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Here we will learn about the mean, including what the mean is and how to find the mean.

There are also mean worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

The **mean **is a type of average calculated by finding the total of the values and dividing the total by the number of values.

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

\text{Mean}=\frac{\text{total}}{\text{number of values}}E.g. Work out the mean

\[\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{5+8+10+11+13}{5}=\frac{47}{5}=9.4\]

The mean is 9.4

The mean (also known as the arithmetic mean) is a measure of central tendency because it describes a set of numbers by identifying a central position within the data.

In order to calculate the mean:

**Find the total of the values.****Divide the total by the number of values.****Write down the answer.**

Get your free mean maths worksheet of 20+ mean, median, mode and range questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free mean maths worksheet of 20+ mean, median, mode and range questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE**Mean** is part of our series of lessons to support revision on **mean, median, mode**. You may find it helpful to start with the main mean, median, mode lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Calculate the mean value of this list of numbers:

2 7 9 10 12**Find the total of the values.**

Add up all the values in the list

\text{Total}=2+7+9+10+12=402**Divide the total by the number of values.**

There are 5 values in the data set. We need to divide the total by 5 .

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{40}{5}=83**Write down the answer.**

If your answer is a decimal, you may need to round your answer to a given number of decimal places or significant figures.

Here the mean is an integer, so there is no need to round.

The mean is 8

Calculate the mean value of this set of numbers.

Give your answer to 1 decimal place.

13 16 17 17 18 20**Find the total of the values.**

Add up all the values in the list

\text{Total}=13+16+17+17+18+20=101**Divide the total by the number of values.**

There are 6 values in the data set. We need to divide the total by 6 .

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{101}{6}=16.8333...**Write down the answer.**

If your answer is a decimal, you may need to round your answer to a given number of decimal places or significant figures. Here we have been asked to round to 1 decimal place.

\text{Mean}=16.8333…=16.8 \ \text{(1 dp)}Calculate the mean value of this set of data. Give your answer to 1 decimal place.

11 13 14 15 19 20 22**Find the total of the values.**

Add up all the values in the list

\text{Total}=11+13+14+15+19+20+22=114**Divide the total by the number of values.**

There are 7 values in the data set. We need to divide the total by 7 .

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{114}{7}=16.2857...**Write down the answer.**

If your answer is a decimal, you may need to round your answer to a given number of decimal places or significant figures.

Here we have been asked to round to 1 decimal place.

\text{Mean}=16.2857…=16.3 \ \text{(1 dp)}Calculate the mean value of this list of numbers.

101 102 105 106 108**Find the total of the values.**

Add up all the values in the list

\text{Total}=101+102+105+106+108=522**Divide the total by the number of values.**

There are 5 values in the data set. We need to divide the total by 5 .

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{522}{5}=104.4**Write down the answer.**

If your answer is a decimal, you may need to round your answer to a given number of decimal places or significant figures.

We have not been asked to round and the mean is a simple decimal.

The mean is 104.4

In order to solve a problem involving the mean:

**Use the mean and number of values to find the total.****Read the question carefully to work the next step.****Find the answer.**

The mean of 4 values is 10 .

Here are 3 of the values:

6 9 12Find the 4 ^{th} value.

**Use the mean and number of values to find the total.**

The mean of 4 values is 10 . We can multiply these together to find the total of the 4 numbers.

\text{Total of 4 values}=\text{mean} \times \text{number of values}=10\times 4=40**Read the question carefully to work the next step.**

We need to find the 4

^{th} value. We can find the total of the first 3 values.

Then we can subtract this total from the total of the 4 values.

\text{Total of 3 values}=6+9+12=27**Find the answer.**

We need to find the difference of the totals.

40-27=13The 4 ^{th} value is 13

Alternatively, you could use the equation for finding the mean. You could use x as the missing value.

Then rearrange and solve.

\[\text{Mean} = \frac{\text{total}}{\text{number of values}}\\
10=\frac{6+9+12+x}{4}\\
10 = \frac{27+x}{4}\\
40=27+x\\
13=x\]

The mean of 5 values is 14 .

Here are 4 of the values:

5 11 13 19Find the 5 ^{th} value:

**Use the mean and number of values to find the total.**

The mean of 5 values is 14 . We can multiply these together to find the total of the 5 numbers.

\text{Total of 5 values}=\text{mean} \times \text{number of values}=14\times 5=70**Read the question carefully to work the next step.**

We need to find the 5 ^{th} value. We can find the total of the first 4 values.

Then we can subtract this total from the total of the 5 values.

\text{Total of 4 values}=5+11+13+19=48**Find the answer.**

We need to find the difference of the totals.

70-48=22The 5 ^{th} value is 22

Alternatively, you could use the equation for finding the mean. You could use x as the missing value.Then rearrange and solve.

\[\text{Mean} = \frac{\text{total}}{\text{number of values}}\\
14=\frac{5+11+13+19+x}{5}\\
14 = \frac{48+x}{5}\\
70=48+x\\
22=x\]

Data Set A has 6 values and a mean of 10 .

Data Set B has 4 values and a mean of 8 .

Find the mean of all 10 values.

**Use the mean and number of values to find the total.**

For Set A – The mean of 6 values is 10 . We can multiply these together to find the total of the Set A numbers.

\text{Total of Set A values}=\text{mean} \times \text{number of values}=10\times 6=60For Set B – The mean of 4 values is 8 . We can multiply these together to find the total of the Set B numbers.

\text{Total of Set A values}=\text{mean} \times \text{number of values}=8\times 4=32**Read the question carefully to work the next step.**

We need to find the mean of all the values combined. We know there are 10 values. We can find the total of all 10 values by adding the total for Set A to the total of Set B .

\text{Total} =\text{total of Set A values} + \text {total of Set B values} = 60+32=92**Find the answer.**

We need to find the mean by dividing the total of all 10 values by 10 .

\text{Mean}=\frac{\text{Total}}{\text{number of values}}=\frac{92}{10}=9.2The mean of all the values is 9.2

Data Set A has 4 values and a mean of 8 .

Data Set B has 7 values and a mean of 6 .

Find the mean of the all 11 values. Give your answer correct to 2 decimal places.

**Use the mean and number of values to find the total.**

For Set A – The mean of 4 values is 8 . We can multiply these together to find the total of the Set A numbers.

\text{Total of Set A values}=\text{mean} \times \text{number of values}=8\times 4=32For Set B – The mean of 7 values is 6 . We can multiply these together to find the total of the Set B numbers.

\text{Total of Set A values}=\text{mean} \times \text{number of values}=6\times 7=42**Read the question carefully to work the next step.**

We need to find the mean of all the values combined. We know there are 11 values. We can find the total of all 11 values by adding the total for Set A to the total of Set B .

\text{Total} =\text{total of Set A values} + \text {total of Set B values} = 32+42=74**Find the answer.**

We need to find the mean by dividing the total of all 11 values by 11 .

\text{Mean}=\frac{\text{Total}}{\text{number of values}}=\frac{74}{11}=6.7272…=6.73 \ \text{(2 dp)}The mean of all the values is 6.73 \text{ (2 dp)}

**Check which average you are being asked for**

Check if you have been asked for the median, mode, or mean average.

**The mean average can be a decimal**

The mean does not have to be a whole number. It can be a decimal or a fraction. It may be a decimal which needs rounding.

1. Find the mean of this list of values:

5 7 8 8 9

7

7.4

7.5

8

\text{Mean}= \frac{\text{total}}{\text{number of values}}\\
\text{Mean}=\frac{5+7+8+8+9}{5}\\
\text{Mean}= \frac{37}{5}\\
\text{Mean}=7.4

2. Find the mean of this list of values:

3 5 6 9

5.7

5.75

5.8

5.9

\text{Mean}= \frac{\text{total}}{\text{number of values}}\\
\text{Mean}=\frac{3+5+6+9}{4}\\
\text{Mean}= \frac{23}{4}\\
\text{Mean}=5.75

3. Find the mean of this list of values. Give your answer to 3 significant figures:

7 8 9 10 10 11

9.16

9.5

10

9.17

\text{Mean}= \frac{\text{total}}{\text{number of values}}\\
\text{Mean}=\frac{7+8+9+10+10+11}{6}\\
\text{Mean}= \frac{55}{6}\\
\text{Mean}=9.16666…\\
\text{Mean}=9.17 \ \text{(to 3 sf)}

4. Find the mean of this list of values. Give your answer to 3 significant figures:

17 18 18 19 20 21 25

18

19

19.8

19.7

\text{Mean}= \frac{\text{total}}{\text{number of values}}\\
\text{Mean}=\frac{17+18+18+19+20+21+25}{7}\\
\text{Mean}= \frac{55}{7}\\
\text{Mean}=19.7142…\\
\text{Mean}=19.7\ \text{(to 3 sf)}

5. The mean of 4 numbers is 9 .

Here are 3 of the numbers

6 8 15

What is the 4 ^{th} number?

7

5

6

8

The total of 4 numbers is:

\text{Total of 4 values}=\text{mean} \times \text{number of values}=9\times 4=36

The total of 3 numbers is: 6+8+9=29

The difference between the totals is: 36-29=7

This is the missing number.

6. The mean of 6 numbers is 12 .

Here are 5 of the numbers

7 9 11 13 18

What is the 6 ^{th} number?

12

14

13

15

The total of 4 numbers is:

\text{Total of 4 values}=\text{mean} \times \text{number of values}=12\times 6=72

The total of 5 numbers is: 7+9+11+13+18=58

The difference between the totals is: 72-58=14

This is the missing number.

1. Here is a list of numbers:

Work out the mean of the numbers in this list.

**(2 marks)**

Show answer

\frac{1+3+4+6+6}{5}=\frac{20}{5}

For adding the numbers and dividing by 5

**(1)**

=5

For the correct answer

**(1)**

2. Here are the ages of people in a family

Work out the mean of the ages in this family.

Give your answer to 3 significant figures.

**(2 marks)**

Show answer

\frac{15+15+19+20+54+59}{6}=\frac{182}{6}

For adding the numbers and dividing by 6

**(1)**

\frac{182}{6}=30.333…=30.3 \ \text{(to 3 sf)}

For the correct answer

**(1)**

3. Dev has 5 tests and achieves an average of 61% .

Here are 4 of the results.

Find the missing result.

**(2 marks)**

Show answer

5\times 61-(48+59+65+73)

For subtracting the total of 4 results from the total of 5 results

**(1)**

305-245=60

For the correct answer

**(1)**

4. HIGHER

5 red bricks have a mean weight of 10 kg .

3 blue bricks have a mean weight of 6 kg .

Find the mean of the 8 bricks.

**(3 marks)**

Show answer

5\times 10=50

3\times6=18

For finding the total weights of the red bricks and the blue bricks

**(1)**

\frac{50+18}{8}=\frac{68}{8}

For dividing the total weight of 8 bricks by 8

**(1)**

=8.5 \ \text{kg}

For the correct answer

**(1)**

You have now learned how to:

- Calculate the mean
- Solve problems involving the mean
- Higher – calculate the combined mean

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