Stage 12 · Data handling
The mean
Total ÷ how many.
How to do it
Method
Total ÷ how many
12, 15, 21: (12 + 15 + 21) ÷ 3 = 16
Another way
Total ÷ how many
12 + 15 + 21 = 48, 48 ÷ 3 = 16
In full
The mean is the total ÷ how many: 12, 15, 21 → 12 + 15 + 21 = 48, 48 ÷ 3 = 16. When the data are in a table, read each item first, then work the same way. A quicker way is to guess, then let what's over and under cancel: guess 15; 12 is 3 under, 21 is 6 over, 6 − 3 = 3, 3 ÷ 3 = 1, 15 + 1 = 16. Back the other way, the number missing: the mean of 12, 19 and ? is 15, so the total must be 15 × 3 = 45, and 45 − 12 − 19 = 14; or by cancelling: 12 is 3 under, 19 is 4 over, 1 over in all, so ? is 1 under 15: 14.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Mean of 8, 29, 20 = ?
Show the answer and working
Answer: Mean of 8, 29, 20 = 19
Mean = total ÷ how many: 8 + 29 = 37, 37 + 20 = 57, 57 ÷ 3 = 19
Example 2
Mean of the books = ?
Show the answer and working
Answer: Mean of the books = 15
Mean = total ÷ how many: 7 + 24 = 31, 31 + 12 = 43, 43 + 17 = 60, 60 ÷ 4 = 15
Example 3
Mean of the buns = ?
Show the answer and working
Answer: Mean of the buns = 30
Mean = total ÷ how many: 31 + 19 = 50, 50 + 34 = 84, 84 + 36 = 120, 120 ÷ 4 = 30
Example 4
The mean is 32: Hiu Ching = ?
Show the answer and working
Answer: The mean is 32: Hiu Ching = 18
The total must be mean × how many, then take the numbers given: 32 × 4 = 128, 128 − 42 = 86, 86 − 26 = 60, 60 − 42 = 18
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