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.

If we add one more asset class (e.g., bonds), we add one more poor family with $100 in just that class; and, one more rich family with $n in every asset class, while other rich families also upgrade to having $n in that new class.

So the rich can get incredibly richer relative to the poor and the median stays at 100.

The only problem is externality pricing.

Building https://negationgame.com

@nor's is the most generalizable solution given, IMO:

For n assets, where the median is $y:
1) Create (n-1) families with $(y+1) of each asset type 
2) For each asset type, create 1 family with ONLY $y of that asset

An odd # of families (n - 1 + n) is always created via this method.