GDP is less about what the average person has than it is the capabilities of a given society. Liechtenstein may have a very high standard of living, but it can't exactly fund a space program with a ~6 billion dollar GDP.
Also, median also has issues dealing with things like the US's vast undocumented workforce. So, you really want to slice things up by income percentile, family type, PPP and non etc.
Median is a mathematical concept that doesn't know or care about a person's immigration status.
The dataset plugged in and the mathematical operation performed on it are two distinct concepts and shouldn't be confused. It's the same reason the IRS lets undocumented citizens and documented citizens performing unsavory work (including drug dealing and prostitution) to file taxes :)
My point is if 50.01% of the population makes 50+k then that's where the median is. You completely miss out on if the bottom 10% making 10k or 30k which has huge social implications.
For an extreme version southern slaves made ~0 income but because they made up less than 50% of the population they disappeared from that statistic.
The dollar amount of the earnings that are under 50% of the population disappears in the statistic, but they are not unrepresented.
Their presence in the tally means that the median skews their way. For each undocumented person earning under minimum wage, the median shifts one person over to the left.
I agree that there should be a better way of displaying that info (at least quartiles) but the median is a surprisingly effective measure.
I'm pretty sure statistics people know good analytical formats to publish these values. Why everyone doesn't use it for GDP/etc is unclear to me, because it seems to me that any flawed method is still better than `arr.sum() / arr.count()`.
Also, median also has issues dealing with things like the US's vast undocumented workforce. So, you really want to slice things up by income percentile, family type, PPP and non etc.