There have been well known claims about sex differences in intelligences: men have IQs higher by several points in adulthood, that men have greater variance in IQ (more geniuses, but also more stupid men), better visuo-spatial skills, etc.
More recent studies have shown that there is no difference in general cognitive ability (g) between men women, and the apparent emergence of a gap during the teenage years in some studies was a result of study designs and samples, not real population differences (see Deary’s 2012 ‘Intelligence’ review).
The question of greater male variance in IQ is interesting, because, within populations that variance has been quite consistent. From a 2012 global study on math achievement:
The VR [variance ratio] measured for any given nation was quite reproducible, that is, it rarely differed by more than 20 percent from one test administration year to the next, among students in different grades, or between the PISA and TIMSS; typically, it differed by at most 10 percent…
However, while it is consistent within nations, it is very different across nations:
Here’s a list of countries and their variance ratios (boy’s variance / girl’s variance):
From this they conclude:
… that both variance and VR in mathematics performance vary greatly among countries. Confirming our earlier finding (), we also conclude that VR is reproducibly essentially unity for some countries. These findings are inconsistent with the greater male variability hypothesis
They also point out the issue of the influence of sampling in causing differences in variance, similarly to how sampling issues seems to have been the cause of the erroneous findings of men having higher IQs – at least in explaining certain countries, such as these:
On another note, in Iran apparently 70% of science and engineering students are women (source)