Women generally test with higher IQs than men overall, within in any population where they have equal access to education. Only in nations where women do not have equal access to education women score lower than men on standardized IQ test. What does that tell you?
I can't post the actual study because you have to pay for it online, but here is an accurate article about it.
There is a theory in anthropology that states that originally, women were in charge of society when our survival hinged on our intelligence. That changed during and after the last ice age where survival became dependent on competition with neighboring tribes. Mankind entered a state of perpetual warfare and the males became the dominant leaders when agrarian societies became the norm. Women roles were slowly subjugated over time. After all, it was easier to just kill your enemy than outsmart them. Eventually, the intelligence of the women who were slightly smarter than the men began to degrade as a result. But their greater potential never diminished genetically.
Just a theory.
Personally I don't think any gender would be smarter than the other in general. Although from my personal experiences about 3/4's of the highly intelligent people I have known have been female. Yes, I remember when I was in school, the brightest ones is always a female. It's good though, hanging out with female friends more intelligent than you.
However, for the most part, as far as animal species go, all humans start out with basically the same level of intelligence. How much they end up with individually depends entirely on nurturing. The only exception to this is some humans who are born with a genetic abnormality that causes a reduction in cognitive ability.