# The wrong way round

*We seem intuitively to understand the meaning of statistical distributions, but our interpretation can be the wrong way round*

You don’t need to be a statistician to know that there are fewer very small, or very large houses than average-sized ones, or that there are fewer people with a very high or very low IQ, than with an IQ around 100 (which is the average). The size and weight of most living creatures (including us) tend to be distributed such that the more extreme individuals in either direction are less prevalent, whether it concerns humans, frogs, shrubs, cows or blue whales. Even natural phenomena like the flow of a river might be close the average most of the time, with highs and lows more infrequent the further they deviate from the average. In other words, we seem to be intuitively quite familiar with the so-called or normal distribution, if not in its mathematical definition, then at least in its manifestation all around us.

**If extremes are rare, is what is rare extreme?**

This gives us a powerful *heuristic*, a rule of thumb. Provided we have some idea of what the average of a particular quantitative characteristic of a category is, we can judge how prevalent a member of that category is, based on this characteristic. If we know, for…