~50% of men probably wear a size 9-11 shoe

That's a "Large" sock

Man with a size 8 shoe could probably still wear a "Large" sock and be fine.

~75% of women wear a size 7-9

Women with 6 or 6.5 should still be able to wear a 7-9 sized sock.

Families have genetically similar feet

I know from my experience, my father, my brother, and I all wear the same size. We all had different preferences and our own socks, but I could have easily worn their socks.