The fact that intra-gender differences are more significant has no bearing on what inter-gender difference we should see.
Maybe we can visualize this a different way, if you had two venn diagrams of interest/ability in males and females they would have two different centers separated by the difference in average interest/ability but would be largely overlapping. That would lead to an expected outcome of maybe 60/40% if 90% of the area overlapped.
Whatever trait you're talking about, if you assert that it is distributed randomly, then it is not correlated with gender. That's just simple semantics. If the trait is correlated with gender, even anomalously so, the trait is not distributed randomly.
The trait I am talking about is interest/ability in science, math, engineering, and software. I am arguing that interest/ability in these areas is not correlated with gender (ie. women are _not_ inherently bad at math and science) and is distributed evenly in the population. The fact that we see only small single-digit numbers of females participating in software development would seem to indicate a serious problem, something is discouraging a large number of people from doing what they like and are good at. I think we should find out what is preventing people from doing what they like and are good at and systematically remove roadblocks preventing them from being successful. When those roadblocks are cultural then the culture which allows people to reach their full potential is going to have superior outcomes to one that is more caste driven and does not allow people to achieve based on non-relevant traits such as their gender, religion, color, etc.
Does my point make more sense now or am I still explaining badly?
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