Are the specific examples that JulianMorrison gave things that are statistically true about girls versus boys. Is it statistically true that girls don't climb trees? (I'm a girl, and tree climbing is awesome!)

Also, there's a difference between what you're talking about (using probability to predict behaviour when you know nothing else about others) and ways to raise children, since parents in part determine the future behaviour of their children. Even if it is statistically true, right now, that girls don't wear Spider-Man suits as often as boys, and get upset rather than angry, I don't think those states are the ideal world states. Treating your children like these stereotypes are true might be a self fulfilling prophecy.

Note that there are some examples that I think would be true. I do think that, on average, girls are more likely to get upset than angry when in a situation of conflict. But not always: I get upset more often, my brother gets angry, my sister gets angry, my dad gets upset. I do think that the average boy, if given a Barbie, is more likely to re-enact battles with it than dress it. But that doesn't mean it's a good parenting strategy to yell at your son because he's an outlier who likes to dress Barbies. (From a purely predictive view, you could probably make a boy happier by giving him something other than a Barbie for his birthday, but that's if you're not the parent and your actions aren't influencing his future preferences.)