80 percent of people believe their performance is above average - and they might all be right!

I've heard it stated several times yet: psychological studies show that "80 percent of people believe their performance is above average". And invariably this is used to show that people are bad at evaluating their own performance, because it obviously can't be right.
Well, it actually can, mathematically. Take a group of ten people, two having a performance of 1 (whatever that means), the other eight a performance of 2. The average performance of people in this group is 1.8 - and 80% are performing above that average. qed
My guess is that most people confuse average and median when they make this argument. I'm not sure that the people who say they are performing above average do so, too...