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"Math Salamanders Free Math Sheets"

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.

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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.

Examples

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.

Examples

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

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

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

Step 1) Put the data into an ordered list.

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

Step 1) Put the data into an ordered list.

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

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

Both lists have 10 data points.

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

Answer: the mode is 0.4.

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 1) Put the data into an ordered list.

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

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

Step 1) Put the data into an ordered list.

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

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

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

Step 1) Put the data into an ordered list.

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

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

Both lists have 10 data points.

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

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

Mean Median Mode Range Worksheets

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

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 involves decimals and negative numbers.

The 4th, 5th and 6th sheets are similar to the first 3 sheets but with increased number of data points.

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.

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.

Bar Graph Worksheets

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.

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