Archive for October 14, 2013

Australia: Cyclones go up to Eleven!

Posted in Bad Statistics with tags , , , , , , , on October 14, 2013 by telescoper

I saw a story on the web this morning which points out that Australians can expect 11 cyclones this season.

It’s not a very good headline, because it’s a bit misleading about what the word “expected” means. In fact the number eleven is the average number of cyclones, which is not necessarily the number expected, despite the fact that “expected value” or “expectation value” . If you don’t understand this criticism, ask yourself how many legs you’d expect a randomly-chosen person to have. You’d probably settle on the answer “two”, but that is the most probable number, i.e. the mode, which in this case exceeds the average. If one person in a thousand has only one leg then a group of a thousand has 1999 legs between them, so the average (or arithmetic mean) is 1.999. Most people therefore have more than the average number of legs…

I’ve always found it quite annoying that physicists use the term “expectation value” to mean “average” because it implies that the average is the value you would expect. In the example given above you wouldn’t expect a person to have the average number of legs – if you assume that the actual number is an integer, it’s actually impossible to find a person with 1.999! In other words, the probability of finding someone in that group with the average number of legs in the group is exactly zero.

The same confusion happens when newspapers talk about the “average wage” which is considerably higher than the wage most people receive.

In any case the point is that there is undoubtedly a considerable uncertainty in the prediction of eleven cyclones per season, and one would like to have some idea how large an error bar is associated with that value.

Anyway, statistical pedantry notwithstanding, it is indeed impressive that the number of cyclones in a season goes all the way up to eleven..