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Succeed with maths: part 2
Succeed with maths: part 2

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1.5 Using different averages

Suppose a group of five employees in a small company each receive a wage of £250 per week and the director receives £2000 a week.

The mean wage per week equation sequence equals five multiplication pound times 250 plus pound times 2000 divided by six equals pound times 542 (to the nearest pound)

However, if the data are sorted into numerical order as below, it is clear that the median (and also the modal) wage is £250:

250, 250, 250, 250, 250, 2000.

So, if there were a dispute about the employees’ pay in the company, their representative could say ‘The average pay in the company is only £250 per week,’ whereas the director might say ‘The average pay is £542 per week.’

Both statements are technically correct, because neither party has stated the type of average they have used. However, both parties have chosen the average that best suits their case!

So, watch out when you see averages used in future – are you being given all the information you need to know about them?

Knowing what average has been used is very important when you are trying to understand data that you encounter. Knowing something about how the data are spread will provide you with additional information that will shed more light on the average value that you are given. Think about the difference to the mean value, if one value is very high for example.

You are now going to look at the spread, or as it is more usually known, the range, of data sets.