Mean, Median, Mode and Range
Mean, median, mode and range are used to describe a set of data. In GCSE Maths, you need to know what each one means, how to calculate it, and when to use it.
Mean: add all values and divide by how many values there are.
Median: put values in order and find the middle.
Mode: the value that appears most often.
Range: largest value − smallest value.
How to find the mean
The mean is sometimes called the average. It shares the total equally between all the values.
Example 1: Find the mean
Find the mean of 4, 7, 8, 11 and 15.
Step 1: Add the values:
4 + 7 + 8 + 11 + 15 = 45
Step 2: Divide by how many values there are:
45 ÷ 5 = 9
The mean is 9.
How to find the median
The median is the middle value. You must put the numbers in order first.
Example 2: Find the median
Find the median of 12, 5, 9, 3 and 7.
Put the numbers in order:
3, 5, 7, 9, 12
The middle value is 7.
The median is 7.
Example 3: Median with an even number of values
Find the median of 4, 10, 6, 12, 8 and 14.
Put the numbers in order:
4, 6, 8, 10, 12, 14
The two middle values are 8 and 10.
(8 + 10) ÷ 2 = 9
The median is 9.
How to find the mode
The mode is the value that appears most often. A set of data can have no mode, one mode, or more than one mode.
Example 4: Find the mode
Find the mode of 2, 4, 5, 4, 7, 8 and 4.
The number 4 appears most often.
The mode is 4.
How to find the range
The range measures how spread out the data is. It is not an average.
Example 5: Find the range
Find the range of 6, 9, 12, 15 and 20.
Range = 20 − 6 = 14
The range is 14.
A very common mistake is finding the median without putting the data in order first. Always sort the numbers before finding the middle.
In exam questions, check whether the question asks for an average or the range. Mean, median and mode are averages. Range is a measure of spread.
Video explanation
A short Worthing Maths Tutor video explanation for mean, median, mode and range can be embedded here later to improve student engagement and time on page.
Practice questions
- Find the mean of 3, 5, 8, 10 and 14.
- Find the median of 9, 2, 6, 4 and 11.
- Find the mode of 7, 8, 7, 10, 12, 7 and 8.
- Find the range of 15, 22, 9, 18 and 30.
- Find the median of 4, 8, 10, 12, 16 and 20.
Answers
- Mean = 8
- Median = 6
- Mode = 7
- Range = 21
- Median = 11
Need help with GCSE algebra?
If your child understands examples in lessons but struggles to apply them independently, structured GCSE maths tutoring can help rebuild confidence and close gaps step by step.