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Measures of average

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# Mean from a frequency table

## Finding the mean from a table

### Example

Sara wanted to know the ages (in whole years) of children on her school bus. She conducted a survey and her results are shown below:

 13 14 11 12 12 15 13 14 12 16 15 11 11 12 11 12 14 16 14 15 14 14 13 12 13 11 11 14 12 13

To find the mean add all the ages together and divide by the total number of children.

If you type all those ages into a calculator it is highly likely that you would make a mistake or forget where you were up to.

It would be better if you could see these results displayed in a frequency table:

Age Frequency
11 6
12 7
13 5
14 7
15 3
16 2

The frequency table shows us that there are six children aged 11, seven children aged 12, five children aged 13...etc.

To find the sum of their ages, calculate:

(6 × 11) + (7 × 12) + (5 × 13) + (7 × 14) + (3 × 15) + (2 × 16) = 390
The total number of children is 6 + 7 + 5 + 7 + 3 + 2 = 30
So the mean age is 390 ÷ 30 = 13

You could also write this information into the table as shown below:

Age Frequency Age × Frequency
11 6 66
12 7 84
13 5 65
14 7 98
15 3 45
16 2 32
Totals 30 390

Mean = 390 ÷ 30 = 13