Ok, I am more one to argue the logic than the numbers, though I still aim for correctness.
First: We need to not equate Rape and Sexism, Rape is a violent crime carried out by violent(for the moment at least) people, on people weaker than them. Sexism is behavioral and in many cases, unrealized and unintentional. That isn't to say there aren't idiots out there with no interest in anything but themselves, thus motivating all sorts of ignorant acts, but as someone above pointed out, sometimes its as simple as offering unnecessary help.
Second: Sexist acts happen dependent on a situation. Guys lose in divorce court/custody disputes, and in a lot of societal pressures. Girls lose in the job market, and in a different set of societal pressures. I think neither gender has it better overall, or at least that no one can prove such, because the impact of an act is relative, based on many MANY factors.
Third: I'd like to posit that equality is a poor term in this case, because racism=/=sexism.
I'd say fairness would be better.
Why you ask? Because in some situations, unlike race, which has little effect on a person's capabilities, girls have(according to wiki) roughly 52 percent the upper body strength of guys and 66 percent the lower body strength of guys. Unlike race where the capabilities are entirely equal, sex actually has an effect.
Equality implies that the same value can be expected from both sides, in many ways, it cannot, look at all of the stupid little studies, or simply read the wiki on sexual dimorphism sometime. Fair means allowing for the inborn strengths and weaknesses of a gender, rather than simply ignoring them as equality must needs do.
Fourth: Numerous does not mean statistically significant, there are girls who hate shopping for example, my girlfriend included. But that doesn't doesn't negate the fact that MOST girls do like shopping, and aiming ads towards them, or portraying such characters on tv isn't going to die out because the 1/20 girls who genuinely defy that stereotype ***** a lot. Wake up call, the other 19 are all out spending money, responding to the ads and identifying with the characters, which means the stereotype will persist.
Some stereotypes are justified, I want to use my job as an example. At my Burger King, we are trained such that if someone orders a meal by number(#1=Whopper Value Meal, etc) we are to give them a small size meal, and with Coke, if the order is drivethru. Know why? Because we strive to get the food ready and to them by the end of 2.5 minutes,and despite the possibility that we will be wrong, asking the necessary questions takes too long. The 1/15 people who wanted a medium with DR. Pepper won't throw enough of a fit to make slowing the other 14 down worth it. Add the fact that people line up, compounding the time lost asking questions, and reasking if the order has multiple meals, and its far more useful to just assume. There are other factors but it remains true.
Sometimes the stereotype is right and the people who don't fit don't like it, but in some cases its better to accept and expect some people to accept the assumption than slog the rest into the muddy waters of DEALING with it, where true injustice can occur, rather than simple misinformation.