The concept in the book that caught the public imagination, and never let go, is that of the average man. Inasmuch as his concept made any sense at all, Quételet was well aware that it was also necessary to consider the average woman, average child and, for various populations, different instances of all of these. He noticed early on that his data for attributes such as height or weight (duly restricted to a single gender and age group) tended to cluster around a single value. If we draw the data as a bar-chart, the tallest bar is in the middle, while the others slope away from it on either side. It presents the characteristic shape of a bell curve, already known to mathematicians, as Quételet acknowledged. The whole shape is roughly symmetrical, so the central peak – representing commonest value – is also the average value. Many types of data show this pattern, and it was Quételet who realised its importance in social science.
Tables and graphs are all very well, but Quételet wanted a snappy summary, one that conveyed the main point in a vivid, memorable manner. So instead of saying ‘the average value of the bell curve for the heights of some class of human males over 20 years of age is 1.74 metres’, he preferred: ‘the average man (in that class) is 1.74 metres tall’. He could then compare average men across different populations. How does the average Belgian infantryman stack up to the average French farmer? Is ‘he’ shorter, taller, lighter, heavier, or much the same? How does ‘he’ compare with the average German military officer? How does the average man in Brussels compare with his counterpart in London? What about the average woman? Average child? Which country’s average man is more likely to be a murderer or a victim? Or be a doctor, devoted to saving lives, rather than a suicide, intent on ending his own? A different average man (or woman or child) is needed for each attribute. As Stephen Stigler put it in The History of Statistics (1986), Quételet considered that ‘the average man was a device for smoothing away the random variations of society and revealing the regularities that were to be the laws of his “social physics”.’