Both generalizations and statistics have one very limited problem, in that even if they can tell you information about the here and now, they say nothing about the future, for there are simply too many variables.
For instance, using a moshol on this very thread, you may prove which yeshiva is likely to have a boy of higher intelligence, now, but you will never prove where next year’s boys are likely to be. Yet statitistictions do this the whole time, and then turn round and tell us that next year, or by the year 2050 x will happen…
Let’s give a simple example. Every shoe store will sell more weekday shoes than shabbos shoes, for the simple reason that not every body wears shabbos shoes. [let’s talk about children’s sizes where a main reason to buy new shoes is the growth of the foot, rather than wear.] Then let’s say we take into account that the shabbos shoe buyers have gone by 4% in the past year. That will then tell us to stock up on 4% more shabbos shoes. Such a figure however does not take into account, that the next year there may be finiancial difficulties leading people to stop spending money on extras.
Basically, statisticions have made numerous predictions about the world, yet new patterns will always keep emerging and eventually proving them wrong.