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Many people find statistics confusing for many reasons, not least because of the ways in which they are often presented, as I have tried to show in previous blogs.  To all this there is often added the confusion of the meaning of the terms used, and none is more commonly misunderstood than the word “average”.  The word is used in everyday speech to cover three distinct mathematical concepts, each of which has its uses.  Often it does not matter much as we do not always need to be precise, but when reporting on statistics people really should be clear as to what they are saying.

I will use a simple, made-up, example which I hope will illustrate my point.  Consider this series of values.  They could be anything: incomes, costs, sales, numbers of employees.  Let’s say each represents the value of sales for a different business for a particular month.   It does not matter whether they are in pounds, thousands or millions – unless one of them is your business!

Company.   Sales.

A                     20

B                     25

C                      25

D                     30

E                      35

F                      50

G                     50

H                     50

I                       75

Total               360

The Mean is the simple average obtained by adding all the values in a series and dividing by the number of items.  In this case 360 divided by 9 making 40.

The Median is the middle value, which will have as many above it as below.  As these are set out in ascending order the median will be the middle i.e. company E, the fifth in the list, with a value of 35.

The Mode is the most commonly occurring value.  In this case it is easy to see that value is 50.

In many cases the three averages are the same, as a lot of things seem to cluster around the middle, but as the above example illustrates, they can be very different.  So you could easily find that the majority of people were below the median and/or the mode, as is the case in real life if we look at incomes, although obviously only half of us will ever be below, or above, the mean.