This fallacy happens all the time on these boards and most people seem totally blind to it. It's important to keep in mind that for most things, 1) individual variance is much greater than group differences, and 2) outliers tend to amplify the group variances even though the average individual is not impacted by this.
Example for one would be that as a group, black Americans tend to test lower on certain iq scores than Jewish Americans when controlling for socioeconomic status. However if you pick one black and one Jew at random from the population and pit them side by side , the actual chance the Jew is going to test higher is only a few percentage points; this is because the variability in the group , whether Jew or black, is much higher than the actual aggregate difference between the two groups as a whole. So while it is an accurate statement to say Jewish people test higher on iq scores than African Americans , and racists on this board will happily run with that, it is incorrect to infer there is a high likelihood that a Jew at random will be smarter than a black at random.
As far as point two, I think a few examples speak for themselves , i.e. Black NBA players or Jewish nobel prize winners are disproportionate to their respective populations by a large margin. However people in both these groups represent statistical outliers and don't have a major impact on the actual athletic or mental capacities of a given random individual in those respective groups.
Now obviously this principle doesn't apply to ALL characteristics ( like a random black is going to be blacker than a random Jew), but it does apply to most "controversial" qualities (intelligence, behavior, penis length etc).
Same with gender; some characteristics like upper body physical strength, will be unequivocally male dominant. While with others the individual variance is higher than the group difference (such as technical aptitude tho this is just my guess)
