As far as gender stereotypes, I think there are two sets:
- reserved, strong/silent male + bubbly socialite female
- devoted and dutifully nurturing female + aggressive dominant male
I have heard that the only MBTI dimension with any correlation to gender was the T/F dimension, with men statistically more likely to be T and women statistically more likely to be F.
@SilkRoad My grandma was fierce and rigid, no-nonsense, reserved and very practical but tender toward those she cared about. My grandparents had fairly traditional gender roles, grandpa was the one who hunted and fixed the cars and appliances, worked in the factory and built the house, my grandma was the one who cleaned the house, fed and clothed her children. But in terms of personality, grandma was the "harsher" one, while grandpa the more jolly and tender one. My mom I think struggled with feeling like she never could please my grandma.
Of course, they lived in rural Adirondacks and never had a computer or took the MBTI and are both dead now, so no chance to ever know. But if I had to say, I would guess ISTJ grandma and ISxP grandpa, leaning toward ISFP.