Averages

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Averages

Averages

You may hear the word 'average' used quite a lot, and not only when people are talking about numbers. If you asked someone how they got on in an exam and they said 'average', they may just mean 'not good, not bad'.

There are more specific sorts of average, three in total:

Arithmetic mean (or mean, or (just to confuse things) average)
Median
Mode

They all have one thing at least in common. They are ways of finding a mid-point in a collection of numbers. So you know that any average is going to be somewhere between the smallest and the largest in the set of numbers you have.

Arithmetic mean

Add up all the numbers you have got, and then divide by the number of numbers you added.

You go into 5 record stores to find the price of a particular CD. The prices you get are 12.99, 10.99, 14.49, 10.59, and 10.99. So the mean is (12.99 + 10.99 + 14.49 + 10.59 + 10.99)/5 = 60.05/5 = 12.01

Median

The median of a collection of numbers refers to the number that is in the middle when you sort them all into order.

Using the example above, we'll first sort them.

10.59 10.99 10.99 12.99 14.49

The middle number of five is the third one along, in this case 10.99.

Mode

The mode of a collection of numbers is the one that occurs most often. If you were going to manufacture shoes and only wanted to make one size what would it be? If you calculated the mean of the shoe size of the population you might end up with a size that actually fitted no one. Whereas if you calculate the mode, you have at least some people that they'll fit perfectly.

In our example above the mode is 10.99 as it occurs twice.
So now you can have a go at the Quiz.

University of Westminster
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