The Mean Average: Total ÷ Count

S5The Mean

Share it out equally: total ÷ count.

The mean is the equal-shares average: add everything, divide by how many.

Four friends' goals: 4, 7, 6, 3.

4 + 7 + 6 + 3 = 20

20 ÷ 4 = 5

Shared equally, that's 5 goals each — the mean.

Mean = total ÷ how many values.

Learn the 3-Step Method

1Add all the values.

4 + 7 + 6 + 3 = 20.

total 20

2Count the values.

There are 4 numbers.

count 4

3Divide total by count.

20 ÷ 4 = 5. The mean is 5.

20 ÷ 4 = 5

💡 Key IdeaReverse trick: if the mean of 5 numbers is 6, the total must be 30 — mean × count = total. Exams love this backwards step.

Worked Example

Jo's test scores are 8, 5, 9 and 6. After a fifth test her mean is exactly 7. What did she score in the fifth test?

Total needed

5 × 7 = 35

→

Total so far

8 + 5 + 9 + 6 = 28

→

✓ Fifth score

35 − 28 = 7

Watch Out! Common Mistakes

Dividing by the wrong count.

(4+7+6+3) ÷ 3 = 6.67 ✕

Count the values! Four numbers → divide by 4: mean 5.

Mean must be in the list.

Not true! The mean of 4, 7, 6, 3 is 5 — and nobody scored exactly 5. The mean is a balance point, not a member.

Forgetting mean × count = total.

The reverse step! ‘Mean 6 of 5 numbers’ hides the fact the total is 30 — most missing-value questions start there.

⬇ Cheat Sheet

THE MEAN

Mean = total ÷ count.
Add every value; count every value.
Reverse: total = mean × count.
Missing value = needed total − current total.

Examples: 4,7,6,3 → 20 ÷ 4 = 5 · mean 7 of 5 tests → total 35.

📖 Continue Your Journey

✓ S1 Tally Charts and Pictograms ✓ S2 Bar Charts ✓ S3 Line Graphs ✓ S4 Pie Charts S5 The Mean S6 Median, Mode and Range S7 Two-Way Tables S8 Venn and Carroll Diagrams S9 Probability Basics S10 Statistics Problem Solving

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Next Lesson: S6 Median, Mode and RangeMiddle, most common, spread.

📄 Free printable: Download the The Mean cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Mean = total of the values ÷ how many values.
4, 7, 6, 3 → total 20, count 4, mean 5.
Backwards: total = mean × count — the key to missing-value questions.
The mean needn't equal any actual value in the list.

Frequently asked questions

How do you calculate the mean?

Add all the values, then divide by how many there are: for 4, 7, 6 and 3, the total 20 divided by 4 gives a mean of 5.

How do you find a missing value from the mean?

Multiply the mean by the count to get the required total, then subtract the values you know: mean 7 across 5 tests needs 35; scores of 8+5+9+6 = 28 leave 7.

Is the mean the same as the average?

'Average' usually means the mean in everyday talk, but maths has three averages — mean, median and mode. The next lesson covers the other two.

S6 Median, Mode and Range