Simple Average

There's an old joke about a statistician that kept his feet in an oven and his head in a freezer because the average temperature was comfortable!

Cairo (2019) also shares an old saying: "whenever Bill Gates participates in a meeting, everyone in the room becomes a millionaire, if we take the arithmetic mean of the group’s wealth"¹.

And from Spiegelhalter (2019): "Interpreting the term ‘average’ as the mean-average gives rise to the old jokes about nearly everyone having greater than the average number of legs (which is presumably around 1.99999)"².

Mean Or Median, Why Does It Matter?

A mean is simple: simple to understand, but also easy to take off course. Take this example:

House prices have a very skewed distribution. [...] But these are generally reported as the 'average house price', which is a highly ambiguous term. Is this the average-house price (that is, the median)? Or the average house-price (that is, the mean)? A hyphen can make a big difference.

In other words, is it the price of the average house (i.e. the median house price), or the average price (simple average)?

Source: David Spiegelhalter. The art of statistics: Learning from data. Penguin UK, 2019. [B042]

Sources

¹: Alberto Cairo. How charts lie, 2019. [B040]

²: David Spiegelhalter. The art of statistics: Learning from data. Penguin UK, 2019. [B042]