that students read about a topic, see an example and then have the opportunity to do a "Try It" example. I would be able to use it in my own stats class in the order that the chapters are given.

They have organized similar to a multiitude of undergrad stats textbooks. One feature that I think is fairly unique is that they emaphaize organization of work. Undergraduate students often have trouble keeping thier work organized in a mathematics (or stats) course. The authors include graphical organizers for doing things like hypothesis tests for example. Students are offered a checklist approach to completing tasks (literally check lists). I like this.

I did not find any real issues here other than what I mentioned earlier . . . that the flow is sometimes a bit odd with headings on one page and a misplaced page break separating the text from the heading. There is sometimes issues with the typography, usual involving symbols. For example on page 380, the bars above x-bar, the symbol for sample mean, is far away (above) the "x". This is likely to confuse students.

I did not spot and such errors. I specifically read through ALL of the end of chapter glossaries.

I did not spot any particular culturally sensitive or offensive material. I think that they could spice this text up with more examples involving issues of social justice, but that is just my personal preference in a stats text.

The text includes instruction on the use of graphing calculators to do calculations, a technology used in many undergrad programs. The Group Projects in Appedix D are interesting and well thought out. They frenquently use error finding examples, a problem that contains errors which students work through to foster critical thinking.

Reviewed by Bill Heider, Instructor, Hibbing Community College on 6/10/15

This book covers all the topics typically covered in an introductory level statistics course from an introduction to probability and the basics f study design through sampling distributions, confidence intervals, tests of one and two samples for ... read more

This book covers all the topics typically covered in an introductory level statistics course from an introduction to probability and the basics f study design through sampling distributions, confidence intervals, tests of one and two samples for means, proportions and variances, the typical Chi square tests including independence, goodness of fit and homogeneity, regression and ANOVA. It does not include non-parametric tests. The p-value method is the only method utilized when performing hypothesis testing. The critical value method is not utilized. One topic missing is s a discussion of determining normality of a data set. The index (and table of contents) in the pdf form of the text is especially useful as it allows the user to click on the page number in the index to scroll to the desired page.

The work is free of errors. Sample problems are drawn from a wide variety of subjects and topics.

Use of the TI 84 calculator is emphasized. Directions for performing calculations on the calculator are included in the solution of example problems. Most examples are generic in the sense that there won't be a need to update the data used. Occasionally there is some data (for example one problem uses the population of Lake Tahoe NV and another uses information from a 2006 survey) that will date the book for users. This does not in any way affect the relevance and/or appropriateness of the problem being taught, it may warrant a need to update with more current data to maintain interest of readers.

Most explanations are clear but in some cases technology is relied upon to perform calculations. For example, when performing the test for independence , it is explained how to calculate the individual terms yet to get the test statistic(the chi square) rather than showing that it is the sum of the individual terms the book states the sum is derived from use of a calculator or technology. It seems it could have been clearer to the reader had the individual terms been shown rather than just being given directions of how to do the calculation using a TI-84 calculator where it does not seem at all clear where the final value is coming from.

The book uses standard language used in statistics. The book follows the same layout from chapter to chapter. Terminology and symbols are explained. Some Examples are worked in each section (where appropriate) with a problem for students to try interspersed among the explanations. Calculator directions are included in the solution where appropriate. There is also a summary of any of the statistics commands available on the TI83/84 family of calculators. There are activities ("labs") at the end of each chapter followed by exercises for the entire chapter at the very end of each chapter (rather than the more typical problem set at the end of each section within the chapter). The answer key is provided at the end of the chapter rather than at the back of the book that does make it easier to check solutions

Each section of a chapter is easily covered in a day or two days at most. One example of where the text departs from the order of most statistics tests is that the hypthesis test for variance is delayed until after the chi square tests are introduced. If one wanted to include the topic with the other one sample tests it ould easilty be done. Diferent options for ordering are given at the begining of the text.

Each section follows the same structure. Vocabulary and an explanation of the topic to be covered in the section followed by examples. Calculator directions are included where they are needed in the solution of a problem. Activities are included at the end of each chapter followed by a summary of key terms and the key concepts/topic for each section of the chapter. A problem set for the chapter and then answers for odd exercises ended each chapter. Once one becomes familiar with the layout it does make it fairly easy for one to search for information..

The interface is wnderful. The ability to click on page numbers in both the table of contents and the index and be moved to the appropriate page in the text is nice. ALl text and imageas in the PDF format are very clear. Highlighting f key concepts and ideas draws reader attention as does bold type for key terminology

Most examples are generic. The examples were often relevent (distribution of populaitons bsed on race for a city were used once; opinion poll differrentieated by sex was used in another) but the topics were not offensive.

The book had links to external sources relevent to the topic. Some video lectures were linked in an associated website. a teaching guide is also available.

Table of Contents

  • Sampling and Data
  • Descriptive Statistics
  • Probability Topics
  • Discrete Random Variables
  • Continuous Random Variables
  • The Normal Distribution
  • The Central Limit Theorem
  • Confidence Intervals
  • Hypothesis Testing with One Sample
  • Hypothesis Testing with Two Samples
  • The Chi-Square Distribution
  • Linear Regression and Correlation
  • F Distribution and One-Way ANOVA

Ancillary Material

About the book.

Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labs.

OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.

About the Contributors

Senior Contributing Authors

Barbara Illowsky , De Anza College

Susan Dean , De Anza College

Contributing Authors

Laurel Chiappetta , University of Pittsburgh

Contribute to this Page

Introduction to Statistics

book-cover

Table of Contents

Course contents.

  • About This Course
  • Course Contents at a Glance
  • Learning Outcomes

Faculty Resources

  • OHM Assessments
  • I Need Help

Module 1: Sampling and Data

  • Introduction to Sampling and Data
  • Definitions of Statistics, Probability, and Key Terms
  • Sampling and Data
  • Frequency, Frequency Tables, and Levels of Measurement
  • Experimental Design and Ethics
  • Section Exercises
  • Answers to Selected Exercises

Module 2: Descriptive Statistics

  • Introduction to Descriptive Statistics
  • Stem-and-Leaf Graphs (Stemplots)
  • Histograms, Frequency Polygons, and Time Series Graphs
  • Measures of the Location of the Data
  • Measures of the Center of the Data
  • Skewness and the Mean, Median, and Mode
  • Measures of the Spread of Data
  • When to use each measure of Central Tendency

Module 3: Probability

  • Introduction to Probability Topics
  • The Terminology of Probability
  • Independent and Mutually Exclusive Events
  • Two Basic Rules of Probability
  • Contingency Tables
  • Tree and Venn Diagrams

Module 4: Discrete Random Variables

  • Introduction to Discrete Random Variables
  • Probability Distribution Function (PDF) for a Discrete Random Variable
  • Mean or Expected Value and Standard Deviation
  • Binomial Distribution
  • Geometric Distribution
  • Poisson Distribution

Module 5: Continuous Random Variables

  • Introduction to Continuous Random Variables
  • Continuous Probability Functions
  • The Uniform Distribution
  • The Exponential Distribution

Module 6: Normal Distribution

  • Introduction to the Normal Distribution
  • The Standard Normal Distribution
  • Using the Normal Distribution

Module 7: The Central Limit Theorem

  • Introduction to the Central Limit Theorem
  • The Central Limit Theorem for Sample Means (Averages)
  • The Central Limit Theorem for Sums
  • Using the Central Limit Theorem

Module 8: Confidence Intervals

  • Introduction to Confidence Intervals
  • A Single Population Mean using the Normal Distribution
  • A Single Population Mean using Student's t Distribution
  • A Population Proportion

Module 9: Hypothesis Testing With One Sample

  • Introduction to Hypothesis Testing with One Sample
  • Null and Alternative Hypotheses
  • Outcomes and the Type I and Type II Errors
  • Distribution Needed for Hypothesis Testing
  • Rare Events, the Sample, Decision and Conclusion
  • Additional Information and Full Hypothesis Test Examples

Module 10: Hypothesis Testing With Two Samples

  • Introduction to Hypothesis Testing with Two Samples
  • Two Population Means with Unknown Standard Deviations
  • Two Population Means with Known Standard Deviations
  • Comparing Two Independent Population Proportions
  • Matched or Paired Samples

Module 11: The Chi Square Distribution

  • Introduction to The Chi-Square Distribution
  • Facts About the Chi-Square Distribution
  • Goodness-of-Fit Test
  • Test of Independence
  • Test for Homogeneity
  • Comparison of the Chi-Square Tests
  • Test of a Single Variance

Module 12: Linear Regression and Correlation

  • Introduction to Linear Regression and Correlation
  • Linear Equations
  • Scatter Plots
  • The Regression Equation
  • Testing the Significance of the Correlation Coefficient

Module 13: F-Distribution and One-Way ANOVA

  • Introduction to F Distribution and One-Way ANOVA
  • One-Way ANOVA
  • The F Distribution and the F-Ratio
  • Facts about the F Distribution
  • Test of Two Variances
  • Relationships in an ANOVA Table

Module 14: Multiple and Logistic Regression

  • Introduction to Multiple and Logistic Regression
  • Model Selection
  • Checking Model Assumptions Using Graphs
  • Introduction to Logistic Regression
  • Appendix A: Review Exercises (Ch 3-13)
  • Appendix A-1: Solutions to Review Exercises (Ch 3-13)
  • Appendix B: Practice Tests (1-4) and Final Exams
  • Appendix C: Data Sets
  • Appendix D: Group and Partner Projects
  • Appendix E: Solution Sheets
  • Appendix F: Mathematical Phrases, Symbols, and Formulas
  • Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators
  • Appendix H: Tables

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Related Articles

Introduction to Statistics

Introduction of statistics and its types.

  • Bar graphs and Histograms
  • Frequency Distribution| Definition, Types, Table, Examples
  • Types of Frequency Distribution
  • Mean in Statistics
  • How to find Mean of grouped data by direct method?
  • How to calculate the mean using Step deviation method?
  • Mode in Statistics | Definition, Formula and Examples
  • How do you find the mode if no number is repeated?
  • Empirical Formula
  • Cumulative frequency curve
  • Mean Deviation
  • Standard Deviation Formula
  • Difference between Correlation and Regression

Statistics and its Types: Statistics is a field of math that generally deals with the collection of data , tabulation , and interpretation of numerical data . In simple words statistics is an area of applied mathematics concerned with data collection analysis, interpretation, and presentation.

It is actually a form of mathematical analysis that uses different quantitative models to produce a set of experimental data or studies of real life. Statistics deals with how data can be used to solve complex problems.

Some people consider statistics to be a distinct mathematical science rather than a branch of mathematics.

Statistics makes work easy and simple and provides a clear and clean picture of the work you do on a regular basis. Statistics is used in a variety of sciences and has huge applications, it is used in Weather Forecasting , the Study of the Stock Market , Insurance Sectors , Betting Industry , Data Science , and others.

In this article, we will learn about, What is Statistics, Types of Statistics, Models of Statistics, Statistics Examples, and others in detail.

Table of Content

What is Statistics?

Types of statistics, descriptive statistics, inferential statistics, data in statistics, representation of data, models of statistics, coefficient of variation, applications of statistics, solved problems – statistics.

Statistics in Mathematics is the study and manipulation of data. It involves the analysis of numerical data, enabling the extraction of meaningful conclusions from the collected and analyzed data sets.

According to Merriam-Webster: Statistics is the science of collecting, analyzing, interpreting, and presenting masses of numerical data

According to Oxford English Dictionary: Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data

Statistics Terminologies

Some of the most common terms you might come across in statistics are:

  • Population: It is actually a collection of a set of individual objects or events whose properties are to be analyzed.
  • Sample: It is the subset of a population.
  • Variable: It is a characteristic that can have different values.
  • Parameter : It is numerical characteristic of population.

Statistics Examples

Some real life examples of statistics that you might have seen:

Example 1: In a class of 45 students, we calculate their mean marks to evaluate performance of that class.

Example 2: Before elections, you might have seen exit polls. Exit polls are opinion of population sample, that are used to predict election results.

There are 2 types of statistics:

Types of statistics is explained in the image added below,

Types of Statistics

Now let’s learn the same in detail.

Descriptive statistics uses data that provides a description of the population either through numerical calculated graphs or tables. It provides a graphical summary of data.

It is simply used for summarizing objects, etc. There are two categories in this as follows.

Measure of Central Tendency

Measure of variability.

Let’s discuss both categories in detail.

Measure of central tendency is also known as summary statistics that are used to represent the center point or a particular value of a data set or sample set. In statistics, there are three common measures of central tendency that are,

Now let’s learn about these in the article below.

It is the measure of the average of all values in a sample set. The mean of the data set is calculated using the formula,

Mean = ∑x/n

For example,

Mean = (Sum of all Terms)/(Total Number of Terms)

⇒ Mean = (21.3 + 20.8 + 19) /3 = 61.1/3

⇒ Mean = 20.366

It is the measure of the central value of a sample set. In these, the data set is ordered from lowest to highest value and then finds the exact middle. The formula used to calculate the median of the data set is, suppose we are given ‘n’ terms in s data set,

If n is Even

  • Median = [(n/2) th term + (n/2 + 1) th term]/2

If n is Odd

  • Median = (n + 1)/2

Data in Ascending order: 15, 19, 20.8, 21.3

⇒ Median = (20.8 + 19) /2 = 39.8/2

⇒ Median = 19.9

It is the value most frequently arrived in the sample set. The value repeated most of the time in the central set is actually mode. The mode of the data set is calculated using the formula,

  • Mode = Term with Highest Frequency

For example, {2, 3, 4, 2, 4, 6, 4, 7, 7, 4, 2, 4}

4 is the most frequent term in this data set.

Thus, mode is 4.

The measure of Variability is also known as the measure of dispersion and is used to describe variability in a sample or population. In statistics, there are three common measures of variability as shown below:

1. Range of Data

It is a given measure of how to spread apart values in a sample set or data set.

Range = Maximum value – Minimum value

2. Variance

Variance describes how much a random variable defers from the expected value and it is also computed as a square of deviation.

S 2 = ∑ n i=1 [(xi – ͞x) 2 / n] n represents total data points ͞x represents the mean of data points x i represents individual data points

It is the measure of the dispersion of a set of data from its mean.

σ= √ (1/n) ∑ n i=1 (x i – μ) 2

Inferential Statistics makes inferences and predictions about the population based on a sample of data taken from the population. It generalizes a large dataset and applies probabilities to draw a conclusion.

It is simply used for explaining the meaning of descriptive stats. It is simply used to analyze, interpret results, and draw conclusions. Inferential Statistics is mainly related to and associated with hypothesis testing whose main target is to reject the null hypothesis.

Hypothesis testing is a type of inferential procedure that takes the help of sample data to evaluate and assess the credibility of a hypothesis about a population.

Inferential statistics are generally used to determine how strong a relationship is within the sample. However, it is very difficult to obtain a population list and draw a random sample. Inferential statistics can be done with the help of various steps as given below:

  • Obtain and start with a theory.
  • Generate a research hypothesis.
  • Operationalize or use variables
  • Identify or find out the population to which we can apply study material.
  • Generate or form a null hypothesis for these populations.
  • Collect and gather a sample of children from the population and simply run a study.
  • Then, perform all tests of statistical to clarify if the obtained characteristics of the sample are sufficiently different from what would be expected under the null hypothesis so that we can be able to find and reject the null hypothesis.

Types of Inferential Statistics

Various types of inferential statistics are used widely nowadays and are very easy to interpret. These are given below:

  • One sample test of difference/One sample hypothesis test
  • Confidence Interval
  • Contingency Tables and Chi-Square Statistic
  • T-test or Anova
  • Pearson Correlation
  • Bivariate Regression
  • Multi-variate Regression

Data is the collection of numbers, words or anything that can be arranged to form a meaningful information. There are various types of the data in the statistics that are added below,

Types of Data

Various types of Data used in statistics are,

  • Qualitative Data – Qualitative data is the descriptive data of any object. For example, Kabir is tall, Kaira is thin, etc.
  • Quantitative Data – Quantitative data is the numerical data of any object. For example, he ate three chapatis, and we are five friends.

Types of Quantitative Data

We have two types of quantitative data that include,

  • Discreate Data: The data that have fixed value is called discreate data, discreate data can easily be counted.
  • Continuous Data: The data that has no fixed value and has a range of data is called continuous data. It can be measured.

We can easily represent the data using various graphs, charts or tables. Various types of representing data set is,

  • Frequency Distribution

Various models of Statistics are used to measure different forms of data. Some of the models of the statistics are added below,

1. Skwness in Statistics

Skweness in statistics is defined as the measure of the asymmetry in a probability distribution that is used to measure the normal probability distribution of data.

Skewed data can be either positive or negative. If a data curve shifts from left to right is called positive skewed. If the curve moves towards the right to left it is called left skewed.

2. ANOVA Statistics

ANOVA statistics is another name for the Analysis of Variance in statistics. In the ANOVA model, we use the difference of the mean of the data set from the individual data set to measure the dispersion of the data set.

3. Degree of Freedom

Degree of Freedom model in statistics measures the changes in the data set if there is a change in the value of the data set. We can move data in this model if we want to estimate any parameter of the data set.

4. Regression Analysis

Regression Analysis model of the statistics is used to determine the relation between the variables. It gives the relation between the dependent variable and the independent variable.

5. Mean Deviation For Ungrouped Data

Suppose we are given ‘n’ terms in a data set x 1 , x 2 , x 3 , …, x n then the mean deviation about mean and median is calculated using the formula,

Mean Deviation for Ungrouped Data = Sum of Deviation/Number of Observation

  • Mean of Ungrouped Data = ∑ i n (x – μ)/n

6. Mean Deviation for Discrete Grouped data

Let there are x 1 , x 2 , x 3 , …, x n term and their respective frequency are, f 1 , f 2 , f 3 , …, f n then the mean is calculated using the formula,

a) Mean Deviation About Mean

Mean deviation about the mean of the data set is calculated using the formula,

  • Mean Deviation (μ) = ∑ i = 1 n f i (x i – μ)/N

b) Mean Deviation About Median

Mean deviation about the median of the data set is calculated using the formula,

  • Mean Deviation (μ) = ∑ i = 1 n fi (x i – M)/N

Coefficient of Variation is calculated using the formula,

CV = σ/μ × 100 Where, σ is Standard Deviation μ is Arithmatic Mean

Various application of statistics in mathematics are added below,

  • Statistics is used in mathematical computing.
  • Statistics is used in finding probability and chances.
  • Statistics is used in weather forcasting, etc.

Example 1: Find the mean of the data set.

x i f i f i x i 2 3 6 3 4 12 5 4 20 8 5 40 Mean = (Σf i x i )/Σf i Σf i x i = (6 + 12 + 20 + 40) = 78, and Σf i = 16 ⇒ Mean = 78/16 = 4.875

Example 2: Find Standard Deviation of 4, 7, 10, 13, and 16 .

Given, xi = 4, 7, 10, 13, 16 N = 5 Σx i = (4 + 7 + 10 + 13 + 16) = 50 ⇒ Mean(μ) = Σx i /N = 50/5 = 10 Standard Deviation = √(σ) = √{∑ i = 1 n (x i – μ)}/N ⇒ SD = √{1/5[(4 – 10) 2 + (7 – 10) 2 + (10 – 10) 2 + (13 – 10) 2 + (16 – 10) 2 ]} ⇒ SD = √{1/5[36 + 9 + 0 + 9 + 36] = √{1/5[90]} = 18

Statistics – FAQs

1. what do you mean by statistics.

Statistics inmathematics is defined as the branch of science that deals with the number and is used to take find meaniful information of the data.

2. What are the types of statistics?

There are two basic types of statics that are, Descriptive statistics Inferential statistics

3. What is statistics and its application?

Statistics is a branch of mathematics that deals with the numbers and has various applications. Various applications of statistics are, It is used for mathematical computing. It is used for finding probability and chances. It is used for weather forcasting, etc.

4. What are the 3 main formulas in statistics?

The three common formulas of statistics are, mean median mode

5. Who is Father of Statistics?

A British mathematician Sir Ronald Aylmer Fisher is regarded as the father of Statistics.

6. What are Stages of Statistics?

There are five stages of statistics that are, Problem Plan Data Analysis Conclusion

7. Who is Known as Father of Indian Statistics?

Indian mathematician Prasanta Chandra Mahalanobis is known as father of Indian Statistics.

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Introduction to Statistics

Dr. Lauren Perry

Welcome to Statistics!

For the student.

There are a lot of ways to approach an introductory statistics class. Historically, the topics found in this text have been taught in a way that emphasizes hand calculations and the use of tables full of numbers.

My philosophy is a little different. This class is designed for students who will need to read statistical results and may need to produce basic statistics using a computer. If you go on to be a scientist and need more statistical know how, this course will give you enough background knowledge to take the inevitable next course in statistics. There is plenty of math in this text, but none of these situations require the ability to do that math by hand.

In many sections, the math is provided and explained but not emphasized. This is intentional. Instead, we focus on the “why”… Why do we care about this topic? Why is this concept important? Why do I run this test when I have that kind of data? …and we focus on the interpretation. What does this number tell us about an experiment? What can we conclude based on these statistical results?

We see statistics all the time in the media - in the form of graphs, tables, averages, predictions about elections or sports, you name it! Hopefully, by learning the whys and the interpretation, you will finish this text feeling like you can read and understand statistical results when you run into them in the real world.

R Programming

This text is designed to teach you introductory statistics with the option to learn some R (a statistical programming language) along the way. As a result, some sections have some introductory material on R. R is an incredibly powerful tool, but we’re going to keep it relatively simple. Using R will save us the headache of doing a lot of calculations by hand.

Since we are only going to use R for a few simple commands, we will run it completely online at the website rdrr.io/snippets (bookmark this website!)

For now, you can run R right here in the course notes! This is exactly what you will see on the rdrr.io website. Type in your command and click the green “Run” button. Try running the command print("Welcome to Statistics!") .

If it prints out “Sorry, something went wrong. All I know is:”, just press the “Run” button again.

For the Instructor

Thanks for checking out my Introduction to Statistics text! Sections are designed to be short, easy-to-read introductions to each concept. Some of the more conceptual sections do not have section exercises, but I am working on adding exercises wherever it seems appropriate. The topics and course ordering reflect the department syllabus for the 3-unit Introduction to Statistics at Sacramento State. I am sure there are topics we’ve left out, but there are only so many things one can cover in 15 weeks.

Each Chapter is designed to take approximately two weeks of class time. In an ideal world, I would cover at least the first eight in a 15 week semester. However, with assessment, activities, student questions, holidays, etc., I usually get through the first seven. Rarely do I get to ANOVA. Despite the time constraints, I am working on including additional topics.

This text is a work in progress and gets updated every semester that I each Introduction to Statistics (which is very nearly every semester) and sometimes during winter and summer breaks.

Currently, I am working on

  • overhauling the entire thing to remove some of the examples borrowed from OpenIntro (another great resource) and from Weiss’ Introductory Statistics from when this was just the typed version of my course notes.
  • adding section exercises and additional topics.
  • including subsections with brief introductions to R programming.

Slides for many of the sections are available on my website, with more being added throughout the Spring 2023 semester: lgpperry.github.io/teaching/stat1/

Please feel free to reach out to me with any questions, comments, or concerns by emailing me at [email protected]

Course Learning Outcomes

The CLOs for Stat 1: Introduction to Statistics at Sacramento State are as follows.

Students will be able to:

  • Organize, summarize, and interpret data in tabular, graphical, and pictorial formats.
  • Organize and interpret bivariate data and learn simple linear regression and correlation.
  • Understand the basic rules of probability.
  • Use the binomial distribution as a model for discrete variables.
  • Use the normal distribution as a model for continuous variables.
  • Apply statistical inference techniques of parameter estimation such as point estimation and confidence interval estimation.
  • Apply techniques of testing various statistical hypotheses concerning population parameters.

Each chapter also has chapter-specific learning outcomes and their corresponding CLOs.

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3.4: Introduction to Probability

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  • Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia
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4.1 Learning Objectives

  • Describe theoretical, empirical, and subjective probability
  • Distinguish among the three uses of probability

The probability of a specified event is the chance or likelihood that it will occur. There are several ways of viewing probability.

One would be experimental in nature, where we repeatedly conduct an experiment. Suppose we flipped a coin over and over and over again and it came up heads about half of the time; we would expect that in the future whenever we flipped the coin it would turn up heads about half of the time. When a weather reporter says “there is a 10% chance of rain tomorrow,” she is basing that on prior evidence; that out of all days with similar weather patterns, it has rained on 1 out of 10 of those days.

Conduct an experiment to determine the probability of the spinner landing on 1?

image showing a spinner with six equal-sized sectors numbered 1 through 6.

Using the experimental method, suppose out of 10,000 spins, 1,711 of those landed on 1. This is normally done on a computer application that can randomly generate outcomes of each spin to avoid someone having to spin the spinner 10,000 times.

To calculate this probability, divide the number of times 1 has occurred which is 1,711 by the number of times the spinner was spun which was 10,000.

The result is 0.1711 or approximately 17% of the time. So 17 times out of 100 spins one would expect the spinner to land on the number 1.

Another view would be subjective in nature, in other words an educated guess or opinion. But this is just a guess, with no way to verify its accuracy, and depending upon how educated the educated guesser is, a subjective probability may not be worth very much.

Determine the probability that the Seattle Mariners would win their next baseball game.

It would be impossible to conduct an experiment where the same two teams played each other repeatedly, each time with the same starting lineup and starting pitchers, each starting at the same time of day on the same field under the precisely the same conditions.

Since there are so many variables to take into account, someone familiar with baseball and with the two teams involved might make an educated guess that there is a 75% chance the Mariners will win the game; that is, if   the same two teams were to play each other repeatedly under identical conditions, the Mariners would win about three out of every four games.

Definition: Probabilities

Empirical Probability uses the results of an experiment to predict the percent chance an event could occur.

Subjective Probability uses intuition or guesswork to predict the percent chance an event could occur.

Theoretical Probability uses the number of possible desired outcomes of an event compared to the number of all possible outcomes of an event to predict the percent chance an event could occur.

Theoretical Probability is defined mathematically as follows:

Suppose there is a situation with \(n\) equally likely possible outcomes and that m of those \(n\) outcomes correspond to a particular event; then the probability of that event is defined as \(\frac{m}{n}\).

We will return to the empirical and subjective probabilities from time to time, but in this course we will mostly be concerned with theoretical probability.

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Home Office workforce diversity statistics: 2022 to 2023

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Published 22 February 2024

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This publication is available at https://www.gov.uk/government/statistics/home-office-workforce-diversity-statistics-2022-to-2023/home-office-workforce-diversity-statistics-2022-to-2023

This publication forms part of the Home Office’s response to Recommendation 28 of the Windrush Lessons Learned Review , which states:

“The department should publish comprehensive annual workforce data, so it can monitor progress.”

The statistics included in this release examine representation by grade where possible, and by different areas within the Home Office. This is important to make sure that the Home Office workforce reflects the communities it serves.

The findings presented in this report are based on data from the department’s central human resources reporting system (known as ‘Metis’), as at 31 March 2023. The majority of the data has been self-reported by staff. Self-reporting is voluntary, and therefore the findings relate only to a subset (section) of the Home Office workforce.

The statistics show that, whilst increasing since 2021, there is still underrepresentation in both the Senior Civil Service ( SCS ) and in the pipeline to SCS for ethnic minority staff. The proportion of SCS with disabilities has increased by 4.0 percentage points in the last year (from 9.1% to 13.1%).

A main focus of the department’s approach to diversity and inclusion is to make sure the Home Office workforce is representative of the communities it serves, while also focusing on accountability and inclusion to support this aim.

The Civil Service Diversity and Inclusion Strategy: 2022 to 2025 highlights the importance of considering a broader definition of diversity, such as socioeconomic, work experience and geographic backgrounds. The Home Office collects data on socioeconomic background, with the aim of providing richer data on representation within the workforce. This data is currently not of sufficient quality to include in this publication, but this information is planned to be included in future publications.

1. Introduction

In March 2023, the Home Office employed over 43,000 people in a wide range of roles, across the UK and overseas, an increase of over 7,300 from March 2022. All business areas increased in size but the change was largely driven by an additional 6,800 staff employed in the Migration and borders operations business area.

For the purposes of this analysis, staff have been grouped according to the area of the Home Office they work in:

  • Migration and borders operations – staff in this area include those working in UK Visas and Immigration ( UKVI ), Border Force, Immigration Enforcement, and His Majesty’s Passport Office
  • Migration and borders policy – includes staff who support on the policy side of migration and borders related work
  • Homeland security – staff in this area work to counter threats from terrorism
  • Public safety – includes staff who support work on policing and fire and rescue services
  • Corporate and support – includes staff that support other functions through a variety of means, including analysis, private offices, HR and IT

These groupings have changed compared with last year’s Home Office workforce diversity statistics 2021 to 2022 . Migration and borders operations and Migration and borders policy were previously grouped under a Migration and borders grouping; however, these have now been separated to better reflect the type of work each area undertakes. Please see the definitions section for further information on groupings.

As shown in figure 1, most staff (79%) are employed in roles related to Migration and borders operations. This includes many operational staff such as Border Force officers, Immigration Enforcement, Passport officers and UKVI caseworkers. Staff working in the following areas account for much smaller proportions of the total workforce:

  • Corporate and support (11%)
  • Public safety (4%)
  • Homeland security (3%)
  • Migration and borders policy (2%)

As a result of the high proportion of Migration and borders operations staff in the data, the representation heavily influenced the department level statistics in this area. To allow a clearer picture of the diversity of the Home Office workforce, the representation rates have been calculated at both the departmental and business area levels where possible.

The following sections report on the representation of Home Office staff by ethnicity, disability, gender and sexual orientation.

Figure 1: Distribution of staff in the Home Office, by business area

Table 1: Distribution of staff in the Home Office, by business area

Source: Home Office workforce diversity statistics: 2022 to 2023; table 1

  • This table does not follow the rounding rules set out in the methodology section . This table rounds to the nearest whole number, please see the separate tables for one decimal place.

Home Office grades are summarised below. They range in ascending order from the most junior staff at Administrative Assistant and Administrative Officer, through to Senior Civil Servants who hold the greatest seniority.

Home Office grades, from least to most senior:

  • Administrative Assistant or Administrative Officer ( AA or AO )
  • Executive Officer ( EO )
  • Higher Executive Officer or Senior Executive Officer ( HEO or SEO )
  • Grade 7 ( G7 )
  • Grade 6 ( G6 )
  • Senior Civil Servant, includes SCS pay bands 1 to 4

Figure 2 shows the proportion of grades in each area of the Home Office. Migration and borders operations is the largest part of the department and has a higher proportion of junior grades compared with the other business areas. This is due to the different type of work undertaken in Migration and borders operations (mostly operational staff) compared with the other areas of the Home Office (policy and support roles). EO was the most common grade for Migration and borders operations (47.5% - over 16,000 staff) followed by AA / AO (26.8% - over 9,000 staff), while for all other areas of the Home Office the most common grades were HEO / SEO .

Please see table 2 of the separate accompanying tables for further information on the number of staff at each grade.

Figure 2: Proportion of grades in each business area of the Home Office

Table 2: Proportion of grades in each business area of the Home Office

Source: Home Office workforce diversity statistics: 2022 to 2023; table 2

2. Comparison to targets and population estimates

In 2018 the Home Office set out a series of representation targets for the department to achieve by 2025. These are set out in table 3, and compared with 2018, then with the 4 most recent years (2020 to 2023).

These overall targets were based by setting them equal to either the UK economically active population or current Home Office representation, whichever was higher at the time of them being set. Since the original targets were produced, the current working age population representation rates for some groups have changed, see table 4 below.

The data provides a snapshot as at 31 March 2023. The data includes overseas and non-paid staff, and most data has been self-reported by staff. Self-reporting of some personal characteristic data is voluntary, and therefore does not provide a complete picture of Home Office workforce diversity.

When considering the representation rates listed for 2018 to 2023, particularly for SCS , the total population size in some groups may be relatively low. An increase or decrease of just a few individuals can have a noticeable effect on the percentages reported. It is expected that there will be some variation in the representation rates from year to year, with the overall trend being the important indicator of success.

Table 3: Progress against diversity targets

  • When the targets were set, this characteristic was referred to as ‘black, Asian and minority ethnic’. This wording in the release has been updated in line with the GOV.UK Style guide .
  • For data collected to 31 March 2022, Metis only allowed staff to record themselves as either ‘heterosexual / straight’ or ‘ LGB ’. For the year to 31 March 2023, a wider range of options were offered, grouped as ‘heterosexual / straight’, ‘ LGB ’ or ‘other’. Please see definitions for further detail.
  • For information on representation rates please see methodology section .
  • This table does not follow the rounding rules and is rounded to the nearest whole number.

The representation rate presented in table 3 is the proportion of people who reported having a specific characteristic (for example, identifying as female), as a proportion of all people who answered the question for that characteristic, (for example, total of all people identified as male or female).

Table 4 provides some context to the representation rates with the latest estimates of the demographics for subgroups within the population:

Table 4: Population diversity estimates

Source: Census 2021

  • These figures come from calculations made on the 2021 Census. This census was conducted in March 2021, while COVID-19 restrictions were in place, and this might also have affected the geographical distribution of respondents.
  • The Home Office employs people in all countries in the UK. Population estimates only refer to England and Wales.
  • The higher target for lesbian, gay and bisexual ( LGB ) staff set by the Home Office in 2018 was based on estimates created for the passage of civil partnership legislation. Since then, the Office for National Statistics ( ONS ) has published estimates from the 2021 Census on sexual orientation which is used as the source for this table. However the LGBT+ population is likely to be larger, please see ‘2021 census: What do we know about the LGBT+ population?’ for reasons why.

2.1 Disability

Figure 3: Proportion of people with disabilities in the Senior Civil Service, 2020 to 2023

  • The dashed line represents the 2025 target – see section 2 ‘ Comparison to targets and population ’ for more information.

Table 5: Proportion of people with disabilities in the Senior Civil Service, 2020 to 2023

The proportion of people with disabilities at SCS level has increased by 4 percentage points from last year.

Figure 4: Proportion of people with disabilities, all staff, 2020 to 2023

Table 6: Proportion of people with disabilities, all staff, 2020 to 2023

The proportion of people with disabilities amongst all staff has increased from 10.5% in 2022 to 11.6% in 2023, and has increased every year since this publication began in 2020.

2.2 Ethnicity

Figure 5: Proportion of people from an ethnic minority background in the Senior Civil Service, 2020 to 2023

Table 7: Proportion of people from an ethnic minority background in the Senior Civil Service, 2020 to 2023

  • This table follows the rounding rules set out in the methodology section . Please see the published data tables for further data.

In the SCS , representation of ethnic minority staff increased by 2 percentage points in the past year, from 7.8% to 9.8%.

Figure 6: Proportion of people from an ethnic minority background, all staff, 2020 to 2023

Table 8: Proportion of people from an ethnic minority background, all staff, 2020 to 2023

The proportion of ethnic minority staff has remained at 23.9% since 2021.

2.3 Sexual orientation

Figure 7: Proportion of lesbian, gay or bisexual staff in the Senior Civil Service, 2020 to 2023

Table 9: Proportion of lesbian, gay or bisexual staff in the Senior Civil Service, 2020 to 2023

Representation of LGB staff in the SCS has increased by 0.4 percentage points in the past year, from 5.1% to 5.5%. It is still below the all-staff target of 6%.

Figure 8: Proportion of lesbian, gay or bisexual people, all staff, 2020 to 2023

Table 10: Proportion of lesbian, gay or bisexual staff, all staff, 2020 to 2023

Representation of LGB staff across all grades has increased by 0.3 percentage points in the past year, from 4.2% to 4.5%. This has increased every year since reporting began in 2020. It is still below the all-staff target of 6%.

Figure 9: Proportion of female staff in the Senior Civil Service, 2020 to 2023

Table 11: Proportion of female staff in the Senior Civil Service, 2020 to 2023

The proportion of female staff in the SCS has increased from 45.1% in 2022 to 48.1% in 2023, passing the target of 47% female representation in the SCS .

Figure 10: Proportion of female staff, all grades, 2020 to 2023

Table 12: Proportion of female staff, all grades, 2020 to 2023

The proportion of female staff has remained around 52% every year. The all-staff target was 52%.

3. Analysis of protected characteristics

This section analyses representation of protected characteristics in more detail, including analysis by grade and business area where possible.

Figure 11: Proportion of staff by age and grade

Table 13: Proportion of staff by age and grade

Source: Home Office workforce diversity statistics: 2022 to 2023; table 3.1

  • Categories with fewer than 10 individuals have been removed from both figure 11 and table 13.

The most represented age group at SCS is 40 to 49 year-olds, with 44.9% of staff in this age group in March 2023.

In March 2023, the proportion of 16 to 29 year-olds was highest at AA and AO grades (26.5%) and lowest among G6 staff (1.3%, excluding SCS as fewer than 10 individuals).

Figure 12: Proportion of staff by age and business area

Table 14: Proportion of staff by age and business area

  • Categories with fewer than 10 individuals have been removed from both figure 12 and table 14.

In March 2023, the 30 to 39 year-olds were the most represented age group for the Homeland security (32.8%) and Public safety (32.3%) areas. For the Migration and borders operations business area, the most represented age groups were 50 to 59 year-olds and 40 to 49 year-olds (25.4% and 24.5% respectively). For the Corporate and support area, the most represented age group were the 40 to 49 year-olds (25.5%), closely followed by 30 to 39 and 50 to 59 year-olds (24.3% and 24.0% respectively). The most represented age groups across Migration and borders policy were 30 to 39 year-olds (30.1%) and 40 to 49 year-olds (29.8%).

3.2 Disability

Figure 13: Proportion of staff with disabilities, by grade and business area

Table 15: Proportion of staff with disabilities, by grade and business area

Source: Home Office workforce diversity statistics: 2022 to 2023; table 4.1

  • Categories with fewer than 10 individuals have been removed from both figure 13 and table 15.
  • The dashed line in figure 12 represents the 2025 target of 12% – see section 2 ‘ Comparison to targets and population ’ for more information.
  • In 2023, 35% of staff records had unknown disability status reported (March 2022: 19%).

The proportion of staff with disabilities in the SCS increased from 9.1% in March 2022, to 13.1% in March 2023. In March 2023, 16.1% of staff at SCS level in the Corporate and support area, reported having a disability, compared with 10.6% in March 2022. For the Migration and borders operations area, 11.4% of SCS staff reported having a disability in March 2023. The numbers of individuals with a disability at SCS level, in the Homeland security and Public safety areas, were too small to be reported individually, for March 2022 and March 2023.

Representation of people with a disability was highest at AA / AO grades, with 14.2% across business areas for March 2023, an increase of 2.1 percentage points since March 2022, (12.1%).

Representation of people with disabilities was highest in the Public safety area, with 14.4% of all Public safety staff reporting as having a disability in March 2023.

Public safety staff at AA / AO grades had a particularly high representation from people with disabilities, at 35.3% for March 2023, (25% in March 2022).

3.3 Ethnicity

Figure 14: Proportion of staff from an ethnic minority background, by grade and business area

Table 16: Proportion of staff from an ethnic minority background, by grade and business area

Source: Home Office workforce diversity statistics: 2022 to 2023; table 5.1

  • Categories with fewer than 10 individuals have been removed from both figure 14 and table 16.
  • The dashed line in figure 13 represents the 2025 target of 24% – see section 2 ‘ Comparison to targets and population ’ for more information.
  • In 2023, 28% of staff records had unknown ethnicity (March 2022: 17%).

In March 2023, 23.9% of Home Office staff were from an ethnic minority background, the same as March 2022. According to the 2021 Census, people from black, Asian, mixed and other ethnic groups made up 19.3% of the working age population in England and Wales.

Representation of staff from an ethnic minority background negatively correlated to grade, and representation tended to be lower at higher grades. In March 2023, 9.8% of SCS staff were from an ethnic minority background compared with 26.9% for AA / AO (March 2022: SCS , 8.8%; AA / AO , 26.0%).

Almost a third of staff working in Public safety roles in the Home Office were from an ethnic minority background, with 30.7% as at March 2023. The next highest representation was in the Corporate and support function, with 29.6% for March 2023.

Figure 15: Proportion of staff reporting their ethnicity

Table 17: Proportion of staff reporting their ethnicity

Source: Home Office workforce diversity statistics: 2022 to 2023; table 6.1

Staff from a white background made up the largest group by ethnicity (76.1%), followed by staff from an Asian or Asian British background (14.8%).

Staff working in Public safety roles had the largest proportion of Asian or Asian British staff, with 18.3% across all grades in March 2023 (March 2022: 19.0%).

Staff working in Corporate and support had the highest proportion of black or black British staff at 8.4%, followed by Public safety at 8.0%.

3.4 Religion and belief

Figure 16: Proportion of staff reporting religion and beliefs across all of the Home Office

Table 18: Proportion of staff reporting religion and beliefs across all of the Home Office

Source: Home Office workforce diversity statistics: 2022 to 2023; table 8.1

  • In March 2023, Buddhist and Jewish staff accounted for 0.4% and 0.2% of all staff, respectively, which cannot be seen on the chart.
  • In March 2023, 25% did not report their religion or belief (March 2022: 12%).

Christian (42.3%) or ‘No religion’ (33.5%) were the most common religious groups across all staff in the Home Office. In all cases, the next most popular responses were ‘Other religion or belief’ (10.9%) and then Muslim (7.0%).

The proportion of people reporting ‘No religion’ increased with the seniority of the grade. In March 2023, this ranged from 29.9% at AA / AO , through to 46.5% at SCS level. The most reported religion or belief at Grade 6 and SCS level was ‘No religion’, in both 2022 and 2023.

For AA / AO , EO , HEO / SEO grades and Grade 7 staff, the most frequently reported religion or belief was Christian.

3.5 Sexual orientation

Figure 17: Proportion of lesbian, gay and bisexual ( LGB ) staff, by grade and business area

Table 19: Proportion of lesbian, gay and bisexual ( LGB ) staff, by grade and business area

Source: Home Office workforce diversity statistics: 2022 to 2023; table 9.1

  • Categories with fewer than 10 individuals have been removed from both figure 17 and table 19.
  • The dashed line in figure 16 represents the 2025 target of 6% – see section 2 ‘ Comparison to targets and population ’ for more information.
  • In 2023, 33% of staff records had unknown sexual orientation (March 2022: 23%).

The policy areas (Homeland security, Public safety and Migration and borders policy) all had the highest level of LGB staff between 6.0% and 6.1% each.

In March 2023, 5.5% of SCS staff were LGB , a 0.4 percentage point increase from March 2022 (5.1%). The numbers in each area were too low to be reported individually.

Across all staff, 4.5% were LGB in March 2023, a 0.3 percentage point increase from March 2022 (4.2%).

Figure 18: Proportion of female staff, by grade and business area

Table 20: Proportion of female staff, by grade and business area

Source: Home Office workforce diversity statistics: 2022 to 2023; table 7.1

  • The dashed line in figure 17 represents the 2025 target of 52% – see section 2 ‘ Comparison to targets and population ’ for more information.

Over half (52.1%) of Home Office staff were female, in March 2022, similar to 52.2% in March 2023.

In March 2023, 48.1% of SCS staff were women, a 3 percentage point increase from March 2022 (45.1%). Over half of SCS staff working in Public safety (59.3%) and Migration and borders policy (59.0%) roles were female in March 2023. This was the highest proportion of all business areas. In March 2023, the proportion of female staff at SCS grade for the other business areas ranged from 41.3% in Migration and borders operations to 50.0% in Homeland security.

There was a higher proportion of female staff at the most junior grades, with 59.2% of AA / AO staff being female in March 2023. However, representation was lower at grades EO (49.3%), HEO / SEO (52.3%), Grade 7 (47.4%) and Grade 6 (47.6%) for March 2023.

4. Working location of staff

This section analyses the geography of the Home Office workforce using the building location of employment within each geographic region of the UK.

Figure 19: Proportion of staff in different regions of the UK, March 2023

Table 21: Proportion of staff in different regions of the UK, March 2023

Source: Home Office workforce diversity statistics: 2022 to 2023; table 10

In March 2023, over a third (34.5%) of Home Office staff were registered to a building in London. This was followed by the North West of England (21.6%), Yorkshire and The Humber (11.3%) and the South East of England (10.6%). Outside of England, staff working in Scotland made up 3.6% of the Home Office workforce, followed by Wales (2.1%), Northern Ireland (1.8%) and Overseas (0.4%).

5. Data sources

Data for this analysis was taken from the department’s ‘Metis’ system, the central system for human resources reporting.

The data provides a snapshot as at 31 March 2023. The data includes overseas and non-paid staff, and most of the data has been self-reported by staff. Self-reporting is voluntary and therefore does not provide a complete picture of Home Office workforce diversity, as some staff choose to withhold information through the ’Prefer not to say’ response. Others may not have been surveyed, so no data is available for these individuals. This is particularly true of overseas staff, for whom the department only holds information regarding gender. There may also be individuals who misreport, either through accident or design. While considered unlikely to be widespread, where percentages are very low, a few individuals would have noticeable effects on the results.

The department continues to explore how to improve its declaration rates, for example by making improvements to the categories an individual can self-define as, as well as consistent messaging on why data is needed, what it is used for, reassurance on data security, how data is stored and anonymity protection.

5.1 SCS data

Data for SCS in the department is taken from the ‘Metis’ system. This is different to the data used in the Civil Service Diversity and Inclusion Dashboard , which uses the Cabinet Office SCS database. Therefore, representation rates calculated here may differ from those calculated using alternative data sources.

6. Methodology

Representation rates have been calculated by excluding individuals with unknown characteristics. These include not being surveyed or responding with ‘Prefer not to say’. In March 2023, the percentages of staff with unknown characteristics were 33% for sexual orientation, 35% for disability, 28% for ethnicity, 25% for religion and 0.39% for geography, and 0.45% of staff grades were unknown. Please see separate data tables with every X.2 table (where X is the table number) providing response numbers.

The respective totals of unknown characteristics for March 2022 were 23% for sexual orientation, 19% for disability, 17% for ethnicity, 12% for religion and 0.08% for geography. Work is ongoing within the department to improve declaration rates. The decrease in 2023 is likely a result of the large number of new staff in the department.

The representation rate is then the proportion of people identified as having a specific characteristic (for example, female) as a proportion of all people with an identified characteristic (for example, total of all people identified as male or female).

In the analysis of representation, where the number of individuals with a characteristic was fewer than 10, the value has been removed and marked with a ~. Fewer than 10 individuals indicate that either representation is very close to 0%, or that the population of people with a disclosed characteristic (for example, ethnicity, age, gender) is so small that representation rates are heavily influenced by individual people and do not provide a reliable narrative of the bigger picture. Less than 10 individuals have also been redacted to protect the anonymity of individual’s with characteristics in smaller groups.

Below each data table, the notes provide more information on any data which has been excluded from the calculations.

6.1 Rounding

Data may be rounded to simplify the presentation of the figures. However, all numeric and percentage calculations are based on unrounded data. Where data is rounded, it may not add up to the totals shown or, to 100% in the case of percentages, because it has been rounded independently.

Unless otherwise stated, all percentages are rounded to the nearest 0.1%.

Similarly, all percentages in the separate data tables are rounded to the nearest 0.1%.

7. Definitions

7.1 business areas.

For the purposes of these statistics, Home Office teams, units and directorates are grouped into 5 areas according to their broad area of work.

7.1.1 Migration and borders operations

Staff in this area include those working in:

  • the operational areas of UKVI
  • Border Force
  • Immigration Enforcement
  • His Majesty’s Passport Office

This grouping has changed compared with last year’s Home Office workforce diversity statistics 2021 to 2022 . Migration and borders operations and Migration and borders policy were previously grouped under a Migration and borders grouping; however, these have now been separated to better reflect the type of work each area undertakes. The data tables published for 2023 have recalculated the 2022 data using the new Migration and borders operations and Migration and borders policy groupings.

7.1.2 Homeland security

Staff in this area work to counter threats from terrorism.

7.1.3 Public safety

This includes staff who support work on policing and fire and rescue services.

7.1.4 Corporate and support

This includes staff that support other functions through a variety of means, including analysis, private office, HR and IT.

7.1.5 Migration and borders policy

This includes staff who support on the policy side of migration and borders related work. This was previously grouped with Migration and borders operations to make the Migration and borders business area grouping.

7.2 Disability

The Equality Act 2010 defines disability as a physical or a mental condition which has a substantial and long-term effect on your ability to do normal day-to-day activities. The HR system before 2020 (Adelphi) asked staff the question “do you have a disability?” The Equality Act definition was not provided, so there may have been some under-reporting. The current system of Metis defines disability and then asks the question “do you have a disability?”.

7.3 Lesbian, gay, bisexual ( LGB )

The Home Office’s Adelphi system recorded people as either ‘Heterosexual / Straight’ or ‘ LGB ’ or ‘Prefer not to say’. In 2020, the department introduced a new HR record system called Metis to replace Adelphi. Metis provides a broader set of categories for sexual orientation. Currently the disclosure rates of these broader categories are too low to report in this publication. The department will review the reporting of the broader set of categories every year.

The 2022 sexual orientation data was reported using the options of either ‘Heterosexual / Straight’ or ‘ LGB ’. For 2023, sexual orientation was reported using the options of either ‘Heterosexual / Straight’ , ‘ LGB ’ or ‘Other’. ‘Other’ includes those reporting as ‘Asexual’, ‘Pansexual’ or ‘Other’.

8. Data quality

8.1 gender identity.

The department has recently introduced an option for staff to declare their gender identity on Metis. Currently, the majority of staff have not declared their gender identity so this is not covered in this publication. The department will review the reporting of gender identity every year.

9. Further information

9.1 forthcoming statistical releases.

Forthcoming publications are pre-announced on the statistics release calendar on the GOV.UK website.

9.2 Feedback and enquiries

Home Office responsible statistician: Amy Baxter Press enquires: [email protected] Telephone: 020 7035 3535

The department is always looking to improve the accessibility of our documents. If you have any issues accessing the information you require or you think accessibility requirements are not being met, please contact the Home Office Statistical Transformation Team mailbox .

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