## Welcome to H3 Maths

Blog Support for Growing Mathematicians

### Average is anything but

April4

A group of 5 students were comparing how much they earned over the weekend. Here are the results:

Jed \$55 (mowing lawns)
Sarah \$30 (pocket money)
Squid (not his real name) \$0 (sad face)
Ginger \$20 (thanks auntie)
Tim \$225 (thanks eBay)

Squid (he has always loved math) said, “Wow, the average earnings was \$66‘” which made Jed, Sarah and Ginger rather sad too. “But,” replied Tim, “the median amount was \$30.” That made Jed and Sarah feel much better.
H3 Comment: What a big difference between the ‘average’ and ‘median’. The average is distorted by the large amount of money that Tim made, while the median (middle of ranked earning) is much closer to a measure of the middle.

Now, let’s apply this to a news article that came out of some real estate figures in Auckland, New Zealand this morning:

The Auckland property market has regained some of its momentum in March, says the city’s largest real agency, citing sales numbers that are almost doubled from February. The average sales price at \$931,673 for March and the median price at \$836,000 also showed a marked increase on those in February,” says the real estate agency’s managing director, Peter Thompson. (see full article here)

That is a whopping difference of over \$99,000 between the average sales price and the median sales price. What happened? Just like the example involving the 5 students, in the case of Auckland house prices (now among the highest in the world) there were some large sales that skewed the data. If you were a buyer you could be misled if you were given the average figure as an indicator of the ‘middle’ value of properties being sold. The median is a better medium to use!

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