Line graphs, the mean and pie charts · Usually met around P6
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 there are: 12, 15, 21 → 12 + 15 + 21 = 48, 48 ÷ 3 = 16. When the data are in a table, read each item first, then do the same. A quicker way is to guess, then let what's over and under cancel out. Guess 15: 12 is 3 under, and 21 is 6 over. 6 − 3 = 3, 3 ÷ 3 = 1, 15 + 1 = 16. To find a missing number, go backwards. 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 and 19 is 4 over, so it's 1 over in all. That means ? 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 7, 27, 14 = ?
Show the answer and working
Answer: Mean of 7, 27, 14 = 16
Mean = total ÷ how many: 7 + 27 = 34, 34 + 14 = 48, 48 ÷ 3 = 16
Example 2
Mean of 62, 61, ? is 54
Show the answer and working
Answer: Mean of 62, 61, 39 is 54
The total must be mean × how many, then take the numbers given: 54 × 3 = 162, 162 − 62 = 100, 100 − 61 = 39
Example 3
Mean of the skips = ?
Show the answer and working
Answer: Mean of the skips = 19
Mean = total ÷ how many: 15 + 18 = 33, 33 + 27 = 60, 60 + 16 = 76, 76 ÷ 4 = 19
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