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Calculating the mean from a frequency table

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

Table showing the ages (in whole years) of 30 children on a school bus

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 easy to make an error.

It can be helpful to see these results displayed in a frequency table:

Frequency table showing the ages of 30 children on a school bus

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:

\((6 \times 11) + (7 \times 12) + (5 \times 13)\)\(+ (7 \times 14) + (3 \times 15) + (2 \times 16) = 390\)

The total number of children is \(6 + 7 + 5 + 7 + 3 + 2 = 30\)

So, the mean age is \(390 \div 30 = 13\)

You could also put this information into a table like the one below:

Table to calculate the mean age, by multiplying the age and frequency of 30 children on a school bus

Mean = \(390 \div 30 = 13\)

Question

Find the mean of the shoe sizes of pupils in Mrs Harris’ class:

Frequency table showing shoe sizes, and frequency
Table to calculate the mean of the shoe sizes of pupils in Mrs Harris’ class

Mean \(= 108 \div 20 = 5.4\)

Notice that the mean value does not have to be a whole number or an actual shoe size.