# I’m Above Average and So Are You

Derek Severs’ short essay “I Assume I’m Below Average” recently went viral on Hacker News. The article begins:

Ninety-six percent of cancer patients claim to be in better health than the average cancer patient.

Ninety-four percent of professors say they are better-than-average teachers.

Ninety percent of students think they are more intelligent than the average student.

Ninety-three percent of drivers say they are safer-than-average drivers.

What the article doesn’t discuss, however, is whether the people in these statistics are actually wrong.

There’s no fundamental reason why you can’t have 90% of people be better than average. For example, more than 99.9% of people have an above-average number of legs. And more than 90% of people commit fewer felonies than average. These examples are obvious, but they’re not so different than some of the examples above.

Any cancer patient that isn’t on the verge of dying probably is doing above average. (Unfortunately, so many cancer patients die, that the 96% number probably is still over-optimistic.)

What about the fraction of students that are above average? It depends on the class. Looking at Stanford’s data for the grade distribution of their graduate Algorithms class, about 78% of students (anyone with an A or A+) have an above-average grade.

This type of skew will happen in any probability distribution where a small number of people bring the average way down. I suspect another example of this is car drivers (consider the fact that, in America, 1 in 7 drivers don’t wear a seatbelt, or that 1 in 50 drivers admit to driving drunk in the past month!). Whether or not university professors fit this type of distribution is harder to tell.

To be clear, the examples given at the beginning are pretty extreme, and people probably are overly optimistic about their standings. But the examples aren’t as extreme as they look at first glance.

This reminds me of an old joke about there being an imaginary town called Lake Wobegon, “where all the women are strong, all the men are good-looking, and all the children are above average.” The joke, of course, is that the children can’t actually all be above average. But almost all of them can be. You just need one to bring the average down. (Poor Timmy.)