Sheet № 179 · Foundation + Higher · AQA · Edexcel · OCR
Finding the Mean –
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 throu
§Key definitions
Question:
Find the mean of these seven test scores: 12, 15, 18, 14, 20, 11, 16.
Answer:
The mean test score is 15.14 (2 d.p.).
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?
§Formulas to memorise
Mean = Sum of all values ÷ Number of values
Sum of all values = Mean × Number of values
Sum = 12 + 15 + 18 + 14 + 20 + 11 + 16 = 106.
Number of values = 7.
Mean = 106 ÷ 7 = 15.14 (2 d.p.).
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.
Total height of 20 pupils = 1.58 × 20 = 31.60 m.
Total height of 21 pupils = 1.60 × 21 = 33.60 m.
Worked example
Find the mean of these seven test scores: 12, 15, 18, 14, 20, 11, 16.
Working:
⚠ 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.