Why do men have greater variance than women in mental test scores? Hedges and Nowell (1995) write that 


  Sex differences in central tendency, variability, and numbers of high
  scores on mental tests have been extensively studied. Research has not
  always seemed to yield consistent results, partly because most studies
  have not used representative samples of national populations. An
  analysis of mental test scores from six studies that used national
  probability samples provided evidence that although average sex
  differences have been generally small and stable over time, the test
  scores of males consistently have larger variance. Except in tests of
  reading comprehension, perceptual speed, and associative memory, males
  typically outnumber females substantially among high-scoring
  individuals.


However, they don't really say anything about the reason for this aside from that "Our results shed little light on the origins of sex differences in [...] variability" (p45).

What theories are there of the reasons for this sex difference in variability on mental tests, and how strong is the evidence to support these theories?
I've heard two theories related to genetics. Mental traits are massively polygenic (many genes with tiny effects). Men (XY) do not have a duplicate X chromosome like women (XX), which means that mutations to an X chromosome that disrupt typical gene expression can affect men more than women, driving variance in mental scores. The second theory is related to the fact that individual men are less likely to pass on their genes than individual women. Counter-intuitively, most of our ancestors are women. Men may have evolved a riskier genetic strategy that produces more high and low cognitive scores in phenotypes. Consider that men also take more risks. This is a behavioral outcome that may have emerged from the same selection pressure.

See also:

https://en.wikipedia.org/wiki/The_Bell_Curve

https://www.amazon.com/Intelligence-That-Matters-Stuart-Ritchie/dp/1444791877