There’s actually a big different in mens and women’s IQ distribution. Men are all over the map, from extremely dumb to extremely smart, but women tend to statistically cluster in the middle with comparatively few outliers. Way less mentally deficient, very few Bobby Fischers.
Shootings an interesting one. Most people familiar with guns notice women take to shooting accurately more easily and quickly than guys (with rifles, not handguns). I’ve seen this lots personally. My theory involves lower heart rate and lower muscle mass being conducive.