When U.S. air force discovered the flaw of averages (2016)

Thought this sounded familiar then realized it's a book review for a book I read a few years back.

It was an interesting book. Recommend it to anyone who finds the article interesting.

Been noted here on HN: the average web form excludes lots of people. Lots of folks cant fill in: First/middle/last name; unique username/password; social security number; street address; bank account.

And not just folks in Micronesia or whatever. Heck my business partner hasn't got a deliverable street address - no mailbox at his house. He has a PO box. Is a nightmare getting Amazon deliveries that aren't lost, or left in the bushes, or returned undeliverable.

Anyway, yes, there is no average person.

Note that this is not some sort of unexpected effect due to humans not behaving mathematically ideally; this is what happens when your intuitions about 1, 2 and 3 dimensions are applied to higher dimensional spaces. Consider the goal of being in the middle 50% of a random value on one dimension; you have a 50% chance. But if you have two dimensions, and you want to be in the middle 50% for both of them, it's a 25% chance. And if you have 3, it's a ~12% chance. This already is counterintuitive, but when you ramp it up to 10 dimensions, it's a ~0.01% chance. That means that if you have a thousand people, only one of them (on average) will be in the middle 50% of all of them. Even the praised end state of the air force, with 9 dimensions and a required support of 90% of individuals of each dimension, implies that only 38% of individuals will be supported overall. (Granted, human dimensions aren't wholly uncorrelated.)

Great explanation. This is an example of the curse of dimensionality. An intuitive way to think about this is that each dimension you add is another “chance” for one of them to fall outside of the range.

Another way to think about it is the often-cited unit n-dimensional sphere. If you were to uniformly sample points from within this n-dimensional sphere, as n increased, the proportion of points lying near the surface of the sphere would increase.