The analogy breaks because the mean is skewable by high incomes and the median is well ... a number such that if you add $1 most people earn less than that.

Bottom 10-percentile would be a good measure maybe for something to lift if you are left leaning or right leaning and see the economy holistically.

When wealth follows a power law distribution, that's very questionable.

https://en.m.wikipedia.org/wiki/Power_law#Lack_of_well-defin...

OP should have written

We (1000 people) eat bread, Uber CEO eats 1000 marble steaks. On average we eat a burger each

If you have 1000 people making $1 along with one person making $1000, the average is about $2 - so 99.9% of people are making less than the average.

You're forgetting that CEO's steak is the size of a skyscraper.