It assumes a normal-ish distribution. Mode would be a better single-number measure, but it’s the income x number of people curve that carries the important message.
I'm sorry I didn't make myself clearer. I'm not talking about GDP, but income (which has a distribution curve).
OTOH, we can see that curve in a global context, of GDP per capita across countries. It's a boring curve, very power-law ish with slightly odd peak in the 30K-40K region.
GDP is not income.
Personal GDP is not defined.