Another thing about variance...

That last post rambled on and somewhat lost it's coherence (me? incoherent? never!), but I did want to point out just one more thing about the effects of differing variances.

Last post was all about how having a greater variance in math ability will lead to gender imbalance as you get further from the mean (which we are assuming is equal, as the evidence would suggest that it is), however all the examples we were dealing with were about going above the mean, that is going towards people who are better and better at math.

But for a distribution that is centered on its mean, (which, once again, the normal is) the exact same thing will happen as you go to the left side of the distribution, that is towards people who are worse and worse at math. You will find the ratio of boys bad at math to girls bad at math skewing more and more towards the boys in exactly the same way you do among those hyper-good at math.

Is this observed? It is! What fun. Why do we never hear people complain about the severe gender imbalances in remedial math courses? Equality for women! We need more dumb girls!

(Relatedly, I always think of this whenever I hear too much complaining about gender imbalances in the "good" jobs and how we never hear about how awful it is that men dominate the "bad" jobs like, just off the top of my head: garbage-man, miner, janitor, felon, prisoner, etc., etc. In fact, did you know that there is a similar gap to the "gender wage gap" among the likelihood to die on the job? Men are significantly more likely to die on the job. So, far from employers being biased against women and showing it by conspiring to keep their wages down, they are actually biased against men and are showing it by literally killing them. Sneaky employers!)