Misleading Averages

There are at least four kinds of averages: mean, mode, median… and the kind that occupy the popular mind. This post is about that fourth one.

‘Average’ does not mean ‘Every’.

There is an infamous public misunderstanding regarding a certain average. It is usually expressed as the ‘average life expectancy’, and comes up when discussing history or, occasionally, foreign aid or mission work. It goes something like this:

The average life expectancy during the late bronze age was 42…

Now, I have no idea, nor do I care, what the average life expectancy during the bronze age was. Indeed it might be necessary to ask exactly where, cause I’m guessing it made a difference. What I am dealing with here is this thought that rummages through people’s head when they hear these words.

Now, let me be clear, I’m not saying that people actually say this, or even that, when they have time to think about it, it is what they think… but I am saying that you can tell, from the way they talk about it, that it is what they assume… what lives in the back of their heads. And that is this image of a bunch of bronze age people looking at one of their number and saying, “Well, you’re 41 today. Super old. Probably be dead sometime this year!”

… and that is not what that means. The ‘average life expectancy’ takes into account, for example, how many children die in infancy. Like, at ‘zero’ years old… just a few days, weeks, or months. So let’s look at some numbers.

Suppose there was a population of a hundred dead people in the bronze age. And half of them died in infancy (zero years old) and the other half died at 75 years old. The ‘average life expectancy’ would be… 37.4 years old. Literally everyone who doesn’t die in their first year lives to 75!

Now, that is not the normal situation… but it is exactly how an ‘average’ works.¹

Average does not mean ‘Exactly’

Now lets look at a similar delusion. Let’s look at… marriage age. It is common to make a comparison between modern and ‘older’ societies when it comes to marriage age. Some people like to use the comparison to emphasise how young people used to be when they would marry.

But then along comes the averagist spouting news about how the ‘average’ person in that age married at… let us say… 21! “There!” they say, triumphantly, “So much for your teenage marriages!”

To which one must reply… “say what?” Because no matter which of the various kinds of average you use, this is nonsense. The ‘average’ age of 21 does not mean people married at 21! Some, sure. But for every 22 year old there was a 20 year old. And for every 23 year old a 19 year old…

And when we get to someone who married at 40… well, no, there wasn’t someone married at 2! There were a whole lot of people married younger than 21 to make up for that old geezer.

Average does not mean Average

The point I am trying to make is that the popular idea of ‘average’ is not represented well by directly porting scientific and mathematical language into the popular press. One cannot merely say ‘The average…” and communicate.

I firmly believe that in order to communicate well in any discussion that requires the use of an ‘average’… an actual scientific average ported over into public discussion, an explanation, not a word or even a phrase, is needed. This will be hard, but is vital to actually communicating. Thus:

In the bronze age, huge numbers of infants died before their first birthday, and life was dangerous even after that. However if you survived your infancy, war, and disease, there was a very good chance you would die in your rocking chair at 70 or even 80 years old…

or

In Elizabethan England the age range for marriages was very different than it is today. Sometimes girls would marry as young as fourteen. But much of that depended on your social situation; and men would hardly ever marry so young.

Etc etc… Which all depends on a much more in depth knowledge of the actual facts of the case… and eliminating a careless use of the word ‘average’. After all, some places in Europe have 1.7 children per couple… but they haven’t invented a way to have 0.7 of a child!

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Von

1. In this case the ‘mean’. The ‘median’ and ‘mode’ would give different answers.