# 11.8.1 Self-Check on Averages

## Exercise 1: Finding the Mean and the Range

Ten children in a class measured how tall they were and want to work out their typical height.

Work out the mean height and range for these 10 children from these measurements:

134 cm, 140 cm, 164 cm, 136 cm, 143 cm, 152 cm, 150 cm, 155 cm, 149 cm, 160 cm.

So the mean height of children in the class is 148.3 cm (to 1 d.p.).

Range = Highest value – lowest value

= 164 cm – 134 cm

= 30 cm

So the range of heights for the 10 children is 30 cm (about 1 foot)!

## Exercise 2: Finding the Median Value

Using the data from exercise 1 work out the median height for the class.

Arranging all the values in ascending order:

134, 136, 140, 143, 149, 150, 152, 155, 160, 164

We have 10 values so need to calculate the mean of the middle two to find the median.

So mean of middle two values = = 149.2 cm.

So the median height for the class is 149.2 cm.

In this case the values are quite close.

## Exercise 3: Finding the Mode or Modal Value

The remaining 10 children in the class were then measured giving a complete set of values.  Find the mode or modal value/s for the height.

134 cm, 140 cm, 164 cm, 136 cm, 143 cm, 152 cm, 150 cm, 155 cm, 149 cm, 160 cm, 134 cm, 144 cm, 147 cm, 150 cm, 154 cm, 162 cm, 144 cm, 142 cm, 153 cm, 130 cm.