The mean is the most commonly used average in GCSE Maths and appears on virtually every AQA, Edexcel and OCR paper at both Foundation and Higher level. You need to know how to calculate the mean from a list of values, use the mean to find a missing value, and decide when the mean is the most appropriate average. This guide walks you through each skill with clear methods, worked examples and practice questions. For an overview of every topic, see our complete GCSE Maths topics list.
What Is the Mean?
The mean is a measure of average found by adding all the values in a data set and dividing by the number of values. It uses every piece of data, which makes it a good overall summary — but it can be distorted by extreme values (outliers).
Key Formulas
The second formula is a rearrangement that is essential for finding missing values when you are given the mean.
When Is the Mean Appropriate?
The mean is best when data is spread fairly evenly and there are no extreme outliers. If the data is skewed or contains outliers, the median may be a better measure of average.
Step-by-Step Method
- Add all the values together to find the total.
- Count how many values there are.
- Divide the total by the number of values.
- If you are given the mean and asked for a missing value, rearrange: multiply the mean by the number of values to get the total, then subtract the known values.
Worked Example 1 — Foundation Level
Question: Find the mean of these seven test scores: 12, 15, 18, 14, 20, 11, 16.
Working:
Sum = 12 + 15 + 18 + 14 + 20 + 11 + 16 = 106.
Number of values = 7.
Mean = 106 ÷ 7 = 15.14 (2 d.p.).
Answer: The mean test score is 15.14 (2 d.p.).
Worked Example 2 — Higher Level
Question: Five numbers have a mean of 8. Four of the numbers are 6, 9, 7 and 11. Find the fifth number.
Working:
Total of all five numbers = Mean × Number of values = 8 × 5 = 40.
Sum of the four known numbers = 6 + 9 + 7 + 11 = 33.
Fifth number = 40 − 33 = 7.
Answer: The fifth number is 7.
Worked Example 3 — Exam Style
Question: The mean height of 20 pupils is 1.58 m. A new pupil joins the class. The mean height of all 21 pupils is 1.60 m. Find the height of the new pupil.
Working:
Total height of 20 pupils = 1.58 × 20 = 31.60 m.
Total height of 21 pupils = 1.60 × 21 = 33.60 m.
Height of new pupil = 33.60 − 31.60 = 2.00 m.
Answer: The new pupil is 2.00 m tall.
Common Mistakes
- Dividing by the wrong number. Always count the number of values carefully — do not confuse the total with the count.
- Forgetting to include all values. When data is presented in a table or list, check you have included every entry before dividing.
- Rounding too early. Keep the full value during your working and round only in the final answer if the question requires it.
Exam Tips
- If the question asks for a missing value given the mean, rearrange to find the total first using Mean × Number of values.
- State your sum and count clearly — this earns method marks even if your final arithmetic is wrong.
- When comparing data sets, note that the mean can be pulled by outliers; mention this if asked which average is most appropriate.
- For averages from grouped data, see estimated mean from grouped data. For key formulas, visit our GCSE Maths formulas page.
Practice Questions
Q1 (Foundation): Find the mean of 4, 7, 10, 3, 6.
Q2 (Foundation): The mean of four numbers is 12. Three of the numbers are 10, 14 and 9. Find the fourth number.
Q3 (Higher): The mean score of a class of 30 pupils is 64. The mean score of the boys is 60 and the mean score of the girls is 70. How many boys are in the class?
Practise finding the mean and other averages free on GCSEMathsAI.
Related Topics
Summary
- The mean is the sum of all values divided by the number of values.
- To find a missing value, rearrange: Total = Mean × Number of values, then subtract the known values.
- The mean uses every data point, which makes it sensitive to outliers.
- Always show your sum and count clearly in exam working to secure method marks.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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