I've got a tangential question: what math, if learned by more people, would give the biggest improvement in understanding for the effort put into learning it?

Take calculus, for example. It's great stuff if you want to talk about rates of change, or understand anything involving physics. There's the benefit; how about the cost? Most people who learn it have a very hard time doing so, and they're already well above average in mathematical ability. So, the benefit mostly relates to understanding physics, and the cost is fairly high for most people.

Compare this with learning basic probability and statistical thinking. I'm not necessarily talking about learning anything in depth, but people should have at least some exposure to ideas like probability distributions, variance, normal distributions and how they arise, and basic design of experiments -- blinding, controlling for variables, and so on. This should be a lot easier to learn than calculus, and it would give insight into things that apply to more people.

I'll give a concrete example: racism. Typical racist statements, like "black people are lazy and untrustworthy," couldn't possibly be true in more than a statistical sense, and obviously a statistical statement about a large group doesn't apply to every member of that group -- there's plenty of variance to take into account. Basic statistical thinking makes racist bigotry sound preposterously silly, like someone claiming that the earth is flat. This also applies to every other form of irrational bigotry that I can think of off the top of my head.

Remember when Larry Summers suggested that maybe part of the reason for the underrepresentation of women in Harvard's science faculty was that women may have lower variance in intelligence than men, and so are underrepresented in the highest part of the intelligence bell curve? What almost everybody heard was "Women can't be scientists because they're stupid." People heard a statistical statement and had no idea how to understand it.

There are important, relevant subjects that people just can not understand without basic statistical thinking. I would like to see most people exposed to basic statistical thinking.

Are there any other kinds of math that offer high bang-for-the-buck, as far as learning difficulty goes? (I've always thought that the math behind computer programming was damn useful stuff, but the engineering students I've talked with usually find it harder than calculus, so maybe that's not the best idea.)