I think that the general difficulty that many people have in understanding statistics is an important problem, because it leads people to misinterpret the world around them. General managers of baseball teams overpay for free agents coming off of good years because they underestimate the chances that the recent good year was just the result of variance around a mediocre mean – or at least they did until the Billy Beane era. Retail investors plow money into expensive mutual funds that have beaten the S&P 500 index for a few years in a row because they underestimate the chances that recent success is the result of pure, dumb luck; more importantly, the scandal of mutual fund expenses goes unchallenged because of the conventional wisdom that you should pay more to get into “better” funds. (I think it is possible, though unlikely, that some fund managers could actually be better than the market; but with all the statistical noise, you are not going to find them unless you look at a very long period of time.)
So I was happy to learn that my second-favorite radio show, Radiolab, was doing an episode on randomness. (You can stream it at that link, or download an MP3 from their podcast.) Their first segment does a good, clear job of debunking the human tendency to make too much of seemingly improbable events. For example, a woman in New Jersey wins the lottery in two consective years; what are the chances? But if you look at all the lotteries and all the lottery winners everywhere, it would be shocking if you didn’t have repeat winners.