I’ve just been reading an engaging book about statistics—The Tiger That Isn’t, by Michael Blastland and Andrew Dilnot—and it’s got me thinking a little harder, as statistics always ought to, about familiar things I thought I already knew everything about.
For instance, how much do you think the mean national income was in the UK, after tax and benefits, for two childless people living as a couple in 2005/6? I’m willing to bet that many will be surprised by the answer, which is £23,000—equivalent to £11,500 each (most people I’ve tested thought it would be higher). Still, statistics are often surprising, and the wise reader learns to expect this. What’s much more interesting is just how limited this mean is as an index of national incomes.
Blastland and Dilnot use the analogy (made famous by the Dutch economist Jan Pen) of a procession of the world’s population, in which people are exactly as tall as they are wealthy. Within this procession, a person of average wealth will also be of average height; remembering that height is a measurement for which the mean is a useful index, as it roughly follows the “normal” distribution of a bell-curve. Global wealth is such, however, that it is not until 80% of humanity have walked diminutively past that you first see a person of average height. Then, in the last few minutes, giants stride into view, each one many miles high, dragging the mean inexorably towards them.