To work out the mean (the arithmetic average) you add up all the numbers in the list, then divide the total by how many numbers there are in the list. For example, the mean of 4, 7 and 10 is (4 + 7 + 10) ÷ 3 = 21 ÷ 3 = 7. That is the only formula you need to remember — everything else is practice.
To work out the mean (also called the arithmetic average) you carry out just two steps: add all the numbers in the list to get one total, then divide the total by how many numbers there were in the list. The formula: mean = (sum of all the numbers) ÷ (how many numbers). For example, the mean of 4, 7 and 10 is (4 + 7 + 10) ÷ 3 = 21 ÷ 3 = 7. That is the only way to work out an arithmetic mean, and every question on the topic is built on those two steps alone.
The formula, step by step
Step 1 — add up all the numbers in the list, without skipping any. Step 2 — count how many numbers there were in the list. Step 3 — divide the total from step 1 by the count from step 2. The result is the mean. Important: the count is how many numbers there are, not the biggest value and not some number from the list.
3 full examples
Example 1 — three numbers: what is the mean of 4, 7, 10? Total: 4 + 7 + 10 = 21. How many numbers: 3. Mean: 21 ÷ 3 = 7.
Example 2 — test scores: a pupil scored 80, 90, 70 and 100 in four tests. What is the mean? Total: 80 + 90 + 70 + 100 = 340. Count: 4. Mean: 340 ÷ 4 = 85.
Example 3 — with a negative number: what is the mean of 5, −3, 8, 2? Total: 5 + (−3) + 8 + 2 = 12. Count: 4. Mean: 12 ÷ 4 = 3. Notice that we added the negative number as usual — a negative number reduces the total, not the count.
| The numbers | Total | Count | Mean |
|---|---|---|---|
| 4, 7, 10 | 21 | 3 | 7 |
| 80, 90, 70, 100 | 340 | 4 | 85 |
| 5, −3, 8, 2 | 12 | 4 | 3 |
| 10, 10, 10 | 30 | 3 | 10 |
Working backwards — when the mean is given and a value is missing
Sometimes you are given the mean and asked to find a missing number. The method: multiply the mean by how many numbers there are to get the total, then subtract the numbers you know. Example: the mean of three numbers is 8, and two of them are 6 and 9. What is the third? The total must be 8 × 3 = 24. The two known numbers add up to 15. The third is 24 − 15 = 9.
Common mistakes when working out the mean
- Dividing by the wrong count — count how many numbers are in the total before dividing, don't guess.
- Leaving out a number from the list — every number has to go into the total, even if it is 0.
- Confusing the mean with the median — the mean is an arithmetic calculation (adding and dividing); the median is the middle number after putting them in order of size.
- Sign errors with negative numbers — a negative number in the list makes the total smaller, but it still counts as one number (you don't skip it).
Summary
Working out the mean is always the same two steps: add up all the numbers, and divide by how many there are. Once you are fluent with those two steps you can find the mean of test scores, temperatures, prices or any other list of numbers. The best practice is to test yourself on short lists (3–4 numbers) until the calculation becomes automatic, then move on to longer lists and the reverse questions where you have to find a missing number. The mean is introduced in Year 6 of the national curriculum and comes up in the KS2 SATs reasoning papers; at KS3 it sits alongside the median, mode and range.
Frequently asked questions
How do you work out the mean?
Add all the numbers in the list to get one total, then divide the total by how many numbers there are in the list. The formula: mean = total ÷ count. For example, the mean of 4, 7, 10 is (4 + 7 + 10) ÷ 3 = 7.
How do you find the mean of just two numbers?
Add the two numbers and divide by 2. For example, the mean of 6 and 14 is (6 + 14) ÷ 2 = 20 ÷ 2 = 10. That is also the number exactly halfway between the two.
How do you work out a mean test score?
Add up all the scores the pupil got, and divide by the number of tests. For example, scores of 80, 90, 70, 100 — total 340, count 4, mean 340 ÷ 4 = 85. If the tests carry different weights (a weighted mean), multiply each score by its weight before adding.
What is the difference between the mean and the median?
The mean is worked out by adding all the numbers and dividing by how many there are. The median is the number that sits exactly in the middle of the list after ordering from smallest to largest. The mean is sensitive to extreme values (a very big or very small number pulls it), whereas the median is not affected by them.
What do you do when the mean is not a whole number?
That is completely fine — the mean does not have to be a whole number. For example, the mean of 3, 4, 5, 6 is 18 ÷ 4 = 4.5. If the question asks for rounding, round as instructed (usually to two decimal places or to the nearest whole number).
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