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Mean
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.
What is the mean?
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
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.
What is the mean?
How to calculate the mean
In order to calculate the mean:
- Find the total of the values.
- Divide the total by the number of values.
- Write down the answer.
How to calculate the mean
Mean, median, mode and range worksheet
Get your free mean maths worksheet of 20+ mean, median, mode and range questions and answers. Includes reasoning and applied questions.
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Mean, median, mode and range worksheet
Get your free mean maths worksheet of 20+ mean, median, mode and range questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREERelated lessons on mean, median, mode
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:
Mean maths examples
Example 1: finding the mean
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=402Divide 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}=83Write 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
Example 2: finding the mean
Calculate the mean value of this set of numbers.
Give your answer to 1 decimal place.
13 16 17 17 18 20Find the total of the values.
Add up all the values in the list
\text{Total}=13+16+17+17+18+20=101Divide 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)}Example 3: finding the mean
Calculate the mean value of this set of data. Give your answer to 1 decimal place.
11 13 14 15 19 20 22Find the total of the values.
Add up all the values in the list
\text{Total}=11+13+14+15+19+20+22=114Divide 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)}Example 4: finding the mean
Calculate the mean value of this list of numbers.
101 102 105 106 108Find the total of the values.
Add up all the values in the list
\text{Total}=101+102+105+106+108=522Divide 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}=104.4Write 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
How to solve a problem involving the mean
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.
Problem solving involving mean examples
Example 5: problem solving
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=40Read 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=27Find 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.
Example 6: problem solving
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=70Read 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=48Find 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.
Example 7: problem solving involving 2 means (HIGHER)
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=32Read 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=92Find 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
Example 8: problem solving involving 2 means (HIGHER)
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=42Read 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=74Find 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)}
Common misconceptions
- 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.
Practice mean maths questions
1. Find the mean of this list of values:
5 7 8 8 9
2. Find the mean of this list of values:
3 5 6 9
3. Find the mean of this list of values. Give your answer to 3 significant figures:
7 8 9 10 10 11
4. Find the mean of this list of values. Give your answer to 3 significant figures:
17 18 18 19 20 21 25
5. The mean of 4 numbers is 9 .
Here are 3 of the numbers
6 8 15
What is the 4 th number?
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?
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.
Mean maths GCSE questions
1. Here is a list of numbers:
Work out the mean of the numbers in this list.
(2 marks)
\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)
\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)
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)
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)
Learning checklist
You have now learned how to:
- Calculate the mean
- Solve problems involving the mean
- Higher – calculate the combined mean
The next lessons are
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