If, as Mark Twain claimed, statistics enable the worst kind of lies, then at least statisticians manage to find the funny side. Take the following cracker from a 2002 paper on using humour to teach the subject. While deer hunting, three statisticians spot a big buck and take aim. One shoots his arrow but misses by three metres to the right. The second fires his arrow, again wide of the mark, this time three metres to the left. To which the third statistician excitedly cries: “We got him! We got him (on average)!"
There are plenty of variations on the same theme. One finds a statistician with his feet in a bucket of ice and his head in an oven, who reports to “feeling just fine, on average”. In another, a statistician drowns while crossing a stream that was, on average, just six inches deep. Each joke underscores an important point about what different kinds of averages omit. For an average to have meaning, we need to know how representative it is.
Does it look like most outcomes? Almost everyone has a body temperature within a couple of degrees of the human average, for example. Or precisely none? The mean average dice roll, after all, is 3.5. More to the point, what does an average disguise? On average, Ocado (OCDO) shares have climbed 3 per cent a year since the start of 2019 but are down 61 per cent over the same stretch.