The Lake Wobegon Distribution at The Universe of Discourse

[T]he remark reminded me of how many people do seem to believe that most distributions are normal. More than once on internet mailing lists I have encountered people who ridiculed others for asserting that “nearly all x are above [or below] average”. This is a recurring joke on Prairie Home Companion, broadcast from the fictional town of Lake Wobegon, where “all the women are strong, all the men are good looking, and all the children are above average.” And indeed, they can’t all be above average. But they could nearly all be above average. And this is actually an extremely common situation.

To take my favorite example: nearly everyone has an above-average number of legs.

The post goes on to use some baseball statistics, in a way that probably won’t give Chad apoplexy, arguing that professional baseball players shouldn’t follow a normal distribution, because they are not selected at random from the population. They should represent the part of the distribution several standard deviations above the average.

One flaw in the reasoning is that not all highly skilled athletes with the right abilities become baseball players, but I think the basic argument is sound.

Of course, college students probably aren’t a normal distribution. Schools screen their applicants, and there can be further skewing within that population; students drop out of classes, and not all courses are created equal. Take physics, for example — there are typically different levels of introductory physics: a so-called physics-for-poets class, a class that require just algebra, and one that requires calculus. Generally speaking your physics ability would correlate somewhat with the class you are taking. Even if the physics-taking population as a whole comprised a normal distribution, each individual class should not: the easiest class should be deficient in students at the high end, and the hardest class should be missing the low end.