Indeed, here is the binomial theorem with the reductions made:
(a+b)10 = a10+10×a9b+ ((10.9)/(2))a8b2+ ((10.9.8)/(2.3))a7b3+ ((10.9.8.7)/(2.3.4))a6b4+ ((10.9.8.7.6)/(2.3.4.5))a5b5+ ((10.9.8.7)/(2.3.4))a4b6+ ((10.9.8)/(2.3))a2b7+ ((10.9)/(2))a2b8+10×ab9+b10.
And after calculating the coefficients, we obtain the following numbers in a symmetrical series:
- 10
- 45
- 120
- 210
- 252
- 210
- 120
- 45
- 10
This is why the curve of Quétélet is called binomial.
Let us assume that we wish to represent by means of Quétélet's curves, two seriations, for instance in regard to the stature of children of the same race, sex and age, but of opposite social conditions: the poor and the rich.
These two curves of Quétélet's, provided that they are based upon an equal and very large number of individuals, will be identical, because the law itself is universal. Only, the curve for the rich children will be shifted along toward the figures for high statures, and that for the poor children toward the low statures.
