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Mean Median Mode Range Worksheets and Help

Welcome to the Math Salamanders Mean Median Mode Range Worksheets. Here you will find a wide range of free printable Worksheets, which will help your child learn how to find the mean, median, mode and range of a set of data points.

These worksheets are aimed at students in 5th and 6th grade.

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Mean Median Mode Range Quicklinks

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Mean Median Mode Range Worksheets

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  • More related Math resources

What is the Mean?

The mean is the average of a set of numbers.

It is found by adding up the set of numbers and then dividing the total by the number of data points in the set.

How to find the mean

Step 1) Add up all the numbers in the set.

Step 2) Divide the total by the total number of data points in the set.

Example 1) Find the mean of 5, 7, 8 and 4

Step 1) Add up the numbers to give a total of 5+7+8+4=24

Step 2) Divide the total by the number of data points. 24 ÷ 4 = 6

Answer: the mean is 6.

Example 2) Find the mean of 8, 2, 5, 7 and 13

Step 1) Add up the numbers to give a total of 8+2+5+7+13=35

Step 2) Divide by the number of data points. 35 ÷ 5 = 7

Answer: the mean is 7.

What is the Median?

The median is the midpoint (or middle value) of a set of numbers.

It is found by ordering the set of numbers and then finding the middle value in the set.

How to find the median

Step 1) Order the numbers in the set from smallest to largest.

Step 2) Find the middle number.

- If there is an odd number of values in the set, then the median is the middle value.

- If there is an even number of values in the set, then the median is the average of the two middle values.

Example 1) Find the median of 5, 7, 8, 2 and 4

Step 1) Put the numbers in order: 2, 4, 5, 7, 8

Step 2) There is an odd number of values in the set so the median is the middle value which is 5.

Answer: the median is 5.

Example 2) Find the median of 23, 27, 16, 31

Step 1) Put the numbers in order: 16, 23, 27, 31

Step 2) There is an even number of values in the set, so the median is the average of the middle two values.

(23+27) ÷ 2 = 25

Answer: the mean is 25

Example 3) Find the median of 7, -4, 9, -7, -2, 5

Step 1) Order the numbers: -7, -4, -2, 5, 7, 9

To get the average, simply add the two values together and divide by 2:

(-2 + 5) ÷ 2 = 1.5

Answer: the mean is 1.5

What is the Mode?

The mode is the most common (or the data point that appears most often) in a set of data.

It can be found by putting the data into an ordered list and seeing which data point occurs most often.

How to find the mode

Step 1) Put the data into an ordered list.

Step 2) Check that you have got the same number of data points.

Step 3) The mode is the data point which is the most common.

Finding the Mode Examples

Example 1) Find the mode of 3, 6, 4, 3, 2, 4, 7, 8, 6, 3, 9

This gives us: 2, 3, 3, 3, 4, 4, 6, 6, 7, 8, 9

Step 2) Check the number of data points in both lists is the same.

Both lists have 11 data points.

Step 3) The mode is the number which occurs most often.

Answer: the mode is 3.

Example 2) Find the mode of 0.6, 0.3, 0.4, 0.2, 0.4, 0.7, 0.6, 0.1, 0.4, 0.9

This gives us: 0.1, 0.2, 0.3, 0.4, 0.4, 0.4, 0.6, 0.6, 0.7, 0.9

Both lists have 10 data points.

Answer: the mode is 0.4.

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What is the Range?

The range is the gap between the smallest and largest data point.

It is found by putting the data into an ordered list and find the difference between the largest and smallest amount.

How to find the range

Step 3) The range is the difference between the largest and smallest data point.

To find the range simply subtract the smallest number from the largest number.

Finding the Range Examples

Example 1) Find the range of 14, 21, 9, 32, 27, 15, 12, 30

This gives us: 9, 12, 14, 15, 21, 27, 30, 32

Both lists have 8 data points.

Step 3) The range is the difference or gap between the largest and smallest numbers.

Answer: the range is 32-9=23.

Example 2) Find the range of 6, 2, -7, 2, -5, 11, 3, -4, 0, 9

This gives us: -7, -5, -4, 0, 2, 2, 3, 6, 9, 11

Answer: the range is 11-(-7)=18.

These printable mean median mode range worksheets have been carefully graded to ensure a progression in the level of difficulty.

Sheets 1, 2 and 3 are designed for 5th graders involve ordering and calculating using positive integers and decimals.

Sheets 4, 5 and 6 are designed for 6th graders and involve ordering and calculating with positive and negative numbers and decimals.

The first sheet involve finding the mean, median, mode and range of some positive whole numbers.

The 2nd sheet involves the use of decimals to 1dp.

The 3rd sheet is similar to the 2nd sheet but has many more data points.

The 4th sheet involves decimals and negative numbers.

The 5th and 6th sheets are similar to the 4th sheets but with increased number of data points.

  • Mean Median Mode and Range Sheet 1
  • PDF version
  • Median Mean Mode and Range Sheet 2
  • Median Mean Mode and Range Sheet 3
  • Median Mean Mode and Range Sheet 4
  • Median Mean Mode and Range Sheet 5
  • Median Mean Mode and Range Sheet 6

Mean Median Mode Range Problems

These printable mean median mode range problem sheets will help your child to use and apply their skills to solve problems.

The first problem sheet is more suitable for 5th grade and the second sheet is aimed at 6th graders.

  • Median Mean Mode and Range Problems 1
  • Median Mean Mode and Range Problems 2

Mean Median Mode Range Walkthrough Video

This short video walkthrough shows the problems from our Median Mean Mode and Range Problems Sheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

  • Mean Worksheets

The sheets in this section will help you to find the mean of a range of numbers, including negative numbers and decimals.

There are a range of sheets involving finding the mean, and also finding a missing data point when the mean is given.

  • Median Worksheets

The sheets in this section will help you to find the median of a range of numbers, including negative numbers and decimals.

On some of the easier sheets, only odd numbers of data points have been used.

On the harder sheets, both odd and even numbers of data points have been included.

  • Mode and Range Worksheets

The sheets in this section will help you to find the mode and range of a set of numbers, including negative numbers and decimals.

There are easier sheets involving fewer data points, and harder ones with more data points.

The sheets in this section will help you to solve problems involving bar graphs and picture graphs.

There are a range of sheet involving reading and interpreting graphs as well as drawing your own graphs.

  • Box Plot Worksheets

Here are our selection of box plot worksheets to help you practice creating and interpreting box plots.

Mean, Median, Mode and Range Online Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at finding and using the mean, median, mode and range of a set of data.

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Mean Median Mode Questions

Mean, Median and Mode are three measures of central tendency, and these are the important topics in statistics. In this article, you will get mean, median, and mode questions and answers, along with some practice questions. These questions and answers will help you to practise for the board exams. Also, these questions cover various types of problems asked on mean, median and mode for Classes 9 and 10.

What is the mean formula?

As we know, the mean is the average of the given data set. This can be calculated using the formula given below.

Mean for ungrouped data = Sum of observations/Number of observations

Click here to get more information about mean .

What is the formula for the median?

The median is the middlemost data value of an ordered data set. This can be estimated using the formulas given below.

When n is odd:

Median = (n + 1)/2th observation

When n is even:

Median = [(n/2)th observation + {(n/2)+1}th observation]/2

Learn more about median here.

What is the mode?

Mode is the most frequently occurring value in the data set.

Get more information about mode here.

Mean Median Mode Questions and Answers

1. Find the mean of the first 10 odd integers.

First 10 odd integers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Mean = Sum of the first 10 odd integers/Number of such integers

= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)/10

Therefore, the mean of the first 10 odd integers is 10.

2. What is the median of the following data set?

32, 6, 21, 10, 8, 11, 12, 36, 17, 16, 15, 18, 40, 24, 21, 23, 24, 24, 29, 16, 32, 31, 10, 30, 35, 32, 18, 39, 12, 20

The ascending order of the given data set is:

6, 8, 10, 10, 11, 12, 12, 15, 16, 16, 17, 18, 18, 20, 21, 21, 23, 24, 24, 24, 29, 30, 31, 32, 32, 32, 35, 36, 39, 40

Number of values in the data set = n = 30

n/2 = 30/2 = 15

15th data value = 21

(n/2) +1 = 16

16th data value = 21

= (15th data value + 16th data value)/2

= (21 + 21)/2

3. Identify the mode for the following data set:

21, 19, 62, 21, 66, 28, 66, 48, 79, 59, 28, 62, 63, 63, 48, 66, 59, 66, 94, 79, 19 94

Let us write the given data set in ascending order as follows:

19, 19, 21, 21, 28, 28, 48, 48, 59, 59, 62, 62, 63, 63, 66, 66, 66, 66, 79, 79, 94, 94

Here, we can observe that the number 66 occurred the maximum number of times.

Thus, the mode of the given data set is 66.

4. Consider the following frequency distribution. Calculate the mean weight of students.

The given distribution has discontinuous class intervals, so we need to make them continuous.

Here, ∑f i = 40 and ∑f i d i = 35

By Assumed mean method,

Mean = a + (∑f i d i /∑f i )

= 43 + (35/40)

= 43 + 0.875

Therefore, the mean weight of the students is 43.875 kg.

5. Find the mean for the following distribution.

Mean = ∑f i x i /∑f i

6. Calculate the median marks of students from the following distribution.

N/2 = 90/2 = 45

Cumulative frequency greater and nearer to 45 is 47, which lies in the interval 40 – 50

Median class is 40 – 50.

Lower limit of the median class = l = 40

Class size = h = 10

Frequency of the median class = f = 20

Cumulative frequency of the class preceding the median class = cf = 27

As we know,

Median = 40 + [(45 – 27)/20] × 10

= 40 + (18/2)

Hence, the median marks of the students = 49.

7. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Find the mode of the above distribution.

From the given,

Modal class = 4000 – 5000

Lower limit of the modal class = l = 4000

Class width (h) = 1000

Frequency of the modal class = f 1 = 18,

Frequency of the class preceding the modal class = f 0 = 4

Frequency of the class succeeding the modal class = f 2 = 9

Mode = l + [(f 1 – f 0 )/ (2f 1 – f 0 – f 2 )] × h

Mode = 4000 + [(18 – 4)/(36 – 4 – 9)] × 1000

= 4000 + (14000/23)

= 4000 + 608.695

= 4608.7 (approximately)

Thus, the mode of the given data is 4608.7 runs

8. If the median of a distribution given below is 28.5, then find the value of x and y.

N/2 = 60/2 = 30

Median of the given data = 28.5

Median class is 20 – 30 with a cumulative frequency = 25 + x.

Lower limit of median class = l = 20

Cumulative frequency of the class preceding the median class = cf = 5 + x

28.5 = 20 + [(30 − 5 − x)/ 20] × 10

28.5 – 20 = (25 – x)/2

8.5 × 2 = 25 – x

17 = 25 – x

x = 25 – 17

Therefore, x = 8

60 = 5 + 20 + 15 + 5 + x + y

60 = 5 + 20 + 15 + 5 + 8 + y

y = 60 – 53

Therefore, the value of x = 8 and y = 7.

9. For a moderately skewed distribution, the mean and median are respectively 26.8 and 27.9. What is the mode of the distribution?

Mean = 26.8

Median = 27.9

Using the relationship between mean, median and mode,

Mode = 3 Median – 2 Mean

= 3 × 27.9 – 2 × 26.8

= 83.7 – 53.6

Therefore, the mode of the distribution is 30.1.

10. If the mean of the given frequency distribution is 35, then find the missing frequency y. Also, calculate the median and mode for the distribution.

Given that the mean of the distribution is 35.

So, (430 + 45y)/(14 + y) = 35

430 + 45y = (14 + y)35

430 + 45y = 490 + 35y

45y – 35y = 490 – 430

Thus, the missing frequency is 6.

Now, we can calculate the mode as follows:

Mode = 30 + [(7 – 4)/(14 – 4 – 6)] × 10

= 30 + (30/4)

Now, using the formula Mode = 3Median – 2 Mean, we can get the value of median.

37.5 = 3 Median – 2 (35)

3 Median = 37.5 + 70

Median = 107.7/3

Recommended Videos

mean median mode and range problem solving questions

Practice Questions on Mean Median Mode

1. Find the mean, median and mode of the following data:

23, 18, 24, 23, 31, 37, 28, 30, 25, 40, 35, 35, 27, 25

2. The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer, and details are tabulated as given below:

Find the mean mileage.

The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?

3. Find the median of the following frequency distribution.

4. Calculate the mode for the following distribution.

5. Suppose the mean and median of distribution are 10.14 and 8, respectively. Find the mode of the distribution using the empirical relationship between mean, median and mode.

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Mean, Median, Mode and Range

The mean, the median and the mode are three different measures of average which we can use. The range is a measure of how spread out data is.

The mode is the value that appears most often.

The median is the middle number (when the numbers are in order).

To calculate the mean add up all the numbers and then divide by how many numbers there are.

The range is the difference between the biggest number and the smallest number.

Example 1: Here are a list of 7 numbers: 7   4   7   9   5   1   2 Find: a) The mode b) The median c) The mean d) The range

a) The mode is the most common number The only number that appears more than once is 7 The mode is 7

b) The median is the middle number (but only when the numbers are in order) We have to put the numbers in order: 1   2   4   5   7   7   9 We can now find the middle number:

The median is 5

c) To find the mean we need to add up all the numbers then divide by how many numbers there are:

1 + 2 + 4 + 5 + 7 + 7 + 9 ⁄ 7 = 35 ⁄ 7 = 5

The mean is 5

d) To find the range we take the smallest number away from the biggest number 9 - 1 = 8 The range is 8

Example 2: Here are a list of 8 numbers: 6   6   13   5   11   11   11   9 Find: a) The mode b) The median c) The mean d) The range

a) The mode is the most common number 11 appears three times, that is more than any other number The mode is 11

b) To find the median (the middle number) we need to put the numbers in order: 5   6   6   9   11  11  11  13

We can see that there is not one middle number, we have 9 and 11 in the middle. When this happens the median is half way between the two middle numbers, the middle of 9 and 11 is 10. We can work this out by adding 9 and 11 and then dividing by 2.

9 + 11 ⁄ 2 = 10 The median is 10

5 + 6 + 6 + 9 + 11 + 11 + 11 + 13 ⁄ 8 = 72 ⁄ 8 = 9

The mean is 9

d) To find the range we take the smallest number away from the biggest number 13 - 5 = 8 The range is 8

Calculate the mode, the median, the mean and the range:

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Always on the lookout for fun math games and activities in the classroom? Try our ready-to-go printable packs for students to complete independently or with a partner!

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Averages and range

Mean median mode

Mean, Median, Mode

Here you will learn about the measures of central tendency, which is the mean, median and mode of data sets, including what they are and how to find them.

Students first learn about measures of central tendency in the 6 th grade and expand this knowledge as they move through middle school and high school statistics.

What is mean median mode?

The mean, median and mode are different measures of center of a numerical data set. They are a way of summarizing a data set with a single number.

The mean is the average of a numerical data set.

To calculate the mean, find the total of the values and divide the total by the number of values .

The “number of values” is sometimes referred to as the “number of numbers”.

Mean, median, mode 1 US

Let’s find the mean of this data set.

Mean, median, mode 2 US

The mean is 4.57 (rounded to 2 decimal places)

Step-by-step guide: Mean in math

The median is the middle number of a numerical data set.

To find the median, we need to arrange the values in numerical order, from the smallest value to the highest value, and find the middle value .

The middle value is the median value.

Let’s find the median of the same data set.

Mean, median, mode 4 US

The median is 5 because it is the middle number of data points.

Step-by-step guide: Median

The mode is the most common number. To find the mode, we need to find the value in the data set that occurs the most number of times.

Let’s find the mode of the data set.

Mean, median, mode 5 US

The number that occurs the most or is most frequent is 6.

The mode is 6.

Step-by-step guide: Mode in math

The range is the difference between the greatest value and the least value of a data set. It is a measure of variability not a measure of center.

Let’s find the range of the data set.

Mean, median, mode 6 US

The range is 6.

Step-by-step guide: Range in math

What is mean median mode?

Common Core State Standards

How does this apply to 6 th grade math?

  • Grade 6 – Statistics and Probability 6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  • Grade 6 – Statistics and Probability 6.SP.A2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
  • Grade 6 – Statistics and Probability 6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

[FREE] Averages and Range Check for Understanding (Grade 6)

[FREE] Averages and Range Check for Understanding (Grade 6)

Use this quiz to check your 6th grade students’ understanding of averages and range. 10+ questions with answers covering a range of 6th grade averages and range topics to identify areas of strength and support!

How to find the mean median mode

In order to find the mean, median or mode:

List the numbers in order from least to greatest.

To find the mean, find the total of the numbers in the data set and divide by the number of values in the data set.

  • To find the median, find value(s) in the middle of the data set.

To find the mode, look for the value(s) that occur the most; there may be more than one mode.

To find the range, find the difference between the largest value and the smallest value.

Mean median mode examples

Example 1: finding the mode.

Find the mode for the given data set.

Mean, median, mode 8 US

  • List the numbers in order from least to greatest. 

Mean, median, mode 8 US-1

4 To find the mode, look for the value(s) that occur the most; there may be more than one mode.

Mean, median, mode 9 US

7 occurs the most, so the mode is 7.

Example 2: finding the median

Find the median for the given data set.

Mean, median, mode 10 US

List the numbers in order from least to greatest

Mean, median, mode 11 US

To find the median, find values in the middle of the data set.

Mean, median, mode 12 US

The value in the middle is 9. The median is 9.

Example 3: finding the median

Find the median of the given data set.

Mean, median, mode 13 US

Find the middle of the data set. There is an even number of values, so we have a middle pair. To find the median, find the average of the two middle numbers or the midpoint of 4 and 6.

Mean, median, mode 15 US

The average of 4 and 6 or the midpoint between 4 and 6 is 5. So, the median is 5.

Example 4: finding the mean

Find the mean of the given data set.

Mean, median, mode 17 US

Although not necessary, it can be helpful to put the values in order.

Mean, median, mode 18 US

To find mean, find the total of the numbers in the data set and divide by the number of values in the data set.

Mean, median, mode 19 US

The mean is 7.6.

Example 5: finding the mean, median, and mode

Find the mean, median, and mode of the data set.

Mean, median, mode 20 US

The mean is 13.

Mean, median, mode 22 US

There are an even number of data points in the data set, so there are two values in the middle, 12 and 13. To find the median, find the average of the two numbers of the midpoint.

Mean, median, mode 34 US

The median is 12.5.

Mean, median, mode 24 US

12 is the value that occurs the most which means it is the mode.

Example 6: finding the mean, median, mode, and range

Mean, median, mode 25 US

The mean is 4.875.

Mean, median, mode 28 US

There are an even amount of values in the data set, 4 and 6 are in the middle. To find the median find the average of 4 and 6 or find the midpoint of 4 and 6.

Mean, median, mode 29 US

The median is 5.

Mean, median, mode 30 US

3 and 6 both occur twice, so there are two modes, 3 and 6. Since there are two modes, the data is bimodal.

The modes are 3 and 6.

Mean, median, mode 31 US

Teaching tips for mean, median, mode

  • Incorporate project based data science learning activities where students have opportunity to collect their own data, as well as do data analysis/statistical analysis on the collected data.
  • Although worksheets and paper-based quizzes have their place, consider alternate forms of formative assessments that engage students to gain a global perspective by having them summarize data in real time with real world data points.

Easy mistakes to make

  • Mixing up the measures of center For example, if a student is asked to find the median and they find the mean.
  • Listing the numbers in descending order instead of ascending order When summarizing data, the best way to list the data is in ascending order (from least to greatest) not descending order (greatest to least).

10, \, 8, \, 5, \, 5, \, 6, \, 7, \, 5, \, 11, \, 4, \, 9, \, 3

Mean, median, mode 32 US

Practice mean median mode questions

1. Find the mode of the given data set.

Mean, median, mode 35 US

The value that occurs the most in the data set is 18. The other numbers only occur once.

2. Find the mode of the given data set.

Mean, median, mode 36 US

The most common values are 19 and 23. These two values occur twice within the data set. The other values only occur once.

3. Find the median of the given data set.

Mean, median, mode 37 US

Put the numbers in order from the smallest number to largest number. Then find the middle value.

Mean, median, mode 37 US-1

The middle value is 17, so this is the median.

4. Find the median of the given data set.

Mean, median, mode 38 US

Put the numbers in order from the smallest to largest. Then find the middle value.

Mean, median, mode 39 US

The middle pairs of values are 35 and 37. The average of these is 36. The median is 36.

Mean, median, mode 40 US

5. Find the mean of the given data set.

Mean, median, mode 41 US

To find the mean, add up all the values in the data set and divide by the number of values in the data set.

Mean, median, mode 42 US

6. Find the mean, median, mode, and range for the given data set (round to two decimal places when necessary).

Mean, median, mode 43 US

Mean = 6.23, Median = 7.2, Mode = 7.2, Range = 7.9

Mean = 6, Median = 6.2, Mode = 7.2, Range = 8

Mean = 7, Median = 7.2, Mode = 7.2, Range = 7

Mean = 6.2, Median = 7, Mode = 7, Range = 7.2

Mean, median, mode 44 US

The value in the middle is 7.2.

The median is 7.2.

Mean, median, mode 47 US

The value that occurs the most is 7.2. The mode is 7.2.

Range = 9.1-1.2 = 7.9

Range = 7.9

Mean, median, mode FAQs

Yes, data sets can be made up of whole numbers (odd numbers and even numbers), integers, decimals, and fractions.

The arithmetic mean is the mean (average value) where you add all the values and divide by the number of values in the set of data.

An outlier is an extremely high or low data point in relation to the rest of the set of numbers in the data set.

The geometric mean is the square root of a product of two numbers.

The standard deviation is a statistical measure that measures the dispersion of data points relative to the mean.

Descriptive statistics is a method of summarizing data. Measures of central tendency are descriptive statistics.

The next lessons are

  • Frequency table
  • Types of data
  • Representing data

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Learn Mean, Median and Mode – Tutorial and Practice Questions

  • Posted by Brian Stocker MA
  • Date April 7, 2014
  • Comments 11 comments

Mean, Median and Mode

Median, Mode and Mean questions appear on standardized tests in most  High School ,  and some  Nursing Entrance Tests

Audio Version of this Post

Mean, median and mode – quick review and tutorial.

Mean, mode and median are basic statistical tools used to calculate different types of averages. Below is a quick tutorial followed by practice questions.

Mean Mean is the most common form of average used. To calculate mean, you simple add up all the values of data given and divide by the number data provided.

Example Find the mean of 8, 5, 7, 10, 15, 21 Sum of values = 8 + 5 + 7 + 10 + 15 + 21 = 66 Number of data = 6 Mean = 66/6 = 11

Median Median refers to the middle value among a set or series of values after they have been arranged in numerical order. Median thus means the middle of the set of values. When two numbers fall in the middle, you simple add the value of the two numbers and divide by 2 to get the middle of the two numbers.

Example Arrange these numbers in ascending order and then find the median First arrange in ascending order 8, 5, 7, 10, 15, 21 = 5, 7, 8, 10, 15, 21

There are 6 numbers on the series and two fall in the middle = 8 and 10 The median = 8 + 10/2  = 18/2 =9

Mode Mode refers to the most occurring number or value among a set of values. Note that it is possible not to have a most occurring number and then the answer becomes ‘No Mode’

Example 8, 5, 7, 10, 15, 21, 5, 7, 2, 5 Mode refers to the most occurring number 8, 10, 15, 2 and 21 occur once

5 occurs 3 times 7 occurs 2 times The most occurring number is 5, which occurs three times.

Statistics Practice Questions

Practice questions.

1. Find the median of the set of numbers: 1,2,3,4,5,6,7,8,9 and 10.

a. 55 b. 10 c. 1 d. 5.5

2. Find the median of the set of numbers:  21, 3, 7, 17, 19, 31, 46, 20 and 43.

a. 19 b. 20 c. 3 d. 167

3. Find the median of the set of numbers:  100, 200, 450, 29, 1029, 300 and 2001.

a. 300 b. 29 c. 7 d. 4,080

4. The following represents age distribution of students in an elementary class. Find the mode of the values: 7, 9, 10, 13, 11, 7, 9, 19, 12, 11, 9, 7, 9, 10, 11.

a. 7 b. 9 c. 10 d. 11

5. Find the mode from these test results: 90, 80, 77, 86, 90, 91, 77, 66, 69, 65, 43, 65, 75, 43, 90.

a. 43 b. 77 c. 65 d. 90

6. Find the mode from these test results: 17, 19, 18, 17, 18, 19, 11, 17, 16, 19, 15, 15, 15, 17, 13, 11.

a. 15 b. 11 c. 17 d. 19

7. Find the mean of these set of numbers: 100, 1050, 320, 600 and 150.

a. 333 b. 444 c. 440 d. 320

8. The following numbers represent the ages of people on a bus: 3, 6, 27, 13, 6, 8, 12, 20, 5, 10. Calculate their mean of their ages.

a. 11 b. 6 c. 9 d. 110

9. These numbers are taken from the number of people that attended a particular church every Friday for 7 weeks: 62, 18, 39, 13, 16, 37, 25. Find the mean.

a. 25 b. 210 c. 62 d. 30

1. D First arrange the numbers in a numerical sequence: 1,2,3,4,5,6,7,8,9, 10. Then find the middle number or numbers. The middle numbers are 5 and 6. The median = 5 + 6/2 = 11/2 = 5.5

2. B First arrange the numbers in a numerical sequence: 3,7, 17, 19, 20, 21, 31, 43, 46. Next find the middle number. The median = 20

3. A First arrange the numbers in a numerical sequence: 29,100, 200, 300, 450, 1029, 2001. Next find the middle number. The median = 300

4. B Simply find the most recurring number. The most occurring number in the series is 9

5. D Simply find the most recurring number. The most occurring number in the series is 90.

6. C Simply find the most recurring number. The most occurring number in the series is 17.

7. B First add all the numbers 100 + 1050 + 320 + 600 + 150 = 2220. Then divide by 5 (the number of data provided) = 2220/5 = 444

8. A First add all the numbers 3 + 6 + 27 + 13 + 6 + 8 + 12 + 20 + 5 + 10 = 110. Then divide by 10 (the number of data provided) = 110/10 = 11

9. D First add all the numbers 62 + 18 + 39 + 13 + 16 + 37 + 25 = 210. Then divide by 7 (the number of data provided) = 210/7 = 30

Common Mistakes Calculating Mean, Median, and Mode

  • Calculating Mean: Not adding up all the numbers correctly and dividing by the wrong number of elements.
  • Calculating Median: Ordering incorrectly;  not understanding the difference between the median and the average. The median is the mid-point number, where half the elements fall above and half below. The mean (or “average”) is the sum of all data divided by the number of data points.
  • Calculating the Mode: Incorrectly identifying the most frequently occurring number(s) or not understanding that a set of data may have multiple modes or no mode at all.
  • Not understanding outliers: Extreme values have a huge effect on the mean, but have less impact on the median and mode.
  • Not understanding the difference between sample and population: The formulas and methods used to calculate measures of central tendency can be different for sample and population.

Mean Mode and Median Video Tutorial

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Tag: Average , Mean , Median , Mode , Practice Questions

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11 comments.

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That dash before the number throws you off, I assumed they were negative numbers.

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Good point and thanks! I have changed to semi colon.

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With the “and” it made it a little harder to order.

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It is good and helps to prepare for exams

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it was super easy

' src=

its a good website – thanks!

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this is a great practice i have a test today on it and you just saved my life

' src=

It was so easy We need difficult ones

' src=

Thanks, I got to practice these sums

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hi, what is the answer for this Find the mean of the following distribution. X 1 2 3 4 5 F 4 5 8 10 3 please tell till 3:00 pm

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u r good thanks

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Problem Solving Averages and Range

Problem Solving Averages and Range

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

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Last updated

29 January 2018

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High School Math : Understanding Mean, Median, and Mode

Study concepts, example questions & explanations for high school math, all high school math resources, example questions, example question #11 : basic statistics.

mean median mode and range problem solving questions

Reorder the numerals in the set, from least to greatest.

mean median mode and range problem solving questions

The mean is the sum of the numerals divided by the number of data points.

mean median mode and range problem solving questions

The mean is 15.

The range is the difference between the maximum and the minimum.

mean median mode and range problem solving questions

The range is 8.

Example Question #1 : Understanding Mean, Median, And Mode

For the following data set:

mean median mode and range problem solving questions

Which is the smallest?

None of the answers

Put the data in order from smallest to largest and then calculate each stastic:  mean, mode, median, range

mean median mode and range problem solving questions

Example Question #1 : Data Properties

Find the median of the following number series:

3, 6, 27, 19, 8, 11, 30, 42, 7, 39

The first step to finding the median is always to put the numbers in the proper order:

3, 6, 7, 8, 11, 19, 27, 30, 39, 42

When we have an even amount of numbers, we find the average (or mean) of the middle two to get the median:

11 + 19 = 30/2 = 15

Example Question #15 : Basic Statistics

With a standard deck of playing cards, what is the probability of picking one red card followed by one black card, without replacement?

mean median mode and range problem solving questions

In a standard deck of playing cards we have:

mean median mode and range problem solving questions

Which statement is true concerning the following data set:

mean median mode and range problem solving questions

First, put the data in order, smallest to largest:

mean median mode and range problem solving questions

Note, the mode is the number most often repeated in the data set and the median is the middle number.

mean median mode and range problem solving questions

Example Question #2 : Understanding Mean, Median, And Mode

Alice recorded the outside temperature at noon each day for one week. These were the results.

Tuesday: 85

Wednesday: 82

Thursday: 84

Saturday: 79

What was the mean temperature for the week?

mean median mode and range problem solving questions

The mean is calculated by adding all the values in a group, then dividing the sum by the total number in the group. 

mean median mode and range problem solving questions

Example Question #3 : Understanding Mean, Median, And Mode

What is the mode of the temperatures?

mean median mode and range problem solving questions

The mode is the number that appears most frequently in a series of numbers.  First, organize the numbers in order from least to greatest.  Then, identify the value that is repeated most frequently.

mean median mode and range problem solving questions

Example Question #4 : Understanding Mean, Median, And Mode

What is the median temperature?

mean median mode and range problem solving questions

The median is determined by ordering the values in the group from least to greatest and identifying the value directly in the middle.  For instance, if five numbers are ordered from least to greatest, the third is the median. 

mean median mode and range problem solving questions

Example Question #11 : Data Properties

What is the probability of rolling an odd sum less than seven when rolling two standard six-sided dice?

mean median mode and range problem solving questions

The odd numbers less than seven are one, three, and five.

mean median mode and range problem solving questions

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PRACTICE PROBLEMS ON MEAN MEDIAN AND MODE

Problem 1 :

Find the (i) mean  (ii) median  (iii) mode for each of the following data sets :

a)  12, 17, 20, 24, 25, 30, 40

b)  8, 8, 8, 10, 11, 11, 12, 12, 16, 20, 20, 24

c)  7.9, 8.5, 9.1, 9.2, 9.9, 10.0, 11.1, 11.2, 11.2, 12.6, 12.9

d)  427, 423, 415, 405, 445, 433, 442, 415, 435, 448, 429, 427, 403, 430, 446, 440, 425, 424, 419, 428, 441

Problem 2 :

Consider the following two data sets :

Data set A : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 12

Data set B : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 20

a)  Find the mean for both Data set A and Data set B.

b)  Find the median of both Data set A and Data set B.

c)  Explain why the mean of Data set A is less than the mean of Data set B.

d)  Explain why the median of Data set A is the same as the median of Data set B

Problem 3 :

The table given shows the result when 3 coins were tossed simultaneously 40 times. The number of heads appearing was recorded.

mean median mode and range problem solving questions

Calculate the :   a)  mean     b)  median     c)  mode

Problem 4 :

The following frequency table records the number of text messages sent in a day by 50 fifteen-years-olds

mean median mode and range problem solving questions

a)  For this data, find the : (i) mean   (ii)  median   (iii)  mode

b)  construct a column graph for the data and show the position of the measures of centre (mean, median and mode) on the horizontal axis.

c)  Describe the distribution of the data.

d)  why is the mean smaller than the median for this data ?

e)  which measure of centre would be the most suitable for this data set ?

Problem 5 :

The frequency column graph alongside gives the value of donations for an overseas aid organisation, collected in a particular street.

a)  construct the frequency table from the graph.

b)  Determine the total number of donations.

c)  For the donations find the :  (i)  mean   (ii)  median   (iii)  mode

d) which of the measures of central tendency can be found easily from the graph only ?

mean median mode and range problem solving questions

Problem 6 :

Hui breeds ducks. The number of ducklings surviving for each pair after one month is recorded in the table.

a)  Calculate the : (i)  mean   (ii)  median   (iii) mode

b)  Is the data skewed ?

c)  How does the skewness of the data affect the measures of the middle of the distribution ?

mean median mode and range problem solving questions

Answers 

(c)  the mean of A is less than the mean of B.

(d)   median is the same.

(3)  (a)   Mean  =  1.4     (b)   median  =  1  (c)     mode  =  1

(4)  

(a)   (i)   Mean  =  5.74  (ii)     median  =  7  (iii)   mode  =  8

mean median mode and range problem solving questions

(c)     bimodal data.

The mean takes into account the full range of numbers of text messages and is affected by extreme values. Also, the value which is lower than the median is well below it.

(e)   The median

(5)  

mean median mode and range problem solving questions

(b)   ∑f  =  30

(c)  (i)   Mean  =  $2.9  (ii)   median  =  $2  (iii)   mode  =  $2

mean median mode and range problem solving questions

(6)  

(a)  (i)  Mean  =  4.25    (ii)   median  =  5   (iii)   mode  =  5

mean median mode and range problem solving questions

c)   By observing the graph, the mean is less than the median and mode.

mean median mode and range problem solving questions

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  • Worksheet on Mean Median and Mode

In worksheet on mean median and mode the questions are based on finding the mean median and mode.

1. Find the mean of the following data.

(b) 16, 18, 19, 21, 23, 23, 27, 29, 29, 35

2.  Find the mean of first ten whole numbers.

3.  Find the mean of first 5 prime numbers.

4. The mean of 8, 11, 6, 14, x and 13 is 66. Find the value of the observation x.

5. The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x and also the value of the observation in the data.

6. Find the mean of the following distribution.

(a) The age of 20 boys in a locality is given below.

(b) Marks obtained by 40 students in an exam are given below.

(d) The daily wages of 50 employees in an organization are given below:

Find the mean daily wages.

(a) 12, 8, 4, 8, 1, 8, 9, 11, 9, 10, 12, 8

(b) 15, 22, 17, 19, 22, 17, 29, 24, 17, 15

(c) 0, 3, 2, 1, 3, 5, 4, 3, 42, 1, 2, 0

(d) 1, 7, 2, 4, 5, 9, 8, 3

8. The runs scored in a cricket match by 11 players is as follows:

7, 16, 121, 51, 101, 81, 1, 16, 9, 11, 16

Find the mean, mode, median of this data.

9. The weights in kg of 10 students are given below:

39, 43, 36, 38, 46, 51, 33, 44, 44, 43

Find the mode of this data. Is there more than 1 mode? If yes, why?

10. The marks obtained by 40 students out of 50 in a class are given below in the table.

Find the mode of the above data.

11. The number of rupee notes of different denominations are given below in the table.

12. Find the median of the following data.

(a) 27, 39, 49, 20, 21, 28, 38

(b) 10, 19, 54, 80, 15, 16

(c) 47, 41, 52, 43, 56, 35, 49, 55, 42

(d) 12, 17, 3, 14, 5, 8, 7, 15

13.  The following observations are arranged in ascending order. The median of the data is 25 find the value of x.

17, x, 24, x + 7, 35, 36, 46

14.  The mean of the following distribution is 26. Find the value of p and also the value of the observation.

Also, find the mode and the given data.

Answers for the worksheet on mean median and mode are given below to check the exact answers of the above questions.

5. 9, 11, 17

6. (a) 11.8

(d) no mode

8. Mean = 39 1/11;

Median = 16

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  1. Mean, Mode, Median, Range Practice Questions

    Mean, Mode, Median, Range Practice Questions - Corbettmaths Mean, Mode, Median, Range Practice Questions Click here for Questions . Click here for Answers . averages, average, means, modes, medians, ranges Practice Questions The Corbettmaths Practice Questions on the Averages and Range

  2. Mean Median Mode Range Worksheets

    Step 1) Add up the numbers to give a total of 5+7+8+4=24 Step 2) Divide the total by the number of data points. 24 ÷ 4 = 6 Answer: the mean is 6. Example 2) Find the mean of 8, 2, 5, 7 and 13 Step 1) Add up the numbers to give a total of 8+2+5+7+13=35 Step 2) Divide by the number of data points. 35 ÷ 5 = 7 Answer: the mean is 7. What is the Median?

  3. How to Find Mean, Mean, Mode and Range: Your Complete Guide

    Step 01: Find the Mean How to Find the Mean of a Data Set The mean is the numerical average of a data set. To determine the mean of the data set, divide the total sum by the total amount of numbers. In this example, to find the total sum, add all seven values in the data set together as follows: 1 + 3 + 4 + 6 + 6 + 7 + 8 = 35 The total sum is 35.

  4. Mean, median, and mode (practice)

    Math > Statistics and probability > Summarizing quantitative data > Measuring center in quantitative data Mean, median, and mode Google Classroom What is the mode of the following numbers? 9, 8, 7, 1, 1 Stuck? Review related articles/videos or use a hint. Report a problem Start over Do 7 problems

  5. Mean Median Mode Questions with Solutions

    Solution: First 10 odd integers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 Mean = Sum of the first 10 odd integers/Number of such integers = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)/10 = 100/10 = 10 Therefore, the mean of the first 10 odd integers is 10. 2. What is the median of the following data set?

  6. Mean Median Mode and Range

    Example 1: Find the mean, median, mode, and range for the following list of values. The mean is commonly known as the "average" which is calculated by getting the sum of all values in the list and then divided by the number of entries. The symbol used to represent the mean is [latex]\bar X [/latex], often read as "x-bar".

  7. PDF Finding the Mean, Median, Mode Practice Problems

    1. What is the mean of the following numbers? 10, 39, 71, 39, 76, 38, 25 a. 42 b. 39 c. 42.5 d. 35.5 2. What number would you divide by to calculate the mean of 3, 4, 5, and 6? a. 6 b. 3 c. 5 d. 4 3. What measure of central tendency is calculated by adding all the values and dividing the sum by the number of values? a. Median b. Mean c. Mode d.

  8. Mean, median, and mode review (article)

    Example Find the mean of this data: 1 , 2 , 4 , 5 Start by adding the data: 1 + 2 + 4 + 5 = 12 There are 4 data points. mean = 12 4 = 3 The mean is 3 . Practice problems Problem A What is the arithmetic mean of the following numbers? 10, 6, 4, 4, 6, 4, 1 mean = Want to practice more of these? Check out this exercise on calculating the mean.

  9. Mean Median Mode and Range Questions and Revision

    Median. The median is often referred to as "the middle", which is precisely what it is.. There are two common ways of finding the middle value(s): Method 1: Put the numbers in order from smallest to largest and find the middle value/middle two values. Cross out the smallest number and the largest number, then cross out the next smallest and largest, keeping going crossing out pairs of ...

  10. IXL

    IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more. 0.

  11. Averages and Range Textbook Exercise

    The Corbettmaths Textbook Exercise on the Mean, Median, Mode and Range. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths ... Books; Averages and Range Textbook Exercise. Click here for Questions . means, modes, medians, mean, mode, median. Textbook Exercise. Previous: Median from a ...

  12. PDF Lesson 13: Mean, Median, Mode, and Range

    LESSON 13: Mean, Median, Mode and Range Weekly Skill: computation and real application Lesson Summary: First, students will solve a problem about buying carpet. In Activity 1, they will do a vocabulary matching activity. In Activity 2, they will do some examples and computation practice.

  13. PDF Notes, Examples, and Practice Exercises

    Mean, Median and Mode Mean What is it? An (arithmetic) mean is the average of a set of n numbers. How do you find it? Add all the elements in a set. Then, divide by the number of elements. Examples: The mean of 7 and 11 is 9. 7+11 The mean of -6, -3, 2, 4, and 4 is .2 (5 elements in the set) Jim's math test scores were 78, 88, 91, and 94.

  14. Mean, Median, Mode

    Example 4: finding the median. Find the median: Make sure the list of numbers is in numerical order. Find the middle of the data set. There is an even number of values, so we have a middle pair. The average of 4 4 and 6 6 is 5 5. (Or the midpoint of 4 4 and 6 6 is 5 5 ). \frac {4+6} {2}=\frac {10} {2}=5 24+6 = 210 = 5.

  15. Maths Genie • Mean, Median, Mode and Range

    The mode is 7. b) The median is the middle number (but only when the numbers are in order) We have to put the numbers in order: 1 2 4 5 7 7 9. We can now find the middle number: The median is 5. c) To find the mean we need to add up all the numbers then divide by how many numbers there are: 1 + 2 + 4 + 5 + 7 + 7 + 9 7 = 35 7 = 5.

  16. Calculating the Mean, Median, Mode & Range: Practice Problems

    The mean, median, mode, & range are fundamental statistical calculations necessary to evaluate and comprehend the significance of a set of numbers. Learn how to calculate mean, medium,...

  17. Mean, Median, Mode, and Range (Problem Solving) Flashcards

    Study with Quizlet and memorize flashcards containing terms like Find the mode of the following numbers. {33,60,33,60,33,57}, Find the range of the following numbers. {69,51,39,27,39}, Find the mean of the following numbers. {12,68,48,36} and more.

  18. Mean Median Mode Range Worksheet

    Help your students prepare for their Maths GCSE with this free mean, median, mode, and range worksheet of 56 questions and answers. Section 1 of the mean, median, mode, and range worksheet contains 48 skills-based mean median mode range questions, in 3 groups to support differentiation. Section 2 contains 4 applied mean, median, mode, and range ...

  19. Mean Median Mode

    6. Step-by-step guide: Mode in math Range The range is the difference between the greatest value and the least value of a data set. It is a measure of variability not a measure of center. Let's find the range of the data set. 7 - 1 = 6 7 − 1 = 6 The range is 6. 6.

  20. Learn Mean, Median and Mode

    Example. Arrange these numbers in ascending order and then find the median. First arrange in ascending order 8, 5, 7, 10, 15, 21. = 5, 7, 8, 10, 15, 21. There are 6 numbers on the series and two fall in the middle = 8 and 10. The median = 8 + 10/2 = 18/2 =9. Mode. Mode refers to the most occurring number or value among a set of values.

  21. Problem Solving Averages and Range

    A mixed bag of problem solving style questions on mean, median, mode and range. Suitable for key stage 3 and key stage 4 student. Answers are included too.

  22. Understanding Mean, Median, and Mode

    Possible Answers: range mean median mode Correct answer: median Explanation: Reorder the numerals in the set, from least to greatest. {12, 12, 14, 17, 20} The number in the middle is the median. {12, 12,14, 17, 20} The most frequent numeral is the mode. {12,12, 14, 17, 20} The mean is the sum of the numerals divided by the number of data points.

  23. Practice Problems on Mean Median Mode

    Solution Problem 2 : Consider the following two data sets : Data set A : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 12 Data set B : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 20 a) Find the mean for both Data set A and Data set B. b) Find the median of both Data set A and Data set B. c) Explain why the mean of Data set A is less than the mean of Data set B.

  24. Worksheet on Mean Median and Mode

    In worksheet on mean median and mode the questions are based on finding the mean median and mode. ... In worksheet on mean median and mode the questions are based on finding the mean median and mode. 1. Find the mean of the following data. (a) 9, 7, 11, 13, 2, 4, 5, 5 ... Math Problem Ans; Free Math Answers; Printable Math Sheet; Funny Math ...