Do those same statistics hold up when controlling for other factors regarding the split between men and women, though, Putin? I raised the counterfactual with black people in part because it's weighty, but there's a point to it besides making the argument into a gotcha question. Before controlling for other factors, black people are disproportionately more criminal than white people, going by arrest counts (which admittedly is a flawed stat, but the discrepancy is sufficiently wide to address that concern). However, the process of becoming a viable political candidate weeds out the overwhelming majority of people in the process, such that the pool of black political candidates is no longer representative of the entire group. Black political candidates are disproportionately wealthy, disproportionately educated and disproportionately less criminal than black people as an entire group.
The same trend holds for white candidates, female candidates and male candidates. The process of becoming a viable candidate screens out so many people that the pool of candidates is no longer representative of the group from which they came, as far as basic demographic trends are concerned.
Of course I don't mean to argue that black people actually shouldn't be elected because they're disproportionately criminal; nor do I expect you to have to defend that, Putin. I'd simply argue that looking at the prison populations is too simplistic for the argument you're making. A look at why men are in jail would help illuminate why. Men are disproportionately violent criminals; the vast majority of murders, rapes, robberies and batteries are perpetrated by men. You would be very hard-pressed, however, to get elected to office as a murderer, rapist, robber or batterer. This is because we don't elect murderers, rapists, robbers or batterers to office.
There might be an argument pertaining to white collar crime, but that would seem to lead to the curious argument that women make better public officials because structural sexism prevents them from getting into high-up positions in the corporate world and thereby makes them less prone to improprieties assorted with those positions. Furthermore I'm not sure that the actual numbers on white collar crime are disproportionately skewed toward men; I'd imagine at least that corruption in politics isn't disproportionately committed by men (while most cases involve men, that's because most politicians are men).
All this to say that I'm not sure you've controlled for all variables in the men/women public officials argument and that if this argument is to hold, that data would need to be compiled and presented somewhere.