There is an even bigger issue: personal preference.

You could argue that women have slightly lower maths ability on average, and lower variance, so that men are over-represented in both the highest and lowest percentiles of aptitude. But when you do the numbers, this does not come close to explaining why so few women are in engineering. One answer is that they have different interests, different preferences (on average).
      But there is another: If we do accept maths aptitude differences, we might expect something like 30% of those top technical minds to be female. But in other fields of ability, those selected women are going to score more highly on average than the men. You are comparing, say, the top 1% of women to the top 2% of men. That minority will make better doctors, better lawyers, better scientists or managers, on average, than their male engineering counterparts. Engineering is competing with other fields for the top people.
      So the proportion of women in engineering will be *even lower* than a simple population aptitude would predict. The 30% becomes 20%, or 10% by such competition that values verbal skill more highly. And that is even before you take personal preference into account.

      I'm not American, so I will not pretend to understand your race issues, but I'd hazard a guess that while IQ differences are greater than for gender, differing personal choices still matter more than differences in ability, even at the extremes of IQ that we are talking about here. And there is nothing to be gained by big corporations fighting that with "diversity policies" and quotas.

    How about just accepting that real diversity and freedom means we make different choices?

I'm not familiar with the US specifically, but that is to be expected if blacks have higher crime rates. For example, a black man is more likely to be a repeat offender than a non-black charged with the same crime. (I'm not saying there is no racism, just that your numbers are no evidence of it.)

There are many correlates. You might as well ask Bill to control for sunscreen consumption, or which magazines they subscribe to. Are you suggesting education level has a direct causal effect on sentencing?? But a quick search says black males have much higher crime rates even controlling for education or IQ.