11.1.6 Using Different Averages

You have now met three different ways of describing an average value: mean, median, and mode.

For Charlie’s first set of scores:

  • The mean score was 425.
  • The median score was 460.
  • The modal score was 490.

These values are very different, and so it is important that when you meet an "average" value, you find out which average is being used.

For example, suppose a group of five employees in a small company each receive a wage of $500 per week and the director receives $3500 a week.

The mean wage is: equation sequence five postfix multiplication dollar 500 postfix plus dollar 3500 divided by six equals dollar 6000 divided by six equals dollar 1000.

However the median (and also the modal) wage is $500.

Adobe PDF IconTo see how the median and mode were calculated take a look at this pencast (click on “View document”).

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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 $500 per week,” whereas the director might say, “The average pay is $1000 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 cause!

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 is spread will provide you with additional information that will shed more light on average value that you are given.

We are now going to look at the spread or range of a data set.

11.1.5 Finding the Mode of a Data Set

11.1.7 Measuring the Spread of a Data Set