## Australia: Cyclones go up to Eleven!

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..

Follow @telescoper
October 14, 2013 at 2:41 pm

Regarding your previous post on

Elektra, I cannot help but point out that Orestes is associated with the key of d minor, the saddest of all keys. What a coincidence. (You’re good, but notthatgood.)October 14, 2013 at 3:02 pm

Apparently there was some discussion at the time that the anti-electron should not be called the positron, but the oreston…

October 14, 2013 at 6:42 pm

When labour market economists and trade unions refer to average wages they nearly always mean male median earnings.

That is why lots of people earn less than this. By definition half of all men earn less than this. And because we still have a big gender pay gap in the labour market way more than half of all women earn less than this.

October 14, 2013 at 8:39 pm

The important thing is not the fraction earning less than the mean, but rather the he difference between the mean and the lowest (and perhaps between the mean and the highest) and, of course, whether the lowest wage is sufficient.

October 14, 2013 at 6:49 pm

Actually they use a mixture of mean and median, and also talk about the “wage of an average person” to add confusion. By definition 50% of the population earns less than the median wage for that population; the fraction earning less than the average (or mean) wage is much higher.

October 14, 2013 at 9:51 pm

I did say “labour market economists and trade unions” – and they nearly always use the Office of National Statistics (ONS) Annual Survey of Hours and Earnings (ASHE) as the baseline data. This does refer to median earnings. But as I said most (sensible) labour market economists will refer to male median earnings.

I’m a public sector trade union official and I (and my union) will always use male median earnings as the benchmark for “average earnings” as it prevents the distortion of the picture by excessively small or large outliers. To be fair even most right wing economists accept the use of median earnings as the best measure.

There is no doubt journalists mangle up the uses of averages when they report things (as they tend to do when they report science or anything that is not arts and humanities based). My own experience of seeing the incorrect use of averages with respect to earning is nearly always in the media. Sometimes if you trace back to the original research that gave rise to the media story you will see the research used the correct terms but the journos mangled it up in search of a good headline.

October 15, 2013 at 8:45 am

It’s a point worth remembering even for rather more complex statistical investigations: e.g. when dealing with random fields the mean field can easily be some kind of unphysical nonsense, in which case you actually want to report the maximum a posteriori. That is, the mean isn’t always a very helpful posterior summary.

October 15, 2013 at 2:44 pm

Yes, there are some probability distributions for which the mean doesn’t even exist.