The average (arithmetic mean) reached its modern central position in statistics via two distinct paths.
One came via astronomy, when its practitioners realised that the best estimate of any measured astronomical quantity was given by the average of all available measurements. This had the added advantage that they didnt have to argue any more about whose measurements were best.
In this sense the average represents the true value of what we are trying to measure.
The social statisticians of the C19th were more interested in the variability of the human condition. But how do you measure variability?
It seems obvious that you need a fixed point from which to measure the individual differences. And it turns out that all sorts of useful mathematical results follow if you choose the average as that fixed point.
Nobody suggests that the average man represents some kind of truth, that a man ought to be 1.75m with a BMI of 22.5, an IQ of 100 & earnings of £25,000 a year.
Medicine however can seem confused about this. Does scientific medicine involve assuming that averages represent truth - the gold standard of treatment? Or, if not, how do the standards of science apply to those pesky & infinitely variable things called patients?
The Sumerians would have been dissatisfied with an explanation that smoking caused the death of a patient from lung cancer. OK, so smoking causes lung cancer, but why him, why now?
Just because Aristotle claimed that no systematic knowledge of them is possible, does that mean doctors are condemned to treat individuals forever as mere exemplars of a class?
