Medians are vulnerable to some interesting statistical paradoxes that means are not.

For example, consider this scenario:

* The median family owns $100k in real estate
* The median family owns $100k in DOGE
* The median family net worth is $100k
* Nobody has any debt

This is possible!

Challenge: figure out how.

Challenge 2: the median family also owns $100k in stocks. Median net worth is still $100k. Figure out how.

Challenge 3: generalize to an arbitrary number of asset classes.

Here's a solution, not sure if it's minimal

Just add one more “poor” family with $100 in stocks & net worth, and $0 in RE and DOGE. Other poor families remain as before.

And, one more “rich” family with $n > 100 in every category, just like the other rich family, for a net worth of $3n.

Median across all families in each category remains at $100.