An “average” (whether a mean/ median etc) is a very lossy compression algorithm.

You’re attempting to describe a whole series of numbers with just one (or two) numbers.

Trying to come up with a good general purpose way to reduce/compress/aggregate data via a lossy algorithm is intractable.

While that all might sound obvious, it can be very hard to internalise this.

(And that’s before getting into the motivated reasoning that biased actors [aka normal people] will use to preference one lossy algorithm over another)