coolharvard is right, "average" is not a useful way of making education decisions.
In particular, a given individual is a mix of talent levels, and education after 18 is largely specialising on the areas that students seems to be good at.
The correlation between 'raw' intelligence between generations is suprisingly small, enough that left wing people try to pretend it does not exist at all.
But correlations between educational outcome between generations is huge.
An interesting fact is the way that the educational level of the mother seems to be the best single predictor of the children's level, and that remains true across pretty much every country.
I suspect that does not surprise many people, although the way that it outweighs parental income as a factor upsets some people.
My own wife is an Oxford educated partner in a huge law firm, and we thus have very smart kids.
But note that I pedantically used the word "predictor", rather than "cause". since an educated mother also correlates with income, and more highly educated mothers are less likely to have issues like being a single parent. My kids see going to a top university as inevitable, because we have set that expectation, and their school environment supports that.
But many kids not only have less scholastically inclined environments, a mix of peer pressure, crap schools, and lack of parental interest mean that the talents of many smart kids are wasted.
In the worst cases some kids are 'homeschooled' where uneducated morons 'teach' the subset of their ignorance they are "comfortable" with.
I can't really form a strong opinion on positive discrimination, but if you wish to do it effectively, then income is not the factor you need to compensate for, but instead you need to discount for mothers, and to a lesser extent fathers.
Although the stats upon which I base this analysis aren't seriously questioned, it is possible that I am literally the only person advocating that position.
That's because positive discrimination is driven by lobbies, and so it is utterly impossible for a skew that works against the interests of educated women could get enough support that the lobbies would even bother to attack it.
I often see these things in terms of 'tests', that allow one to be objective.
A rational scheme of positive discrimination would discriminate against my family, with two white grads from decent schools, private education for the kids, and living in a nice area.
If you look at most of the lobbies in that area, you quickly see that they want stuff for people like themselves.