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NCERT Solutions of Class 11th: Ch 4 Presentation of Data

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  • Chapter 4: Presentation Of Data

NCERT Solutions for Class 11 Statistics Chapter 4 - Presentation of Data

NCERT Solutions are an extremely helpful study material while preparing for the CBSE Class 11 Statistics examinations. This study material provides students with a thorough knowledge of the topics covered in this chapter, and the NCERT solutions designed by the subject-matter wizards are easily understandable.

Statistics is a part of Mathematics that deals with the gathering, formation, analysis, elucidation, and presentation of data.

NCERT Solution for Class 11 Commerce Statistics Chapter 4 – Presentation of Data furnishes students with all-inclusive data on all the concepts. As the students have to learn the basic fundamentals of the subject of Statistics in Class 11, they need to study the concepts in a detailed way.

Concepts covered in this chapter are listed below:

  • Introduction
  • Textual Presentation of Data
  • Qualitative Classification
  • Quantitative Classification
  • Tabular Presentation of Data
  • Temporal Classification
  • Spatial Classification
  • Tabulation of Data and Parts of a Table
  • Geometric Diagram
  • Pie Diagram
  • Frequency Diagram

NCERT Solutions for Class 11 Statistics Chapter 4 provides a wide range of illustrative examples, which helps the students to comprehend the topics covered in the chapter quickly. The above-mentioned are the solutions as per the CBSE syllabus. For more solutions and study materials of NCERT Solutions for Class 11 Statistics , visit BYJU’S or download BYJU’S – The Learning App for more information.

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  • NCERT Solutions For Class 11 Statistics
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NCERT Solutions for Class 11 Statistics - Free PDF Download

Class 11 Statistics is an important subject that students need to give prime attention to during studying. It includes the mathematical concepts related to statistical topics that develop the conceptual foundation of students. To make it easier, download and refer to the exercise solutions for all the Class 11 Statistics Chapters and make your study sessions more productive. Learn how the experts have simplified the concepts to follow and score more in the exams.

Class 11 students have to deal with a lot of factual information associated with the subject. NCERT Solutions are the best guide for learners to overcome difficulties in learning Statistics Class 11 . You can easily download NCERT Solutions for Statistics Class 11 in PDF format from Vedantu’s website after registering your account. NCERT Solution for Class 11 Statistics benefits learners with a step-by-step and detailed explanation of all the chapters. NCERT Statistics Class 11 has solutions that can help you answer properly and prepare for your final examinations and thus NCERT Solution for Class 11 Statistics reduces your research time.

Detailed Overview of Class 11 Statistics NCERT Solutions

Importance of cbse class 11 statistics chapters solutions.

Class 11 Statistics is the foundation subject that teaches what data is and how to collect and organise it. This subject teaches how to use various statistical tools along with the elaboration of the formulas to use. This is where the students will need the support of complete study material along with the exercise solutions.

The exercise solutions formulated by the experts will be ideal to follow and complete studying one chapter after the other. A solution to the exercise chapters will thus act as the 11th Statistics Guide that students can use to complete preparing the chapter perfectly.

The answers formulated for the fundamental questions in these exercises are answered methodically so that students can easily comprehend them and practice. The format followed to answer Class 11 Statistics exercise answers will enable students to give accurate answers and score more in the exams.

Hence, students can refer to the solutions when they know how many Chapters in Statistics Class 11 are in an exam and prepare well.

Benefits of Opting for NCERT Solutions Class 11 Statistics

The solutions have been framed according to the chapters to form individual files. It means you can easily find the separate files on the list conveniently and take a step ahead to complete your preparation for the exams.

Download these solutions and resolve your doubts faster. Make your study sessions more productive and time efficient. You can easily move on to the next chapter with guidance from these solutions.

Follow the answering format formulated by the experts for these exercise questions and practice. It will make your statistical and problem-solving skills sharper. You will be able to score more in the exams when you follow these precise formats and complete attempting the entire exam paper within the stipulated time.

Vedantu’s NCERT Solutions for Statistics gives students a boost in solving practical and application-level questions from the chapters, equipping them to shine in their class homework and cracking their exams. These solutions are crafted by experienced professionals aligning them with the CBSE latest guidelines and making them completely reliable and accurate.

NCERT Solutions for Class 11 Statistics - Chapter-wise List

Given below are the chapter-wise NCERT Solutions for Class 11 Statistics. These solutions are provided by the Statistics experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

NCERT Solutions for Class 11 Statistics

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NCERT Solutions for Class 11 Statistics includes a variety of practice problems to tackle, and it's divided into nine chapters. The solutions for each chapter are comprehensively presented in a simple language to ensure students are able to understand the core concept.

Statistics Class 11 NCERT Solutions cover answers to exercise questions from all chapters, in Hindi and English. These solutions are available in PDF format for free download. They are as per the latest syllabus curated according to the present guidelines.

NCERT Solutions for Class 11 Economics are also available on Vedantu.

Class 11 Indian Economic Development NCERT Solutions

Class 11 Economics NCERT Solutions

Statistics for Economics in Class 11 NCERT Solutions PDF

All the in-text and exercise questions given from all chapters in the book are covered in the Class 11 NCERT Solution Statistics for Economics are provided by Vedantu. All of the questions are answered in detail and in an easy-to-understand language thereby making it easier for students to learn the chapters.

Why Do We Need to Refer to NCERT Solutions Class 11 Statistics?

Statistics is associated with collecting information, management, interpretation and analysis. All such processing, aggregation, dissemination and interpretation of economic data take place with the guidance of Statistics. The importance of the subject in the study of Economics is very well-acknowledged. All these assessments are not only made by inferring. These are also validated by strong statistical evidence in the form of statistical data gathered from different resources. It will benefit economic experts to bring out the advantages and drawbacks of any national Economic policy or government decision.

The attributes of Statistics is numerically expressed. It reflects the systematic information, and the collection of data available from different sources can be correlated. A great number of factors may influence statistical data or analysis.

CBSE Economics curriculum for Class 11 consists of a segment called Statistics for Economics, which systematically explores the aggregation, preparation and analysis of structured and unstructured data on various simple economic implications. It also provides students with the knowledge of statistically significant methods for evaluating and analyzing economic data and drawing meaningful concrete data hypotheses.

In comprehending the subject of Economics, Statistics play a vital role such as the relation between price and quantity, supply and demand, economic output, GDP, per capita income of nations, etc. Class 11 Statistics Solution helps the learners of Class 11 to understand the chapters with proper and accurate information. NCERT Solutions Class 11 Statistics has detailed explanations of 9 chapters. NCERT Solutions Statistics Class 11 covers chapters like the Introduction, Collection of Data, Organisation of Data, Presentation, Measures of Central Tendency, Correlation, Useful Indexes and Statistical Tools. Statistics Solutions Class 11 offers a wide range of examples that are relevant to the content and gives a better understanding of the concept to students. Thus, NCERT Statistics Class 11 PDFs can be regarded as excellent preparatory material for exams, and Vedantu helps students by providing them with one of the best materials.

Enhances Regular Study Habit

NCERT Solutions Class 11 Statistics is explained in a very lucid language that is easy to understand and comprehend. Since these Solutions are a rich source of questions and detailed answers are supplied, students find it helpful to answer the questions related to the chapters as NCERT Solution for Class 11 Statistics offers learners various exercises that they can refer to after comprehending the whole chapter. These not only strengthen the foundations of Economic Statistics of the students, but they also pave the way for the ability of students to attempt and crack different kinds of questions very easily. A regular habit can be developed by regularly following NCERT Solutions Class 11 Statistics. Statistics Class 11 NCERT Solutions PDFs are really useful for self-study purposes. Statistics Solutions Class 11 offers students to do their homework as the answers are given after every chapter which in turn makes the learners cope with the problems related to irregular study habits.

Student-Friendly Solution Guide

Statistics involves various factual pieces of information and data that need to comprehend with proper analysis Statistics Solutions Class 11 becomes the best guide to students which provides a step-by-step explanation to the doubts and also helps with proper answering formats. Statistics Class 11 NCERT Solutions serves as a student-friendly solution guide to all learners because it is designed by the best educators who are highly experienced. They also update NCERT Solution for Class 11 Statistics from time to time to cope with the changes that CBSE introduces which equips learners to know the updated versions of Class 11 Statistics Solution. The questions are prepared such that students get access to questions and answers which have higher probabilities of being asked in the exam.

NCERT Statistics Solutions for Class 11 always keep students one step ahead in their journey to success in the exam. These solutions also come in handy for various competitive exams, and can thus immensely help students in their exam preparation.

Why Are NCERT Solutions for Statistics (Economics) in Class 11 Important?

Class 11 Statistics (Economics) NCERT Solutions broadens the conceptual knowledge base of students and provides a comprehensive study of the mandated curriculum. All of the essential theorems and formulas from Class 11 Statistics have been solved in their entirety in these solutions, which aids in laying a strong foundation of concepts. Importantly, the NCERT Solution Statistics (Economics) for Class 11 is a good starting point for students preparing for competitive exams like NEET , IIT JEE , BITSAT , and VITEEE . The knowledge of ideas becomes straightforward and in-depth when the NCERT book is supported by solutions. Furthermore, because it is meant to provide a step-by-step explanation, students can go right to the solutions. Examine the Class 11 Solutions and take advantage of the available resources.

Why Do We Need Vedantu’s NCERT Solutions Class 11 Statistics?

Vedantu is the best educational website in India which has solutions in PDF format for all the subjects starting from Primary to Higher grade classes. With your email ID, you can create your account on Vedantu’s website and download NCERT Solutions for Statistics Class 11 . The solutions cater to various learning abilities of the learners and thus helps to gain confidence in the subject.

In simple words, students are able to access all the questions and answers in their textbook using the Statistics NCERT Solutions Class 11. NCERT Solutions for Class 11 Economics Statistics act as a chapter-wise study guide for students.

For more information and a seamless learning experience, access additional NCERT solutions and study materials for Class 11 Statistics on Vedantu’s website.

Here you can download NCERT Solutions Class 11 and books.

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Download ncert solutions class 11 statistics pdf.

Perform the chapter wise PDF download Class 11 Statistics and make your preparation better. Learn how to attempt fundamental questions and clarify your doubts related to the use of concepts, principles, and formulas described in the chapters. Focus on how the experts have solved the problems in the exercises and practise more. This is how you can develop your conceptual foundation and complete the entire syllabus in no time.

Important Related Links for NCERT Class 11

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FAQs on NCERT Solutions For Class 11 Statistics

Q1.  How will I benefit using Vedantu’s NCERT Solutions Statistics Class 11?

For children of all academic calibre, NCERT Solutions Class 11 Statistics downloaded from Vedantu is understandable. Statistics Solutions Class 11 covers all detailed concepts and is framed to prevent wastage of time in a planned manner. Not only do they help students memorise the entire subject matter, but they also include crucial key points to score well.

Q2. Where can we Find Accurate NCERT Statistics Class 11 PDF?

NCERT Statistics Class 11 PDF can be downloaded from Vedantu’s website which has 100% accurate solutions for all the classes. NCERT Solutions Statistics Class 11 can also be referred from the Vedantu app downloaded from the Google Play store. NCERT Statistics Class 11 PDF can easily be downloaded and can be referred to later thus makes it very handy for students.

Q3. How to prepare for Class 11 Statistics?

The best way to start your preparation to score well in the Class 11 Statistics is by following a routine regularly. This will help the student learn about time management. Apart from this, the student should also cultivate the habit of making notes so that it is easier to look for them before the examination for revision. Making notes will also help them retain what they have learnt. Lastly, it is advised that the students refer to the NCERT Solutions to attain much more clarity and insight into the chapter.

Q4. Is Class 11 Statistics hard?

No, Statistics of Class 11  is not at all hard but to do well in the examination, it is important that the student is aware of what they have studied. To attain this, the students should develop the habit of making their own notes so that they remember all the concepts that they study. Along with this, they also should highlight the important areas and revise them time and again. Lastly, they can refer to the NCERT solutions for a much deeper insight into the chapter.

Q5. What is the syllabus for Class 11 Statistics?

The syllabus for Class 11 Statistics include;

Introduction

Collection, Organization and Presentation of Data

Statistical tools and Interpretation

Development Policies and Experience (1947-90). Economic Reforms since 1991.

Current Challenges facing Indian Economy

Development experience of India -A Comparison with Neighbours (OTBA)

Q6. What is the marks distribution for Class 11 Statistics?

The mark design for Class 11 Statistics is as follows:

Introduction Collection, Organization and Presentation of data = 13 marks

Statistical tools and Interpretation = 27 marks

Development Experience (1947-90) and Economic Reforms since 1991= 13 + 12 marks

Current Challenges facing Indian Economy =15 marks

Development experience of India -A Comparison with Neighbours (OTBA)= 10 marks

Project work = 10 marks.

To get more than 90 per cent, the students should refer to the NCERT solutions. The exercises that these solutions offer will prepare the students for the exams and thereby help them answer any question with confidence.

Q7. Are the NCERT solutions by Vedantu trustworthy?

Yes, the NCERT solutions by Vedantu are completely trustworthy. They are prepared by experts, closely concentrating on the CBSE curriculum and providing the exercises that are relevant to the syllabus designed by CBSE. These exercises are designed with the aim of providing quality education to the students so that they are thorough with whatever they study. With adequate practice from these solutions, the student will easily be able to score more than 90 percent in the examination. Students can easily download these solutions from the website of Vedantu or the Vedantu app. Vedantu provides all the study material free of cost. 

NCERT Solutions For Class 11 Statistics Chapter 4 Presentation Of Data

Class 11 statistics chapter 4 presentation of data.

NCERT Solutions For Class 11 Statistics Chapter 4 Presentation Of Data, (Statistics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions withinside the very last asked from those. 

Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions.  To assist students solve all of the questions and maintain their studies with out a doubt, we have provided step by step NCERT Solutions for the students for all classes.  These answers will similarly help students in scoring better marks with the assist of properly illustrated solutions as a way to similarly assist the students and answering the questions right.

Answer: the following questions, 1 to 10, choosing the correct answer. Question 1. Bar diagram is a (a) one-dimensional diagram (b) two-dimensional diagram (c) diagram with no dimension (d) None of these Answer: (a) Bar diagrams are one-dimensional diagrams. Though these are represented on a plane of two axis in form of rectangular bars, the width is of no consequence and only the length depicts the frequency.

Question 2. Data represented through a histogram can help in finding graphically the (a) mean (b) mode (c) median (d) All of these Answer: (b) Histogram gives value of mode of the frequency distribution graphically through the highest rectangle.

Question 3. Ogives can be helpful in locating graphically the (a) mode (b) mean (c) median (d) None of these Answer: (c) Intersection point of the less than and more than ogives gives the median.

Question 4. Data represented through arithmetic line graph help in understanding (a) long term trend (b) cyclicity in data (c) seasonality in data (d) All of the above Answer: (a) Arithmetic line graph helps in understanding the trend, periodicity, etc in a long term time series data.

Question 5. Width of bars in a bar diagram need not be equal. (True/False) Answer: False Bar diagram comprises a group of equispaced and equiwidth rectangular bars for each class or category of data.

Question 6. Width of rectangles in a histogram should essentially be equal. (True/False) Answer: False If the class intervals are of equal width, the area of the rectangles are proportional to their respective frequencies and width of rectangles will be equal. However, sometimes it is convenient or necessary to use varying width of class intervals and hence unequal width of rectangles.

Question 7. Histogram can only be formed with continuous classification of data. (True/False) Answer: True A histogram is never drawn for a discrete variable/data. If the classes are not continuous they are first converted into continuous classes.

Question 8. Histogram and column diagram are the same method of presentation of data. (True/False) Answer: False Histogram is a two dimensional diagram drawn for continuous data and the rectangles do not have spaces in between while column diagram is one dimensional with space in between every column (bar).

Question 9. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False) Answer: True Histogram gives value of mode of the frequency distribution graphically through the highest rectangle.

Question 10. Median of a frequency distribution cannot be known from the ogives. (True/False) Answer: False Intersection-point of the less than and more than ogives gives the median.

Question 11. What kind of diagrams are more effective in representing the following? (a) Monthly rainfall in a year (b) Composition of the population of Delhi by religion (c) Components of cost in a factory Answer: (a) The monthly rainfall in a year can be best represented by a bar diagram as only one variable i.e., monthly rainfall is to be presented diagrammatically. The rainfall is plotted on Y-axis in the corresponding month that is plotted on the X-axis. (b) Composition of the population of Delhi by religion can be represented by a component bar diagram. A component bar diagram shows the bar and its sub-divisions into two or more components. Thus, the total population can be sub divided in terms of religion and presented through a component bar diagram. (c) Different components of cost in a factory can most effectively be depicted through a pie chart. The circle represents the total cost and various components of costs are shown by different portions of the circle drawn according to percentage of total cost each component covers.

Question 12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form? Answer: Share of urban workers and non workers in India

Question 13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table? Answer: A histogram is a set of rectangles with bases as the intervals between class boundaries (along X-axis) and with areas proportional to the class frequency. If the class intervals are of equal width, the area of the rectangles are proportional to their respective frequencies.

However, sometimes it is convenient or at times necessary, to use varying width of class intervals. For graphical representation of such data, height for area of a rectangle is the quotient of height i.e., frequency and base i.e., width of the class interval. When intervals are equal, all rectangles have the same base and area can conveniently be represented by the frequency of the interval.

But, when bases vary in their width, the heights of rectangles are to be adjusted to yield comparable measurements by dividing class frequency by width of the class interval instead of absolute frequency. This gives us the frequency density for the purpose of comparison. Thus  Frequency density ( Height of rectangle )= Class Frequency  Width of the class interval 

Question 14. The Indian Sugar Mills Association reported that, ‘sugar production during the first fortnight of December, 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December, 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why? (iii) Present these data diagrammatically. Answer: (i) Data in tabular form. Sugar Production in India

(ii) The data can effectively be presented diagrammatically using the multiple bar diagram. This is because multiple bar diagrams are used for comparing two or more sets of data for different years or classes, etc.

presentation of data ncert solutions

Question 15. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost. Represent the data as multiple time-series graphs. Answer:

presentation of data ncert solutions

Benefits of NCERT Solution for Class 11

NCERT Solution for Class 11 contains extremely important points, and for each chapter, each concept has been simplified to make it easier to remember and increase your chances of achieving excellent exam results. Exam Preparation References Here are some tips on how these solutions can help you prepare for the exam.

  • This helps students solve many of the problems in each chapter and encourages them to make their concepts more meaningful.
  • NCERT Solution for Class 11 encourage you to update your knowledge and refine your concepts so that you can get good results in the exam.
  • These NCERT Solution For Class 11 are the best exam materials, allowing you to learn more about your week and your strengths. To get good results in the exam, it is important to overcome your weaknesses.
  • Most of the questions in the exam are formulated in a similar way to NCERT textbooks. Therefore, students should review the solutions in each chapter in order to better understand the topic.
  • It is free of cost.

Tips & Strategies for Class 11 Exam Preparation

  • Plan your course and syllabus and make time for revision
  • Please refer to the NCERT solution available on the  cbsestudyguru  website to clarify your concepts every time you prepare for the exam.
  • Use the  cbsestudyguru  learning app to start learning to successfully pass the exam. Provide complete teaching materials, including resolved and unresolved tasks.
  • It is important to clear all your doubts before the exam with your teachers or Alex (an Al study Bot). 
  • When you read or study a chapter, write down algorithm formulas, theorems, etc., and review them quickly before the exam.
  • Practice an ample number of question papers to make your concepts stronger. 
  • Take rest and a proper meal.  Don’t stress too much. 

Why opt for cbsestudyguru NCERT Solution for Class 11 ? 

  • cbsestudyguru  provide NCERT Solutions for all subjects at your fingertips.
  • These solutions are designed by subject matter experts and provide solutions to every NCERT textbook questions. 
  • cbsestudyguru  especially focuses on making learning interactive, effective and for all classes.
  • We provide free NCERT Solutions for class 11 and all other classes.

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NCERT Solutions Class 11 Statistics Chapter 4

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The topic of Statistics deals with the quantification of data. It revolves around specific numbers to represent qualitative information. Simply, it is a collection of data. But that’s not all. As Economics students, one must learn data processing techniques that collect, tabulate, classify and present data. In addition, one needs to learn more about data reduction and condensation. Finally, one must also become familiar with the techniques of data analysis and interpretation. Along with the solutions of NCERT Solutions For Class 11 Statistics Chapter 4 ,Extramarks also provides answers of NCERT Solutions Class 12 for Class 12, NCERT Solutions Class 11 for Class 11,  NCERT Solutions Class 10 for Class 10, NCERT Solutions Class 9 for Class 9, NCERT Solutions Class 8 for Class 8 , NCERT Solutions Class 7 for Class 7 and NCERT Solutions Class 6 for Class 6.

NCERT Solutions For Class 11 Statistics Chapter 4 – Presentation of Data

The NCERT Solutions For Class 11 Statistics Chapter 4 ‘Presentation of Data’ is available for reading or download on this page. Students who are in Class 11 or preparing for the Class 11 Statistics exam can refer to the NCERT Solutions For Class 11 Statistics Chapter 4 Statistics Book for review. Class 11 Statistics Chapter 4 e-book PDF is always useful to use when students do not have access to a physical copy.

NCERT Solutions For Class 11 Statistics Chapter 4 Presentation Of Data

All answers to NCERT Solutions For Class 11 Statistics Chapter 4 and Class 11 Statistics NCERT Solutions Chapter 4 are available on Extramarks. The students who are studying Statistics using NCERT textbooks and want to understand Chapter 4 “Presenting Data”. They, after learning the lesson, look for answers in the NCERT Solutions For Class 11 Statistics Chapter 4 to their questions. They can get all the answers in the NCERT Solutions For Class 11 Statistics Chapter 4.

Data Can Be Represented In Two Forms. They Are As Follows:

Today, the presentation of data is paramount. After all, anything beautiful will never fail to capture our attention. Data presentation refers to presenting or establishing data in an attractive and useful way so that it can be easily interpreted. The three main forms of data presentation  are:

The discussion of data representation begins with its crudest and most ambiguous form, the textual representation. In such a presentation, the data in question is simply plain text, i.e. usually contained within a paragraph. This is typically used when the data is not very large.

This type of representation is useful when students are looking to supplement qualitative statements with certain data. For this purpose, the data should not be represented too large in tables or charts. It should only be a statement that serves as appropriate evidence for the qualitative evidence and helps the reader form an idea of ​​the extent of a phenomenon. All the related answers are available in the NCERT Solutions For Class 11 Statistics Chapter 4

Tables allow for an attractive, clear, and orderly presentation of even large amounts of data. Data is organized in rows and columns. Because data tables are easy to create and read, they are one of the most common forms of data representation. All the solutions of problems related to Tabular form are easily accessible on the NCERT Solutions For Class 11 Statistics Chapter 4

Data table components

Table number: Each table should have a specific table number for easy access and location. This number can be easily mentioned anywhere it serves as a reference, giving students direct access to the date mentioned in that particular table.

Title: The table should include a title that clearly informs the reader of the data included, the period of the study, the location of the study, and how the data is categorized.

Headnotes: Headnotes further support the purpose of the title and give more information about the table. Header notes generally represent units of data within parentheses at the end of the table title.

Stubs: These are the titles of the rows within the table. A stub therefore displays information about the data contained in a particular row.

Caption: Caption is the title of the column in the data table. In fact, this is equivalent to a stub, showing the information contained in the column.

Body or field: The body of a table is the entire contents of the table. Each element of the body is called a “cell”.

Footnotes: Footnotes are rarely used. Add a title for the table, if desired. Source: If data from a secondary source is used, this source should be indicated below the footnote.

Construction of Data Table

Some basic ideas of making a table are:

Title should be appropriate for the purpose of the study: The title of a table should provide an overview of the table.

Compare: If two rows or columns need to be compared, they can be placed close to each other.

Alternate placement of catches: If the rows in the data table are long, the exploits can be placed on the right side of the table.

Title: The title should be written in the singular. For example, `good`  instead of `goods`.

Footnotes: Footnotes should only be provided if necessary.

Column size: Column size should be uniform and proportionate. Use abbreviations: Titles and subtitles must not contain abbreviations.

Units: There should be a clear specification of the unit above the columns.

For Diagrammatic representation, a bar chart is one of the most common types of data representation.

Simple bar Diagram

Multi-Bar Chart

Percentage Bar Chart

Sub Divided Bar Chart

All of the above topics have been detailed in Chapter 4 of the NCERT Solution Class 11 Statistics. The 15 questions in this chapter provide an appropriate overview of “Data Presentation”.

Questions Given in the NCERT Solutions for Class 11 Statistics for Economics Chapter 4

Questions that are given in the textbook of NCERT are very important for every student who is preparing for Class 11 Exams. Therefore, Extramarks provides all the solutions of NCERT Solutions For Class 11 Statistics Chapter 4 on the website on Extramarks. Students can refer to the NCERT Solutions For Class 11 Statistics Chapter 4 solutions, as these are prepared by the expert team of Extramarks.

Each question in the NCERT solutions is followed by a correct, concise and relevant answer. The answers given in the NCERT Solutions For Class 11 Statistics Chapter 4 solution also follow the CBSE model of the exam. This helps students have a brief idea of ​​the types of questions they are likely to face in the final exams. Here is an overview of the types of questions in Chapter 4 of the Class 11 Statistics NCERT Solution:

Students of Class 11 have a lot of questions in their NCERT books and for the solutions, they can refer to  NCERT Solutions For Class 11 Statistics Chapter 4. No matter what question of the Class 11 Statistics syllabus it is, the answer given in  NCERT Solutions For Class 11 Statistics Chapter 4. If a student gets stuck at a question and needs an answer for reference, they can refer to  NCERT Solutions For Class 11 Statistics Chapter 4. All answers from Class 11 Statistics are available in NCERT Solutions For Class 11 Statistics Chapter 4. Students can refer to  NCERT Solutions For Class 11 Statistics Chapter 4 for answers of all questions.

All the answers are explained lucidly in the NCERT Solutions For Class 11 Statistics Chapter 4. NCERT Solutions For Class 11 Statistics Chapter 4 can be referred to for the answers. For every problem a student cannot solve, solutions are available on the NCERT Solutions For Class 11 Statistics Chapter 4. Students must refer to the NCERT Solutions For Class 11 Statistics Chapter 4 to understand how to form their answers in the actual exam. Students can take help of  NCERT Solutions For Class 11 Statistics Chapter 4 for understanding the answers. The answers are available in NCERT Solutions For Class 11 Statistics Chapter 4. One can refer to NCERT Solutions For Class 11 Statistics Chapter 4 even during their revision sessions. Along with that, students also benefit from online courses and online study resources like NCERT Solutions For Class 11 Statistics Chapter 4.

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FAQs (Frequently Asked Questions)

1. what types of questions are available in ncert answers to statistics class 11 for economics chapter 4.

Chapter 4 of the NCERT Answers to Class 11 Statistics has 15 questions. Some of these questions are conceptual and objective in nature. Some questions in this chapter are based on “true or false” statements. Some questions require students to represent given data. All the solutions can be checked on  NCERT Solutions For Class 11 Statistics Chapter 4

2. What does the 11th Class Statistics textbook talk about?

This chapter is about data presentation. Data is information that is collected and needs to be organized to investigate a hypothesis or to come to a conclusion. This chapter covers textual, tabular, and graphical representation of data. The solutions can be easily interpreted from NCERT Solutions For Class 11 Statistics Chapter 4. The data when presented will make it easier for you to study and analyse, and also more appealing to the eye. Data is presented in a clear way that facilitates understanding.

3. Is Class 11 Chapter 4 of Statistics important?

Statistics Chapter 4 Class 11 is a chapter in the Statistics textbook titled Data Presentation. This chapter allows one to understand how one can present and analyse data. Students, consciously or unconsciously, process data, organize it, and use it to achieve better results. Understanding how the data is presented also allows one to intelligently plan the research, prepare and understand how one can use the minimum of resources to achieve maximum results. The knowledge gained in the chapter will be useful in education and in real life.

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presentation of data ncert solutions

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Class 11 Statistics Chapter 4 Presentation of Data PDF

Ncert solutions for class 11 statistics, chapter 4 presentation of data.

  • Chapter 1 Introduction
  • Chapter 2 Collection Of Data
  • Chapter 3 Organisation Of Data
  • Chapter 4 Presentation Of Data
  • Chapter 5 Measures Of Central Tendency
  • Chapter 6 Measures Of Dispersion
  • Chapter 7 Correlation
  • Chapter 8 Index Numbers

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NCERT Solutions for Class 11 Economics Presentation of Data PDF Download

The answers in the NCERT Solutions for Class 11 Economics Presentation of Data are explained in a point wise manner so that students can understand all types of questions. Through this point wise approach, students can solve doubts and confusions;  accordingly can score well in questions related to Class 11 Economics Presentation of Data. 

NCERT Solutions for Class 11 Economics Presentation of Data PDF

The Presentation of Data is the important one which utilises multiple concepts to give students a holistic overview. To have a proper holistic overview, students need to practise more and more questions from the NCERT Solutions for Class 11 Economics Presentation of Data PDF. This portable document format of Presentation of Data questions is easily available on the Selfstudys website. 

How to Download the NCERT Solutions for Class 11 Economics Presentation of Data?

To download the NCERT Solutions for Class 11 Economics Presentation of Data, students need to follow the given steps; those steps are: 

  • Visit the Selfstudys website. 

NCERT Solution for Class 11 Economics Presentation of Data, NCERT Solution for Class 11 Economics Presentation of Data PDF, NCERT Solution for Class 11 Economics Presentation of Data PDF Download, Exercise Wise NCERT Solution for Class 11 Economics Presentation of Data, Formula wise NCERT Solution for Class 11 Economics Presentation of Data

  • Bring the arrow towards the NCERT Books & Solutions which can be seen in the navigation bar. 
  • A drop down will appear, select NCERT Solutions from the list. 

NCERT Solution for Class 11 Economics Presentation of Data, NCERT Solution for Class 11 Economics Presentation of Data PDF, NCERT Solution for Class 11 Economics Presentation of Data PDF Download, Exercise Wise NCERT Solution for Class 11 Economics Presentation of Data, Formula wise NCERT Solution for Class 11 Economics Presentation of Data

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NCERT Solution for Class 11 Economics Presentation of Data, NCERT Solution for Class 11 Economics Presentation of Data PDF, NCERT Solution for Class 11 Economics Presentation of Data PDF Download, Exercise Wise NCERT Solution for Class 11 Economics Presentation of Data, Formula wise NCERT Solution for Class 11 Economics Presentation of Data

  • Now select Economics from the list of subjects. 
  • Again a new page will appear. Now students can select Presentation of Data to solve questions and refer to answers. 

Features of the NCERT Solutions for Class 11 Economics Presentation of Data

The features of the NCERT Solutions for Class 11 Economics Presentation of Data are considered to be important part; some of the features are discussed below:

  • Formulas are Included: Questions in the NCERT Solutions for Class 11 Economics Presentation of Data revision includes formulas so that students can understand the question and formula in a better way. 
  • Numerical Questions are Given: In the NCERT Solutions for Class 11 Economics Presentation of Data theory, numerical questions are given. So that students can learn to approach numerical questions of Presentation of Data. 
  • All Levels of Questions are Asked: Inside the NCERT Solutions for Class 11 Economics Presentation of Data PDF, all levels of questions are included so that students don’t feel confused while attempting the final exam. 
  • Theory Based Questions are Included: Theory based questions of Presentation of Data questions are included in the NCERT Solutions so that by practising students can get theoretical knowledge. 
  • Available in the PDF: The questions of from NCERT Class 11 Economics Solutions are available in the portable document format so that students can d0wnload from their electronic device. 
  • Free Accessibility: Students can access the Presentation of Data questions from the Class 11 NCERT Economics Solutions at any hour of the day as it is easy accessibility. 

Benefits of the NCERT Solutions for Class 11 Economics Presentation of Data

While and after solving the questions from the NCERT Solutions for Class 11 Economics Presentation of Data can be benefited a lot, those benefits are: 

  • Provides Foundation: By solving Presentation of Data questions from the NCERT Class 11 Economics Solutions, students can build a strong and solid foundation. By building a strong foundation, students can score good marks in the Presentation of Data questions. 
  • Get an Idea Important Topics: Solving questions from the NCERT Solutions for Class 11 Economics Presentation of Data revision can help students to get an idea about important topics and concepts. 
  • Explains in an Easy Language: Answers in the NCERT Solutions for Class 11 Economics Presentation of Data theory are explained in an easy language so that students can easily understand all levels of questions without any difficulty. 
  • Helpful for Exam Preparation: In the NCERT Solutions for Class 11 Economics Presentation of Data PDF, all the questions and answers are explained in a proper way so automatically students can prepare well for the final exam. 
  • Saves Time: Students can save their time as well as effort to search Class 11 Economics questions and answers as it is already available in the NCERT Solutions of Presentation of Data.  
  • Offers Plenty of Questions to Practise: The NCERT Class 11 Economics Solutions for Presentation of Data offers plenty of questions to practise. By practising these questions, students can easily build a strong foundation. 

How to Implement the NCERT Solutions for Class 11 Economics Presentation of Data in the Preparation?

To implement the NCERT Solutions for Class 11 Economics Presentation of Data in the preparation, students can follow the given steps; those steps are: 

  • Read the Chapter: To implement the NCERT Solutions for Class 11 Economics Presentation of Data revision in the preparation, students need to first read the chapter in a proper way. By understanding the chapter in a proper way, students can remember the important topics while solving questions from Presentation of Data. 
  • Solve the Questions: After reading Presentation of Data, students are advised to solve questions from the Class 11 Economics textbook. It is advisable for students to solve questions on their own before referring to the NCERT Solutions for Class 11 Economics Presentation of Data theory.
  • Refer to the Solutions: Once students solve questions, students need to refer to the NCERT Solutions for Class 11 Economics Presentation of Data PDF so that they can match their answers. 
  • Practise More Questions: Students are advised to solve Presentation of Data questions from the NCERT Class 11 Economics Solutions. 
  • Revise Regularly: To implement the Presentation of Data questions from the NCERT Class 11 Economics Solutions in the preparation, students need to revise the whole chapter regularly. By revising, students can keep the concepts of Economics Presentation of Data fresh in their mind.
  • Seek Help: In order to implement the Presentation of Data questions from the NCERT Class 11 Solutions in the preparation, students need to seek help from the concerned teachers. By seeking the required help, students can score well in the Presentation of Data Economics questions. 

When to Utilise NCERT Solutions for Class 11 Economics Presentation of Data in the Effective Way?

To utilise the NCERT Solutions for Class 11 Economics Presentation of Data in the effective way; some of it are discussed below: 

  • To Have a Conceptual Understanding: The NCERT Solutions for Class 11 Economics Presentation of Data revision can be utilised to clarify doubts and to get a deep understanding of concepts. 
  • To Complete Homework Assignments: The NCERT Solutions for Class 11 Economics Presentation of Data theory can be utilised to complete the homework assignments and accordingly can check the answers. 
  • To Prepare for Exams: Students can prefer utilising the NCERT Solutions for Class 11 Economics Presentation of Data PDF to understand the concepts and improve problem solving skills. By understanding the concepts of Presentation of Data, students can prepare well for the Class 11 Economics final exam. 
  • To Revise: Through the Class 11 NCERT Economics Solutions, students need to revise the concepts and topics of Presentation of Data. 
  • For Self Assessment: In order to self assess while preparing for Presentation of Data, students can prefer utilising the NCERT Class 11 Economics Solutions. By self assessment, students can identify the weak areas of Presentation of Data and accordingly they can work upon.
  • After Completing the Chapter: Once students complete Presentation of Data from the Class 11 Economics textbook, they can prefer utilising the NCERT Solutions to practise more and more questions. 

How to Analyse the Mistakes After Solving Questions from the NCERT Solutions for Class 11 Economics Presentation of Data?

It is important for students to analyse the mistakes after solving questions from the NCERT Solutions for Class 11 Economics Presentation of Data; steps to analyse are discussed below:

  • Identify the Mistakes: After solving NCERT Solutions for Class 11 Economics Presentation of Data revision, students need to identify the mistakes. Accordingly they can identify what kind of mistakes they have made: misinterpretation of Presentation of Data questions, conceptual error. 
  • Understand the Cause: Once students have identified the mistakes while attempting questions from NCERT Solutions for Class 11 Economics Presentation of Data revision, they need to understand the cause of the mistakes. Understanding the cause of the mistakes after attempting Presentation of Data questions, students can minimise the mistakes in future. 
  • Correct the Mistakes: At the moment they identify the cause of mistakes after solving questions from the NCERT Solutions for Class 11 Economics Presentation of Data theory, they need to rectify the mistakes. By rectifying the mistakes, students can build a strong foundation for the Class 11 Economics Presentation of Data. 
  • Keep a Record: It is advisable for students to keep a record of mistakes after solving questions from NCERT Solutions for Class 11 Economics Presentation of Data PDF so that they keep a track of their progress. 
  • Practise Same Questions: Students need to practise the same set of Presentation of Data questions from the NCERT Class 11 Economics Solutions so that they can rectify the mistakes easily. 
  • Stay Motivated: To rectify all the mistakes after solving Presentation of Data questions from the NCERT Class 11 Economics Solutions, students need to stay motivated and focused.

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Question 1:

Using some hypothetical data, and descriptive form of data presentation: Describe the impact of strike by the traders in your city.

The strike by traders in our city has caused shortage of onions by 50% and pushed up onion prices by 75%.

Page No 116:

Question 2:.

Using some hypothetical data, and descriptive form of data presentation: Decribe the impact of increase in the price of petrol on the demand for cars and scooters.

Due to rise in the price of petrol by 30%, the demand for cars and scooters has gone down by 50%.

Page No 124:

Construct a table presenting data collected by you on preferential liking of your class-mates of different teachers in your school.

Construct a table on marks in English secured by the students of Class X in your school in the house examination.

Question 3:

Construct a table on the runs scored by different players in the inter-school cricket tournament hosted by your school.

Page No 125:

Check with your Principal. Request him to provide you information on the number of students in the school over the last 10 years. Present the data in a table based on temporal classification.

Go to the office of Registrar, Births and deaths, of your town. Make a request for data on the number of births and deaths registered during different years over the last 10 years. Present the data in the form of table, showing temporal classification of data.

Page No 126:

Get information on the native state of the students in your school. Present the data in the form of a table, showing spatial classification of data.

Get information on the location of Head-office of different banks in your locality. Present the data in the form of  a table, showing spatial classification of data.

Page No 137:

In 2019-20, the contribution of primary, secondary and tertiary sectors to India's GDP (hypothetical figures) was 17.6%, 28.2% and 54.2% respectively. In 2020-21, these shares were 17.7%, 27.0% and 55.3% respectively. Present this information in the form of a table.

Contribution of Primary, Secondary and Tertiary Sector to India’s GDP (in %)

Prepare a sketch of such a table that exhibits the following types of information on the number of students of your college: (i) Faculty-wise: Arts, Commerce and Science. (ii) Class-wise: XI; B.A. (I); B.A. (II); and B.A. (III). (iii) Sex-wise: Boys and Girls.

                                      Distribution of Students                                 (according to faculty, class and sex)

            Exports from India to USSR and UK                     (2018 - 2021)                 (in Rs crore)

Question 4:

Point out the mistakes in the following table. Rearrange it correctly.

The following are the mistakes in the given table. 1. The table does have a title and a head note. 2. The sub-entries and the captions have not been noted carefully. 3. The total of the rows and the columns is not provided.               Number of Students      (according to subject and sex)

Page No 138:

Question 5:.

Following information relates to the marks securd by 50 students in Economics. Present the following information in the form of a table.

Marks Obtained by Students in Economics

Question 6:

Following information relates to the marks secured by 50 boys and girls in their paper in Economics. Present the information in the form of a table.

Marks obtained by Students in Economics

Question 7:

Draw a blank table to show the distribution of population according to sex, literacy, and income.

Question 8:

Present the following information in a suitable tabular form: (i) In 2020, out of total 2,000 workers in a factory, 1,550 were members of a trade union. The number of women workers employees was 250, out of which 200 did not belong to any trade union. (ii) In 2021, the number of union workers was 1,725 of which 1,600 were men. The number of non-union workers was 380, among which 155 were women.

The information given in the question can be summarised as follows. Year 2020 Total no. of workers in the factory = 2000 Total no. of trade union workers = 1550 Total no. of non-trade union workers = (2000 − 1550) = 450 Total no. of women worker = 250 Total no. of non-trade union women worker = 200 Total no. of trade union women worker = (250  −  200) = 50 Total no. of trade union men worker = (1550  −  50) = 1500 Total no. of non-trade union men worker = (450  −  200) = 250 Total no. of men workers = 1500 + 250 = 1750 Year 2021 Total no. of trade union workers = 1725 Total no. of trade union men worker = 1600 Total no. of non-trade union women worker = (1725  −  1600) = 125 Total no. of non-trade union workers = 380 Total no. of non-trade union women worker = 155 Total no. of non-trade union men worker = (380  −  155) = 225 Total no. of workers in the factory = 1725 + 380 = 2105 Total no. of men workers = 1600 + 225 = 1825 Total no. of women workers = 125 + 155 = 280                                       

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NCERT Solutions for Class 11 Economics -Statistics for Economics – Chapter 4 – Presentation of Data

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Exercise : Solutions of Questions on Page Number : 56

Q1 :Bar diagram is a (i) one-dimensional diagram (ii) two-dimensional diagram (iii) diagram with no dimension (iv) none of the above Answer :   Bar diagrams are One-dimensional diagrams. These are represented on a plane of two axis and depicts the relationship between the two variables (plotted on the either axis) in form of rectangular bars.

Q2 :Data represented through a histogram can help in finding graphically the (i) mean (ii) mode (iii) median (iv) all the above Answer :   Graphically mode can be determined by presenting the data in the form of Histogram. The highest Histogram indicates the modal class. The intersection point of the lines diagonally joining the two top corners of the modal rectangles to the corners of the adjacent Histograms indicates the Modal Value.

Q3 :Ogives can be helpful in locating graphically the (i) mode (ii) mean (iii) median (iv) none of the above Answer : Graphically, Median can be determined by the intersection point of Less than Ogive and More than Ogive. The value of x-axis corresponding to the intersection point indicates the median.

Q4 :Data represented through arithmetic line graph help in understanding (i) long-term trend (ii) cyclicity in data (iii) seasonality in data (iv) all the above Answer : Data represented through arithmetic line graph (or time series graph) helps in understanding the long-term trend and periodicity.

Q5 :Width of bars in a bar diagram need not be equal (True/False). Answer : The above statement is false as all bars in a bar diagram need to be of equal width. Moreover, all bars are at equal distance from each other.

Q6 :Width of rectangles in a histogram should essentially be equal (True/False). Answer :   The above statement is false, as the width of all rectangles in a histogram may or may not be equal. The width of a rectangle depends on the width of its corresponding class interval.

Q7 :Histogram can only be formed with continuous classification of data (True/False). Answer :   Yes, a Histogram can only be formed with the continuous classification of data. The frequency distribution of a continuous series is graphically presented in form of a Histogram. If the given data is not continuous, then it is to be converted into exclusive series before presenting the data in the form of Histogram. Histograms can never be prepared for discrete series.

Q8 :Histogram and column diagram are the same method of presentation of data (True/False). Answer: The above statement is false. This is because Histogram and column diagram are different method of presentation. While the Histogram is a Two-dimensional diagram, the bar diagram is a One-dimensional diagram. Histograms are prepared for the continuous series, whereas the bar diagrams are prepared for the discrete series. Further, Histograms are drawn continuously without any space between two consecutive Histograms, whereas the space is must between two bars in a bar diagram.

Q9 :Mode of a frequency distribution can be known graphically with the help of histogram (True/False). Answer : The above statement is true. Graphically, mode can be determined by presenting the data in the form of Histogram. The highest Histogram indicates the modal class. The intersection point of the lines diagonally joining the two top corners of the modal rectangles to the corners of the adjacent Histograms indicates the Modal Value.

Q10 :Median of a frequency distribution cannot be known from the ogives (True/False). Answer : The statement is false. Graphically Ogives can be determined by the intersection point of the less than Ogive and more than Ogive. The value of x-axis corresponding to the intersection point indicates the median.

Q11 :What kinds of diagrams are more effective in representing the following? (i) Monthly rainfall in a year (ii) Composition of the population of Delhi by religion (iii) Components of cost in a factory Answer : (i) The monthly rainfall in a year can be best represented by a bar diagram as only one variable i.e. monthly rainfall is to be compared visually. The highest bar diagram indicates the highest rainfall in the corresponding month that is plotted on the x-axis. (ii) Composition of the population of Delhi by religion can be represented by a simple bar diagram. Plotting different religion on the x-axis and the number of people on the y-axis, one can easily compare the number of the population religion-wise.. (iii) In order to represent different components of cost in a factory, a pie chart is more effective. The entire circle represents the total cost and various components of costsare shown by different portions of the circle.

Q12 :Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form? Answer : Share of Rural and Urban Non-workers in India

Source: Census of India, 2001 We can infer from the above table that the absolute number of the rural non-workers is greater than the absolute number of the urban non-workers. The higher ( lower) share of the rural non-workers (urban non-workers) reveals lower degree of urbanisation in India. NOTE: As there is no Example 4.2 in the book, so the following data have been adapted from Census of India, 2001.

Q13 :How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table? Answer :   A Histogram of equal class intervals has equal width of all rectangles indicating the same class intervals. In contrast, a Histogram of unequal class intervals has rectangles of varying width as per their corresponding class intervals. Before constructing a Histogram, frequencies of unequal class intervals are to be adjusted. The adjustment factor of each class is calculated with the following formula.

presentation of data ncert solutions

And the adjusted frequency will be calculated by dividing the original frequency by adjustment factor.

Q14 : The Indian Sugar Mills Association reported that, ‘Sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why? (iii) Present these data diagrammatically. Answer :

(ii) With a view to present the data diagramatically the multiple bar diagram can be effectiveliy used.

presentation of data ncert solutions

Q15 :  The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.

Represent the data as a multiple time series graph Answer:

presentation of data ncert solutions

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Chapter 4 Presentation of Data

NCERT Solutions for Class 11 Economics Chapter 4 - Presentation of Data

26. Bar diagram is a: (a) one-dimensional diagram (b) two-dimensional diagram (c) diagram with no dimension (d) none of these

Ans. (a) one-dimensional diagr

Explanation:

Bar diagram is a one-dimensional diagram as these are presented on a plane having two axis in form of rectangular bars. The width is of no concern and only the length shows the frequency of the class interval.

27. Data represented through a histogram can help in finding graphically the: (a) mean (b) mode (c) median (d) all of these

Ans. (b) mode

Histogram gives the value of mode of the frequency distribution presented graphically with the help of the tallest rectangle.

28. Ogives can be helpful in locating graphically the: (a) mode (b) mean (c) median (d) none of these

Ans. (c) median

Intersection point of the more than and less than ogives gives the value of the median.

29. Data represented through arithmetic line graph help in understanding: (a) long term trend (b) cyclicity in data (c) seasonality in data (d) all of the above

Ans. (a) long term trend

Arithmetic line graph assists in knowing the periodicity, trend, etc. in a long term time series data.

30. Width of bars in a bar diagram need not be equal. (True/False)

Ans. False. Bar diagram consist of a group of equiwidth and equispaced rectangular bars for each set of data.

31. Width of rectangles in a histogram should essentially be equal. (True/False)

Ans. False. When the class intervals are of same width, then the rectangular area are proportional to their corresponding frequencies and width of rectangles are equal. But, sometimes it is useful or required to use different width of class intervals and hence width of rectangles are unequal. 

32. Histogram can only be formed with continuous classification of data. (True/False)

Ans. True. A histogram is useful for showing only continous data and not for discrete series or data. If the classes are not continuous in nature, then one have to first convert it into continuous intervals.

33. Histogram and column diagram are the same method of presentation of data. (True/False)

Ans. False. Histogram is a two-dimensional diagram which is useful for showing continuous data and the rectangles do not have the spaces between them, whereas column diagram is one-dimensional diagram having spaces between every bar or rectangle.

34. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)

Ans. True. Histogram gives the value of mode of the frequency distribution presented graphically and gives the value through the tallest rectangle. 

35. Median of a frequency distribution cannot be known from the ogives. (True/False)

Ans. False. Intersection point of the more than and less than ogives gives the value of median. 

36. What kind of diagrams are more effective in representing the following? (a) Monthly rainfall in a year (b) Composition of the population of Delhi by religion (c) Components of cost in a factory

Ans. (a) The monthly rainfall in a year can be easily represented by using a bar diagram because of only one variable, i.e., monthly rainfall. The months are plotted on x-axis and rainfall on Y-axis.

(b) Composition of the population of Delhi by religion is best represented by using a component bar diagram. It displays the bar and its sub-divisions into two or more components. Therefore, the total population can be sub divided on the basis of religion and presented using a component bar diagram.

(c) Components of the cost in a factory can easily be represented using a pie chart. The circle signifies the total cost and several components of the costs are presented by different portions of the circle drawn as per the percentage of total cost. 

37. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?

Ans. Share of urban workers and non-workers in India 

38. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?

Ans. A histogram is a set of rectangles having bases as the intervals between class boundaries shown on X-axis and having areas proportional to the class frequency shown on y-axis. In case, the class intervals are of equal width, the rectangular area are proportional to their corresponding frequencies. Though, sometimes it is useful or at times it is required, to use different width of class intervals. So, in this case, the height for rectangualr area is the quotient of height, that is, frequency and base, that is, width of the class interval. But if we have equal intervals, then all the rectangles will have the same base and area can be easily represented by the frequency. How ever, if the bases vary in their width, then the heights of rectangles need to be adjusted by dividing class frequency by class interval’s width in place of absolute frequency. This gives us the frequency density. Thus, Frequency density = Width of the class frequency of the class interval.

39. The Indian Sugar Mills Association reported that, ‘sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why? (iii) Present these data diagrammatically.

Ans. (i) Sugar Production in India

(ii) This data can be effectively presented in diagrammatic form using the multiple bar diagram because multiple bar diagrams are used for comparison of two or more sets of data for different classes, years, etc.

Sugar Production

40. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.

Represent the data as multiple time-series graphs.

GDP

NCERT Solutions for Class 11 Economics Chapter 2 Free PDF Download

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  • Chapter 4 Presentation Of Data

Statistics For Economics Chapter 4 Presentation Of Data

Ncert solution for class 11 statistics statistics for economics.

Presentation Of Data Here is the CBSE Statistics Chapter 4 for Class 11 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 11 Statistics Presentation Of Data Chapter 4 NCERT Solutions for Class 11 Statistics Presentation Of Data Chapter 4 The following is a summary in Hindi and English for the academic year 2021-2022. You can save these solutions to your computer or use the Class 11 Statistics.

Bar diagram is a: One-dimensional diagram   two-dimensional diagram    diagram with no dimension   none of the above

One-dimensional diagram

  • https://www.wiredfaculty.com/share/Q0JTRUVOU1QxMTAyMzk2MA==

Data represented through a histogram can help in finding graphically the: mean mode median all the above

presentation of data ncert solutions

 Ogives can be helpful in locating graphically the: mode mean median none of the above

Data represented through arithmetic line graph help in understanding: long term trend cyclity in data seaonality in data all the above.

long term trend

Width of bars in a bar diagram need not be equal. A. False

Width of rectangles in a histogram should essentially be equal. a. false,  histogram can only be formed with continuous classification of data. a. true, histogram and column diagram are the same method of presentaton of data. a. true, mode of a frequency distribution can be known graphically with the help of histogram. a. true, median of a frequency distribution cannot be known from the ogives. a. false, what kind of diagrams are more effective in representing the following: (i) monthly rainfall in a year. (ii) composition of the population of delhi by religion. (iii) components of cost in a factory..

(i) Bar Diagram.

(ii) Sub-divided or Component Bar Diagram.

(iii) Component Bar Diagram.

Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?

Increase in the share of urban non-workers:

Lower level of urbanisation (in percentage)

Alternatively : (Increase in the share of urban non-workers (for the state of Delhi) :

(in percentage)

(Note : arbitrary figures have been taken.)

How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?

Procedure of drawing a histogram differ when class-intervals are unequal in comparison to equal class-intervals in a frequency table. In the case of equal class-intervals, no adjustment is made. In this case, the width of the rectangles would be of equal width, whereas the length of the rectangles would be different in proportion to the frequencies of the class-intervals.

In case of unequal class-intervals, frequencies of unequal class-intervals are adjusted. For adjustment, following steps are taken into account:

1. We first locate the lowest class-interval. We make no adjustment in this class-interval.

2. We adjust the frequencies of all other classes with the lowest class-size using the following formula:

Adjusted frequency

presentation of data ncert solutions

3. The histogram is made on the basis of adjusted frequencies and not the frequencies given originally.

4. We below given the adjusted frequency for the further clarification. Class-Interval f Adjusted frequency

presentation of data ncert solutions

It may be pointed out that the width of the rectangles would be different

The Indian Sugar Mills Association reported that, ‘Sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why ? (iii) Present these data diagram-matically.

(ii) We will use multiple bar diagram.

presentation of data ncert solutions

The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost. Year Agriculture and Allied Sectors Industry Services (1) (2) (3) (4) 1994 – 95 5.0 9.2 7.0 1995 – 96 – 0.9 11.8 10.3 1996 – 97 9.6 6.0 7.1 1997 – 98 – 1.9 5.9 9.0 1998 – 99 7.2 4.0 Year Agriculture and Allied Sectors Industry Services (1) (2) (3) (4) 1994 – 95 5.0 9.2 7.0 1995 – 96 – 0.9 11.8 10.3 1996 – 97 9.6 6.0 7.1 1997 – 98 – 1.9 5.9 9.0 1998 – 99 7.2 4.0 8.3 1999 – 2000 0.8 6.9 8.2 8.3 1999 – 2000 0.8 6.9 8.2 Represent the data as multiple time series graphs.

presentation of data ncert solutions

What is meant by presentation of data?

Presentation of data means exhibition of the data in such a clear and attractive manner that these are easily understood and analysed.

What is a table?

A table is a systematic organisation of data in columns and rows.

What are the kinds of tables?

1. General purpose table. 2. Special purpose table. 3. Original table. 4. Derived table. 5. Simple or one way table. 6. Complex table.

What is simple table?

A simple table is that which shows only one characteristic of the data.

What is tabulation?

Tabulation refers to the method or process of presenting data in the form of rows and columns.

What is a complex table?

A complex table is one which shows more than one characteristics of the data.

What are the two principal components of a table?

1. Table Number, 2. Title and Head Note.

What is meant by bar diagram?

Bar diagrams are those diagrams in which data are presented in the form of bars or rectangles.

What is a multiple bar diagram?

Multiple bar diagrams are those diagrams which show two or more sets of data simultaneously.

What is a circular or pie diagram?

Pie diagram is a circle divided into various segments showing percent values of a series.

What does subdivided bar diagram show?

Sub-divided bar diagrams show total values as well as part values of a set of data.

What are the frequency diagrams?

Frequency diagrams those diagram which present frequen distribution diagramatically.

What is a frequency curve?

A frequency curve is a curve which is plotted by joining the mid-points of all tops of a histogram by free hand smoothed curves.

What is meant by an Ogive?

Ogive or Cumulative frequency curve is the curve which is constructed by plotting frequency data on the graph paper, in the form of smooth curve.

How is frequency polygon drawn?

Frequency polygon is drawn by joining the mid-points of all tops of a histogram using a foot-rule (to make a straight line).

What are time series graphs? Or What are arithmetic line graphs?

Graphs showing arithmetic values of variables are called time-series graphs.

How many types are there of time series graphs?

(i) One variable graph. (ii) Two or more than two variable graphs.

State two merits of graphic presentation of time series data.

Two merits of graphic presentation are : (i) Simple and understandable information, (ii) Lasting impact.

State two limitations of graphic presentation of time series data.

1. Limited use and 2. Misuse

Give the types of classification.

These are types of classification. (i) Quantitative i.e. in terms of magnitudes.

(ii) Chronological (or Temporal) i.e. on the basis of time.

(iii) Geographical (or Spatial) i.e. areawise.

(iv) Quantitative i.e. according to some attribute.

What is quantitative classification?

If the data are classified on the basis of same characteristics capable of quantitative measurement such as height, age, income, expenditure, marks scored by students in class etc., the classification is known as quantitative classification.

Define chronological classification.

When the data are classified on the basis of time, it is known as chronological classification. Here, one variable is time.

Explain geographical classification.

When the data is classified on the basis of place, it is known as geographical classification.

What is qualitative classification?

If the data are classified on the basis of some attribute or quality (descriptive characteristic) such as sex, literacy, beauty, honesty, intelligence, education, etc., the classification is known as qualitative classification.

Define two fold classification?

When on the basis of presence and absence of an attribute the data are classified into two classes, one possessing that attribute and the other not possessing that attribute it is called two-fold classification.

Define variable.

A quantity which can assume a range of numerical values is called a variable and each value within the range is called variate or observation.

Distinguish between classification and tabulation.

Classification forms a basis for tabulation and is done prior to tabulation. Tabulation is systematic arrangement of data in column and rows.

Give two advantages of tabulation.

That the advantages of tabulation are as under:

1. The tabulated data can be more easily understood.

2. The data becomes attractive and leaves a lasting impression.

Define diagrams and graphs.

Diagrams and graphs are pictorial representation of statistical data. They are also called diagrammatic representation of data.

Give two advantages of diagrammatic representation of data.

Advantages of diagrammatic representation of data:

1. Diagrams give a very clear picture of data.

2. Comparison between different samples with the regard to certain statistical measures like mean, median and mode can be easily made without using any statistical technique.

Give two limitations of diagrammatic presentation.

Limitations of diagrammatic representation:

1. A limited set of data can be presented in the form of a diagram.

2. Diagram do not present the small differences properly.

Give the types of diagrams.

presentation of data ncert solutions

Why bar diagrams are one dimensional?

Bar diagrams are one dimensional because their height represents the size of the figure but not the width.

Define simple bar diagram.

In simple bar diagram equal width is given to all the lines to make them look as rectangles e.g. students, prices, etc.

Give limitations of bar diagrams.

Limitations of bar diagram:

1. They can be used only when the given figures do not vary much and the proportion between the figure is small.

2. This can be used to show only one variable.

Define component or sub-divided diagram.

Component or sub-divided diagram are useful for presenting several items of a variable graphically and enable us to make comparative study of different parts among themselves and study the relationship between each part and the whole.

What are multiple bar diagrams?

Multiple bar diagrams are used when two or more sets of inter-related variables are to be presented graphically for comparison. A set of simple adjacent bars is drawn. Comparisons can be made either between two or more variable or magnitudes of one variables in two or more aspects.

Explain percentage bar diagram.

Sub-divided or component bar diagram presented graphically on precentage basis give percentage bar diagram.

Explain Pie-diagram.

Pie diagram is a circle divided into component sectors with areas proportional to the size of the corresponding component. They are prepared on percentage basis. This diagram is used to compare the relationship between various components. For drawing the Pie-diagram, percentage of each sector is converted into degrees keeping in view that the whole circle covers 360°.

Explain histogram.

An histogram is a graphical representation of a frequency distribution of a continuous series. It represents the class frequencies in a frequency distribution by verticle rectangles meeting each other from left to right. Histograms are two dimensional figures in which both length and breadth of the rectangles are considered.

Explain frequency curve.

A frequency curve for a grouped frequency distribution is a smooth freehand curve drawn by joining the mid-points of the upper horizontal sides of the histogram drawn over that frequency distribution.

What is the basis of classification in the following table : Population of a country Year Population in Crores 1998 15 1999 20 2000 22 2001 23 2002 25

The basis of classification is time.

Give an example of qualitative classification.

Example of qualitative classification :

Literacy in Bihar (in percentage)

Draw less than cumulative frequency curve with the help of following frequency distribution : Marks in Maths No. of Students 0 – 20 6 20 – 40 5 40 – 60 33 60 – 80 14 80 – 100 6 Total 64

presentation of data ncert solutions

We have to draw a histogram with the help of following data. What amendment will be make in class intervals for doing so? Weight (in kg.) Class interval No. of Students frequencies (f) 10 – 19 4 20 – 29 12 30–39 15 40 – 49 20 50 – 59 10 60 – 69 5

Here the series is not continuous. Hence, we have to make it continuous for doing so, we will divide the difference of class boundaries by 2. The resultant figure i.e. 5 by be deducted from the lower limit and added in the upper limit. Hence:

Give an example of quantitative classification.

Example of quantitative classification :

Prepare a table showing spatial classification.

Example of spatial classification:

Exports by India to other countries in a particular year

Give an example of the spatial classification.

Example of spatial classfication:

Exports by India to other countries

Give an example of temporal classification.

xample of temporal classification:

The sale proceeds of a tea shop during the Year 1995 - 2000

Give purposes of classification.

Following are the objectives (purposes) of classification:

1. To condense the mass of data in such a manner that similarities and dissimilarities are reedily apprehended and relationships studies.

2. To facilitate comparisons.

3. To have a bird’s eye-view of the significant feature of the data.

4. To englight important information while giving less prominence to insignificant items.

5. To utilise the data for tabulation and further statistical analysis.

6. To eliminate unnecessary details contained in the raw data.

7. To present the complex, scattered in a concise, logical and understable form.

Explain the objectives of tabulation.

Following are the objectives of tabulation:

1. In tabulation the data are presented systematically in columns and rows in a concise form. Thus, data becomes more meaningful and lot of time is saved in its study and understanding.

2. When the data are arranged in tables with titles and table number, they can be easily identified and made use of a source reference for future studies.

3. Tabulation of data shows the trend of the information under study and depicts the patterns with in the figures which cannot be understood in a descriptive form of presentation.

4. It is only after tabulation that data becomes fit for statistical processing.

Explain the advantages of diagrammatic representation.

ollowing are the advantages of diagrammatic representation :

2. Comparison between different samples with the regard to certain statistical measures like mean, median, mode etc. can be easily made without using any statistical technique.

3. Diagrams can be used universally at any place and at any time.

4. Diagrams can be used for numerical type of statistical analysis.

5. It saves time and energy and it is economical.

6. The data can be remembered easily.

Explain limitations of diagrammatic representation.

1. Diagrammatic presentation of data is just an approximation of the actual behaviour of the variables.

2. Only a limited set of data can be presented in the form of a diagram.

3. Diagrammatic presentation of data is a time- consuming process.

4. It is not very easy to arrive at final conclusion after seeing the diagram.

5. Diagrams do not show small differences properly.

6. Diagrams can be analysed mentally and are not amendable to further statistical treatment at the tabular presentation. Diagrams are drawn on false baseline.

7. Diagrams can be used only for comparative study.

8. Diagrams are capable of being misused easily.

Present the following information in a suitable tabular form: In 1960, out of total of 1750 workers of a factory, 1200 were members of a trade union. The number of women employed was 200, of which 175 did not belong to a trade union. In 1965, the number of union workers increased to 1580 out of which 1290 were men, on the other hand, the number of non-union workers fell down to 208 of which 180 were men. In 1970, there were 1300 employees who belonged to a trade union and 50 who did not belong to a trade union. Of all the employees in 1970, 300 were women of who only 8 did not belong to trade union.

Sexwise distribution of Union and Non-union Members for 1960, 1965, 1970

Draw a simple bar diagram to show the following figures relating to manufacturing of fans. Years 1994 1995 1996 1997 1998 No. of fans 1200 1700 1900 2800 2100

presentation of data ncert solutions

The following table gives the result of B.Com. students of a college for four years. Year No. of Students Division First Second Third 1993 10 30 50 1994 12 45 70 1995 14 50 60 1996 11 40 75 Represent the above data by a suitable diagram.

presentation of data ncert solutions

Show the following data by a suitable diagram. (Million Rs.) Year Exports Imports Balance of trade 1993 95 115 – 17 1994 110 140 – 30 1995 115 96 + 19 1996 120 100 + 20

presentation of data ncert solutions

Give steps in the preparation of Pie diagram.

Following are the steps involved in the preparation of Pie diagram:

1. Convert each component as a percentage of the total.

2. Multiply the percentage by 360/100 = 3.6 to convert into degrees.

3. Starting with the twelve o’clock position on the circle (clockwise) draw the largest component circle.

4. Draw other components in clockwise succession in descending order of magnitude except for each-all components like all others and miscellaneous which are shown last.

5. Use different columns or shades to distinguish between different components.

6. Explain briefly the different components either within the components in the figure or outside by arrows.

Show the following data by means of a suitable diagram. Production of Tea, Cocoa, Coffee Tea 3260 tons Cocos 1850 tons Coffee 900 tons Total 6010 tons

presentation of data ncert solutions

Prepare a histogram for the following data (equal intervals): Wages 325 – 350 350 – 375 375 – 400 400 – 425 425 – 450 Frequency 30 45 75 60 35

presentation of data ncert solutions

Give the difference between frequency polygon and histogram.

Difference between frequency polygon and histogram:

1. Frequency polygon is an improvement over histogram because it provides a continuous curve indicating the causes of rise and fall in the data. On the other hand, frequency polygon is an approximate curve, but still it is more usefui as compared to histogram.

2. In the frequency polygon, it is assumed that the frequency distribution in a particular class-width whereas histogram may be used to represent frequency distribution with equal as well as with unequal class width.

3. In case of frequency polygon, it is assumed that all frequencies in a particular class are concerned at the mid point of that class whereas in case of histogram, it is supposed that they are evenly spread over the class interval.

How histograms can be conveniently converted into small frequencies when class intervals are equal?

When class intervals are equal i.e. when all rectangles have the same base, area can conveniently be represented by the frequency of any interval for purposes of comparison. When bases vary in their width, the heights of rectangles are to be adjusted to yield comparable measurements. In such a situation frequency density (class frequency divided by width of the class interval) instead of absolute frequency.

Draw a histogram and a frequency polygon for the following data: Weight nearest to the Pounds 102 – 113 113 – 124 124 – 135 135 – 146 146 – 157 157 – 168 168 – 179 No. of Men 1 1 4 14 12 5 3

presentation of data ncert solutions

Differentiate between percentage subdivided bar diagram and subdivided bar diagram.

Distinction between percentage subdivided bar diagram and subdivided bar diagram are as follow :

Give the rules for constructing diagrams.

ollowing are the rules of constructing diagrams:

1. Every diagram should be suitably and briefly titled. It can be mentioned either at the top of the diagram or below it.

2. It should suit to the size of the paper.

3. It should be neat and attractive.

4. It should be clearly indexed.

5. Diagrams should contain footnotes and a proper spacing between the figure.

6. The details in the diagrams should be self explanatory.

Convert the following frequency into relevant frequency to draw a histogram. Class Intervals Frequency 0 – 10 10 10 – 20 2 20 – 40 30 40 – 70 15

Write down the steps involved in the construction of percentage sub-divided bar diagram..

Following are the steps involved in the preparation of percentage sub-divided bar diagram:

1. Convert the data into percentage form by dividing 100.

2. Cumulative frequency is obtained.

3. Separate bars are prepared for different years. But all the bars have same length or of 100.

4. Then as per cumulative frequency bars are sub-divided into different categories shown by different marks expressed in percentages.

Differentiate between General Purpose Table and Special Purpose Table.

General Purpose Table has no special importance as it is used by different persons in a different manner. Generally, it is given on the back of reports or circulars etc.

Special Purpose Table are given for specific purposes. They serve the purpose of that particular group for which they have been prepared. These are brief in nature and are targeted towards a particular objective.

Draw histogram with the help of the data given below and determine mode. Daily Wages (in Rs.) No. of Wage earners 45 – 49 2 50 – 54 3 55 – 59 5 60 – 64 3 65 – 69 6 70 – 74 7 75 – 79 12 80 – 84 17 85 – 89 9 90 – 94 7 95–99 6 100 – 104 4 105 – 109 2 110 – 114 3 115 – 119 3

Before making the histogram, we have to convert the class intervals :

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Value of exports and imports of India are given in the following table. Draw arithmetic line graph for time series data given in the table. Value of Exports and Imports of India in 100 crore Year Export Import 1977 – 78 54 60 1978 – 79 57 68 1979 – 80 64 91 1980 – 81 67 125 1981 – 82 88 143 1982 – 83 98 158 1983 – 84 117 171 1984–85 119 197 1985 – 86 125 201 1986 – 87 157 222 1987 – 88 202 282 1988 – 89 211 353 1989 – 90 326 432 1990 – 91 440 479 1991 – 92 532 634 1992 – 93 698 731 1993 – 94 827 900 1994 – 95 1064 1227 Year Export Import 1995 – 96 1186 1369 1996 – 97 1301 1542 1997 – 98 1416 1761

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Give an example of discrete frequency distribution.

The formation of discrete frequency distribution is quite simple. The number of times a particular value is repeated is noted down and mentioned against that values instead of writing that value repeatedly, e.g. in the distribution 3, 4, 6, 6, 8, 8, 8, 8, 1, 1, 1, we can write:

How classes can be formed while presenting the data?

Classes can be formed in two ways :

(i) Exclusive type, (ii) Inclusive type.

(i) Exclusive Type : When the class intervals are so fixed that the upper limit of one class is the lower limit of the new class, it is known as exclusive method of clasfication.

For example:

In this method, higher value of the variable in the class is not included in that class. i.e.

(ii) Inclusive Type : In this method, the students getting say 39% marks will be included in the class 30 - 39 itself i.e.

The following table gives the result of M.Sc. students of a college for four years. Year Number of Students First Second Third 1993 10 30 50 1994 12 45 70 1995 14 50 60 1996 11 40 75 Represent the above data by a suitable diagram.

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The following table gives the number of students sex-wise studying in Degree Arts College. Class Number of Students Boys Girls Total Prep. 150 75 225 T.D.C. Part I 120 65 185 T.D.C. Part II 80 50 130 T.D.C. Part III 60 40 100 Represent the above data by a suitable diagram.

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Depict the following data by a suitable diagram: Year Export Import Balance ofTrade (Export-Import) 1993 95 115 –17 1994 110 140 –30 1995 115 96 + 19 1996 120 100 + 20

presentation of data ncert solutions

The table below gives the ages of drivers of cars involved in total accidents during a certain year. Draw a pie-chart to represent the data. Age of drivers Percent of total Under 20 15 20 – 40 60 40 – 60 20 Over 60 5 Total 100

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The following frequency distribution gives the marks of 92 students: Marks No. of Students 4 – 8 3 8 – 12 9 12 – 16 15 16 – 20 18 20 – 28 20 28 – 40 15 40 – 56 12 Draw a histogram with the above data.

This is a case of unequal class intervals.

presentation of data ncert solutions

Differentiate between ‘less than’ and ‘more than’ ogives.

Difference between ‘less than’ and ‘more than’ ogives:

What does the total area under a frequency curve represent?

The total area under a frequency curve represents the total frequencies.

How is a frequency polygon different from a frequency curve?

Both frequency polygon and frequency curve are drawn by joining the mid-points of all tops of a histogram. But in case of frequency polygon, the points are joined using a foot rule to make a straight line, but in case of frequency curve, the points are joined using free hand.

When does a histogram becomes a frequency polygon?

A histogram becomes a frequency polygon when we draw a line joining mid-points of the tops of all rectangles in a histogram by using a first rule.

Which are cumulated-frequencies or values?

Frequencies are comulated.

Which are arrayed-values or frequencies?

Values are arrayed.

Below is given inclusive series. Convert it into exclusive series. Also write down the method of conversion of inclusive series into exclusive series. Weekly wages No. of workers 40 – 49 7 50 – 59 17 60 – 69 25

Conversion of Inclusive series into Exclusive series:

Method of conversion of inclusive series into exclusive series :

1. First find the difference between the upper limit of a class interval and the lower limit of the next class interval.

2. Half the difference is added to the upper limit of each class interval and remaining half is deducted from the lower limit of each class-interval. In the question the upper limit of the first class interval is 49 and the lower limit of the second class interval is 50. The difference between them is one and its half is 0.5, 0.5 will be subtracted from 40, and 0.5 will be added to 49. Hence, first class interval will be 39.5 – 49.5.

Write down the recognition of cumulative series.

The series will be cumulative, if the words- less than, more than, above, below, over, under, upto, exceeding, not exceeding etc, are given before all limits of the class-intervals.

You are given a pie chart showing amount spent on expenditure. Find out the percentage expenditure spent on food and clothing.

presentation of data ncert solutions

2. Expenditure on clothing

presentation of data ncert solutions

How is histogram constructed when class-intervals are unequal?

For constructing histogram of unequal class-intervals, first we note a class of the smallest intervals. Other classes are noted in the increasing order of their intervals. If the size of one class-interval is twice the smallest size in the series, frequency of that class is divided by two. Suppose the class with the smallest interval is 5 – 10 and the class with the largest interval is 10 – 20, the frequency of which is 12. Here the class interval of the bigger class is 10 which is twice as much as the size of the class-interval of the smallest class i.e. 5. The bigger class interval is divided into two parts 10 – 15 and 15 – 20 and accordingly the frequency of the bigger class, 12 would be divided by 2 i.e. 12+ 6. In this way there will be following adjustment.

Why are foot-notes used in the table?

Foot-notes are used to explain the complex nature of a table.

Where should be the sources be placed in the table?

At the end of the table on the right side.

Which graph can determine the value of median?

Ogive curve.

Write down the formula for calculating adjustment factor for any class.

Adjustment factor for any class =  Class interval of the concerned class                                                          Lower class interval

The class interval of the concerned class is 10 – 20 and the class interval of the smallest class is 5 – 10. Calculate adjustment factor.

Adjustment factor = 10/5 = 2

Name the types of classification used in tabular presentation.

Tabular presentation is based on four fold classification of data viz (i) qualitative, (ii) quantitative, (iii) temporal and (iv) spatial.

What does the title of a table explain?

The title of a table gives a brief explanation of the contents of a table.

What should be the features of title of a table?

Features of a title : 1. The title should be brief. 2. It should be clear. 3. It should be in carefully selected words.

Where should the title of a table be placed?

The title of a table should be placed in a prominent place usually below the table number.

Which is the principlal part of a table? Or Which is the most important part of a table?

Body of the table is the most important part of table. It contains the real data.

What is a mani-fold table?

A mani-fold table is that table which shows more than three characteristics of the data.

Which diagrams are used to present the statistical data?

Following diagrams are used to present the statistical data:

(i) Bar diagram, (ii) Histogram, (iii) Polygon, (iv) Ogive etc.

Give any two points of difference between tables and diagrams.

Difference between tables and diagrams:

Write down the advantages of tabular presentation of data.

Advantages of tabular presentation of data:

1. Tabulated data can be easily understand and interpreted.

2. Tabulation facilitates comparison as data are presented in compact and organised form.

3. It saves space and time.

4. Tabulated data can be presented in the form of diagrams and graphs.

Histogram is prepared in: Individual series   Discrete series Continuous series   Neither of the above

Continuous series

While preparing time series graphs, we show on the x-axis   Income Time   Expenses All the above

Following point(s) should be taken into consideration in the graphic presentation of statistical data:   scale false base line   appropriate title all the above.

All the above

Which table shows the data arranged in ascending order ? Table A Rs. 60 Rs. 61 Rs. 56 Rs. 57 Rs. 59 Table B Rs. 57 Rs. 58 Rs. 59 Rs. 60 Rs. 61 Table C Rs. 61 Rs. 60 Rs. 59 Rs. 58 Rs. 57 Table D Rs. 60 Rs. 61 Rs. 56 Rs. 57 Rs. 59

The class interval of 64 – 66 is : 64 65 66 2, the mid-point of 64 – 66 is : 64 65 66 2, lower limit of the class 64 – 66 is: 64 66 2 65, ogive can be obtained on the graph paper by: one method two methods three methods four methods.

Two methods

Following curve is: Normal curve Reverse j-shaped curve   Mixed curve   Positively skewed curve

Mixed curve

We can calculate the following graphically with the help of ‘less than’ and ‘more tljan’ ogive. mean median   mode mean deviation

From the diagram, we come to know that 20 is : mean mode   median standard deviation, mock test series.

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Presentation of Data NCERT Solutions | Economics Class 11 - Commerce PDF Download

Page No 56:

Question 1: Bar diagram is a (i) one-dimensional diagram (ii) two-dimensional diagram (iii) diagram with no dimension (iv) none of the above Answer:  Bar diagrams are One-dimensional diagrams. These are represented on a plane of two axis and depicts the relationship between the two variables (plotted on the either axis) in form of rectangular bars. Question 2:Data represented through a histogram can help in finding graphically the (i) mean (ii) mode (iii) median (iv) all the above Answer:  Graphically mode can be determined by presenting the data in the form of Histogram. The highest Histogram indicates the modal class. The intersection point of the lines diagonally joining the two top corners of the modal rectangles to the corners of the adjacent Histograms indicates the Modal Value. Question 3: Ogives can be helpful in locating graphically the (i) mode (ii) mean (iii) median (iv) none of the above Answer:  Graphically, Median can be determined by the intersection point of Less than Ogive and More than Ogive. The value of x-axis corresponding to the intersection point indicates the median. Question 4: Data represented through arithmetic line graph help in understanding (i) long-term trend (ii) cyclicity in data (iii) seasonality in data (iv) all the above Answer:  Data represented through arithmetic line graph (or time series graph) helps in understanding the long-term trend and periodicity. Question 5: Width of bars in a bar diagram need not be equal (True/False). Answer: The above statement is false as all bars in a bar diagram need to be of equal width. Moreover, all bars are at equal distance from each other. Question 6: Width of rectangles in a histogram should essentially be equal (True/False). Answer: The above statement is false, as the width of all rectangles in a histogram may or may not be equal. The width of a rectangle depends on the width of its corresponding class interval. Question 7: Histogram can only be formed with continuous classification of data (True/False). Answer: Yes, a Histogram can only be formed with the continuous classification of data. The frequency distribution of a continuous series is graphically presented in form of a Histogram. If the given data is not continuous, then it is to be converted into exclusive series before presenting the data in the form of Histogram. Histograms can never be prepared for discrete series.

Page No 57:

Presentation of Data NCERT Solutions | Economics Class 11 - Commerce

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