From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997

Introduction to 'Measures of Location'

So you think teaching about the mean, median and mode are boring? Well, maybe, but there are some interesting little side alleys to this topic that are worth exploring.

Before I go into detail on these, I must say I was intrigued to see that the topic of finding an average in Statistics, Concepts and Controversies by David S. Moore is delayed until page 237! This illustrates two very important points - calculating summary statistics is a waste of time until the user decides what is important about the data and which summary statistics may be useful. Well maybe that is only one important point.

Which Average?

The choice of measure of location requires understanding of the properties of each measure. The A Rather Average Worksheet contains three nice problems on this topic.

Simpson's Paradox

Have you ever noticed that a government can give tax cuts to the population and still earn more money than ever before? Did you realise that it is possible for Steve Waugh to have a better batting average than his brother Mark in each of two Ashes Series and yet have a worse average overall? Read the article Simpson's Paradox to learn about these and other intriguing examples of this phenomenon.

Sex and Dating

The results of a sex survey conducted in the Chicago area gave the average number of lifetime sex partners for men as 6, and for women as 2. This statistic wasn't questioned until someone posting to the rec.puzzles newsgroup asked, 'Hey, is this possible?' Read the article Sex Survey to find out more. Note: you may need to change the context before you introduce this little puzzle to students!

Abolish the Mean!

I once had a clever idea - we can ignore the mean as a descriptor of a dataset and put the entire burden of locating a dataset onto the median. So I told some statisticians about it. If you are interested in their responses read The Mean? Who Needs It!

Finally, did you know that the great majority of people have more than the average number of legs? Amongst the 19 million people in Australia there are probably 2 000 people who have only one leg and no one has three or more legs. Therefore the average number of legs is: (2000 x 1 + 18 998 000 x 2) /
19 000 000= 1.999895. Since most people have two legs...