Averages are used in lots of situations: batting averages in cricket, wages and salaries, road speed (er sorry, safety) cameras. They’re taught in school as basic maths. Take several measurements, add them up and divide by the number of measurements. Mathematicians call it the mean. For example, take a sweet manufacturer who sells boxes of chocolates. Each box is marked ‘average contents 10’. The manufacturer checks 10 boxes and records the contents.

Sweets per box

11

10

10

10

10

10

10

10

10

9

Total 100

Mean 10

The advantage of using the mean is its simplicity. The drawback is that this simplicity can hide knowledge from us. Take this example:

Sweets per box

25

16

9

23

10

10

2

2

2

1

Total 100

Mean 10

Here the data has the same mean, but the data points are spread very differently. Compare the maximum and minimum values in each of the examples. Note the number of 10s in the first example and how few there are in the second.

So, in these very simple examples would you prefer to buy a box of chocolates from example 1 or 2. In the first you will get 9, more likely 10, but may be eleven. But in example 2 you might be lucky and get more than 20 or unlucky and get only 2. If you only got 2 sweets I suspect you wouldn’t be very happy.

Averages only tell part of the story and can hide the bigger picture.

This is the danger of using averages.