# “Facts are stubborn things, but statistics are pliable” – Mark Twain

There is no denying that Auckland’s property prices have been rising rapidly.  What really gets to me though is the way that the media use statistics in their stories – in particular interchanging ‘median’ and ‘average’ in relation to house prices and incomes.

To illustrate my frustration here are a couple of definitions, and an example..

An average is calculated by adding all of the values in a sample together and dividing by the sample size.

The median is the middle figure if all of the values in the sample are listed in order (either ascending or descending – it doesn’t matter).

For example, let’s say you have 11 recent house sales (in \$) in your set of data.

The figures are:

From this set of data, you can see that the middle figure is \$803,000.  This is the median.

To calculate the average, all 11 figures are added together and then divided by 11.  In this example, the average is \$1,072,545.

So, if you were writing a story and wanted to make it sound more dramatic, you could choose the average, instead of the median.

Using the average is misleading though when the data includes a range of prices from \$482,000 up to \$2,710,000.

Just bear this in mind when reading alarmist media reports on rising prices.  Yes, prices are rising, but if a few very expensive houses sell during a month, then the average for that month is going to rise a lot faster than the median, so be sure to pay attention to which statistic the author has chosen to use.

A very large (or very small) piece of data added to your sample will skew the average up (or down), but because the median is simply the middle number, it is not affected to the same extent.

For example if we add a couple more property sale prices to the above example, say \$600,000 and \$3,000,000, the median is still the middle number, so stays at \$803,000, but the average is now \$1,184,462!  The media love this because they can hype everyone up with the rapid increase in prices by using the average, rather than the median.

Often average income is referred to too, and this makes people feel miserable because they don’t earn the ‘average income’.  The average does not mean that half the people earn above and half earn below that figure (that is the median), the average income is hugely affected by CEO’s and other very high income earners, whereas the middle figure (median) is much lower.

“There are three kinds of lies: lies, damned lies and statistics” – Mark Twain