Actually, average can mean median, mode or mean. I was using (I thought obviously..but perhaps not) the median definition. The point stands - it's odd to say that the problem here is that half the people are of below average intelligence. Since that's (roughly) what you'd expect.

The problem instead is that our "rights" are treated as privileges that can be revoked when the powers that be deem it convenient. Our rights should be rights regardless of our intelligence. Though perhaps the responsibility for securing those rights falls most heavily upon the cleverest among us..in which case the problem isn't that there are folks of below average intelligence, it's that those particularly blessed with keen minds aren't doing enough to defend the rights of us all.

Usually the word average means arithmetic mean, but the median is also an average.

https://en.wikipedia.org/wiki/Average

All modern IQ tests that I am aware of have normal distributions (ie, the mean, median, and mode are all the same) by design. If one of several IQ measures is not your cup of tea for scoring mental ability, that is fine, but I highly suspect that whatever you pick instead will also have a normal distribution.

(not necessarily symmetric)

Another example I've seen: the average wealth of a room with Bill Gates and a hundred homeless people is a couple hundred million dollars per capita.