I'm super confused by this reply. The article says that the stddev of the distribution of male IQ is larger than the stddev of the distribution for female IQ, and also seems to state the mean and median are equal. GGP threw out 60/40 as their believed split of men to women being good engineers. I took this to mean that GGP was saying he believed engineering talent to be independent of gender when IQ was present, and that engineering required a higher than average IQ. More formally:

  P(good engineer | IQ) * P(IQ | gender) == P(good engineer | gender)

In that model the 60/40 split comes from a conditional distribution of gender given an IQ above some threshold. So something like:

  julia> women = sum([randn() > 1 for i=1:10_000_000])
  julia> men = sum([(randn() * 2) > 1 for i=1:10_000_000])
  julia> women / (women + men)
  0.3395449535000696

Which isn't exactly 60/40, but is fairly close. It says that [iff the 60/40 split is true], the stddev difference needed is less than 2x.

If you prefer exact math, the ratio above is

  erfc(1/sqrt(2)) / (erfc(1 / (2 * sqrt(2))) + erfc(1 / sqrt(2))) =~ 0.339593

and the exact solution for a 60/40 split is

  1 / (sqrt(2) * inverseerfc((3/2) * erfc(1/sqrt(2)))) =~ 1.4

Though FWIW I find the simulation version more intuitive (likely because of a misspent youth programming rather than a misspent youth mathing :p).

Can you explain the model you were using to motivate the mean vs median calculation? I feel like I'm missing something interesting.