Why the median rent tells you more than the average

Take a hundred flats and add one penthouse at twenty times the going rate. The average rises noticeably and the median does not move at all. For quantities with a long upper tail, the mean answers a question about the total, and the median answers the question people were actually asking.

What everyone sees

The average is treated as the default summary because it is familiar and easy to compute. For symmetric distributions it is a good choice. Rents, incomes, house prices, waiting times and file sizes are not symmetric, and for a skewed distribution the mean sits above most of the observations, which makes it a poor description of a typical one.

What is actually happening

Tukey’s account of exploratory analysis argues for summaries chosen to resist a small number of extreme values, treating resistance as a property to select for rather than a refinement, since a single outlier can move a mean arbitrarily far while the median moves by one rank. Huff catalogued how the choice between summaries is used in practice to produce whichever figure supports a case, noting that the word average alone does not specify which statistic was computed. Neither summary is wrong. They answer different questions, and for a skewed quantity only one of them is close to the value most cases take.

Why it stays hidden

The substitution hides in the vocabulary. Average is used loosely for any central summary, so a mean can be published under a word that most readers interpret as typical. The distribution is almost never shown alongside it, and without the shape there is no way to tell how far apart the two summaries were.