11+ Maths · Topic explained
The mean
Three friends have different numbers of sweets. How can they share fairly?
The big idea
The mean is what each would get if the total were shared out equally.
Picture it
Level the towers: blocks from the tall ones fill the short ones.
Key words
- mean
- Add all the values, then divide by how many there are.
- total
- All the values added together.
- average
- One number that sums up a set; the mean is one kind.
Worked examples
- 1Warm-up
Find the mean of 4, 8 and 6.
- 4 + 8 + 6 = 18
- 3 numbers: 18 ÷ 3 = 6
- 211+ standard
The mean of five numbers is 7. Four of them are 5, 9, 4 and 8. Find the fifth.
- Total of all five = 7 × 5 = 35
- 5 + 9 + 4 + 8 = 26
- Fifth = 35 − 26 = 9
- 311+ standard
Leo's mean score in 3 tests is 15. After a 4th test his mean is 16. What did he score in the 4th test?
- 3 tests: 15 × 3 = 45
- 4 tests: 16 × 4 = 64
- 4th test = 64 − 45 = 19
- 411+ standard
Find the mean of £2.40, £3.10 and £1.70.
- £2.40 + £3.10 + £1.70 = £7.20
- £7.20 ÷ 3 = £2.40
The common mistake
The mistake
Scores 4, 0 and 5: the mean is 9 ÷ 2 = 4.5.
Instead
The 0 still counts: 9 ÷ 3 = 3.
Why: A score of zero is still one of the values, so it counts in 'how many'.
Where it comes up in the 11+
Find a mean, or work backwards to a missing value: mean × how many = total.
The video
Video coming soon
We're making a short video that explains the mean step by step. Until then, everything it covers is on this page.
Free printable
The mean worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
Download the worksheet (PDF)Free account needed: it takes a minute.
Quick quiz
Have a go first, then tap to see the answer.
1. What is the mean of 3, 5 and 10?
- 5
- 6
- 18
- 7
Show the answerHide the answer
6
3 + 5 + 10 = 18, and 18 ÷ 3 = 6.
2. What is the mean of 2, 0, 7 and 3?
- 3
- 4
- 12
- 2
Show the answerHide the answer
3
2 + 0 + 7 + 3 = 12, and there are 4 values: 12 ÷ 4 = 3.
3. Four children have a mean age of 10. What is their total age?
- 14
- 40
- 2.5
- 10
Show the answerHide the answer
40
Total = mean × how many = 10 × 4 = 40.