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​What's the difference between the mean, median and mode? Why are there so many different types of average?!

The average we're all familiar with is called the mean average - "add them all together and divide by how many there are", but sometimes another type of average makes more sense.

As an example, consider a company with 8 employees, earning the following amounts per week.

£200
£220
£250
£280
£300
£350
£400
£6,000.

For the mean average, we add them all together (to give £8000), then divide by how many there are (8 of them), to give £1000 a week - this is the mean average weekly wage of the company, but all but one of the employees earns less than this, the average is skewed (messed up) by the boss who gets way more money than everyone else!

For the median average, we list the amounts in ascending or descending order (conveniently, this has already been done), then select the middle salary. Since there are an even number of employees, there are two values which are both equally in the middle - £280 and £300 - so we take a (mean!) average of those two. The median average is £290 a week.

In this case, the median average (£290/week) gives a better idea of the wages of a typical employee, compared with the mean average (£1000/week).

The mode average is usually used when data are in categories, such as shoe sizes, and is simply the category which occurs most often.

For example, here is a table of shoe sizes and frequencies for a class of 27 year 11 pupils.

Size    |    frequency
 6        |    2
 7        |    3
 8        |    4
 9        |    8
10       |    5
11       |    4
12       |    1

the mode is simply the category which occurs most often, in this case the shoe size 9, with 8 people in the class having that shoe size.

John H. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

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