I have a pet gripe (well quite a few actually but I’ll stick to one at a time) about people using and misunderstanding ‘average’. I often hear talk about ‘average wage’ and concerns about ‘below average GCSE results’. Generally when people talk about ‘average’ they are referring to the ‘mean’ but as this is not usually explicit, the conclusions drawn from the data can be misleading as by definition 50% of the values are below the mean and 50% are above it!
There are three types of average measure; the ‘mean’ the ‘median’ and the ‘mode’.
- The Mean
- The Median
To find the median, you put the values in order, then find the middle value. If there are
two values in the middle then you find the mean of these two values.
two values in the middle then you find the mean of these two values.
- The Mode
The mode is the value which appears the most often in the data. It is possible to have more than one mode if there is more than one value which appears the most.
The best illustration of how misleading averages can be is to calculate the average number of legs people have.
If you calculate the ‘mean’ then on average people have fewer than two legs! This is because some people have one leg,
some have no legs but apart from ‘Jake the Peg’ the famed tri-dexter revealed by the incomparable Rolf Harris, none has more than two.
some have no legs but apart from ‘Jake the Peg’ the famed tri-dexter revealed by the incomparable Rolf Harris, none has more than two.
A better result is obtained by using either the mode or median which will then deliver the result we’d expect, that on average people have two legs.
So the next time someone bandies about ‘averages’ ask them which one they are using!
