Averages

There’s a Russian proverb about the uselessness of blind averaging: “Ñ?реднÑ?Ñ? температура в больнице 36,6!” It means “the average temperature in the hospital is 36.6!”

This is probably best visualised as a cartoon where a Soviet bureaucrat is reporting this proudly to a Soviet superintendent while saluting him. In the background there would be two beds: one with a patient that has a very high fever and one with a corpse giving the 36.6 average. [Aside: in Soviet medicine and probably in former Soviet countries today what was considered normal body temperature was very exact: 36.6 -- and even 37.0 was/is taken to be a sign of fever.]

This joke is there to remind people that the differences matter — and in many situations the actual spread of values is much more important than an average (which can be very misleading). This is what the site GapMinder.org is all about: letting us see the “vital stats” of each individual country, or even different regions. One of the aims is to show concepts like third world for the simplistic bits of claptrap they are. And it works great.

They’ve recently released a special Powerpoint about life expectancy which I recommend viewing. It was made as teaching material for secondary schools but the sad thing is that most of us (including me) need to see this. Life expectancy is something that’s particularly prone to the problem of averages. In Japan it’s 82.6, in Swaziland 31.88. This does NOT mean that Japanese people live an amazing 2.6 times longer than people in Swaziland. This does not mean that there are no old people in Swaziland (although there are much fewer). Differences in life expectancy are most dramatically affected by the percentage of children who die before the age of 5. That’s the main hurdle, and those who make it to the other side can often expect to live to say 50 or 60. Which isn’t great by the standards of developed countries but it is much better than the misleading average of 31.88.

There is a further problem with averages. Because I have cognitive biases, when I look at a table and see Swaziland=31.88 my brain can’t help but picture a 31 year old dying as if it’s a typical example. By having this image planted in my mind subconsciously I may be less likely to think of (say) infant vaccinations as the preventative measure that will increase life expectancy the most. Our brains are bad enough at dealing with numbers — we should not finish the job by accepting simplified averages where they are completely misleading.