# 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:

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:

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:

Mean = $$390 \div 30 = 13$$

Question

Find 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.