"Think of how stupid the average person is, and realize half of them are stupider than that." — George Carlin
I think the average person is definitely intelligent. It's just that we are very prone to mixing intelligence with knowledge in addition to also forgetting how long it took us to learn things that are so automatic for us we see them as trivial.
and who considers themselves to be in that lower half? Probably a lot less than half of the population
Shouldn't that be the median person for the quote to actually hold?
Given that most measures of intelligence follow nearly normal distributions (as long as you stay away from the tails), I think it doesn’t matter that much.