Above average

From the person most likely to be the next President of those United States:

“Now, I wouldn’t keep any school open that wasn’t doing a better than average job. If a school’s not doing a good job, then you know it may not be good for the kids.”

This, as you’d expect, has occasioned some discussion on the internets.

There’s nothing mathematically impossible about the idea of nearly all schools being above average.  Nearly everyone has more than the average number of legs.  Darwin, Australia, has had better than average Christmas weather on 49 of the last 50 years — in 1974, Cyclone Tracy destroyed 80% of houses in the city, which tends to pull the average down.

In other settings, it’s not even an unreasonable idea that you’d routinely close a large fraction of establishments.  It’s roughly what happens to restaurants, for example: lots of them are started, most fail, the remaining ones tend to be pretty close to the optimal price:quality tradeoff line.

In this quote, though, neither explanation really flies: it’s not that nearly all schools are the same except for a few really bad ones, and it doesn’t really make sense to close half the schools in the country, because even if you’re in favour of free competition between schools, most schools are too far apart to compete effectively.

What we’re seeing here is the broadening of ‘average’ to mean ‘ok’, which is one of the reasons it’s less useful as a technical term than it used to be.  If you want to be precise, ‘mean’ is better.