Even more surprising, when Daniels averaged all his data, the average hand did not resemble any individual’s measurements. There was no such thing as an average hand size. “When I left Harvard, it was clear to me that if you wanted to design something for an individual human being, the average was completely useless,” Daniels told me. […]
He decided to find out. Using the size data he had gathered from 4,063 pilots, Daniels calculated the average of the 10 physical dimensions believed to be most relevant for design, including height, chest circumference and sleeve length. These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension. So, for example, even though the precise average height from the data was five foot nine, he defined the height of the “average pilot” as ranging from five-seven to five-11. Next, Daniels compared each individual pilot, one by one, to the average pilot.
Before he crunched his numbers, the consensus among his fellow air force researchers was that the vast majority of pilots would be within the average range on most dimensions. After all, these pilots had already been pre-selected because they appeared to be average sized. (If you were, say, six foot seven, you would never have been recruited in the first place.) The scientists also expected that a sizable number of pilots would be within the average range on all 10 dimensions. But even Daniels was stunned when he tabulated the actual number.
Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions.
Cette histoire est super intéressante, parce qu'elle illustre un phénomène qui ne s'applique pas seulement à la morphologie des gens, mais quasiment à tout: la moyenne, grandeur pourtant utilisée de manière systématique, n'a quasiment jamais de sens …
Un autre exemple que j'aime bien pour illustrer ce phénomène :
Prenez une série de cubes, de largeur croissante : 1cm, 2cm, 3cm, etc. jusqu'à n cm.
Leur volume est donc la suite : 1mL, 8mL, 27mL, …, n³ mL.
Le «côté moyen» vaut (n+1)/2. Donc le volume d'un tel cube vaut (n+1)³/8.
Mais le volume moyen vaut n(n+1)²/4. Il ne peut donc pas y avoir de «cube moyen», qui ait à la fois le volume moyen et le côté moyen !