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But the anecdote you're relating doesn't really say anything about the ability of a normal distribution to describe a population. It's just a natural consequenc

But the anecdote you're relating doesn't really say anything about the ability of a normal distribution to describe a population. It's just a natural consequence of having a high-dimensional multivariate distribution without accounting for correlation or covariance, along with a low sample size. If you have 4,063 pilots and you take the middle 30% of ten (assumed independent) factors, you're looking at 0.3^10 * 4,063 = 0.02 people who actually fall into that bin, on average -- it's more a dimensions game than anything profound. That's not to refute the anecdote's takeaway, but the same reasoning doesn't apply to a unidimensional unimodal distribution.

bambax 5y ago
Yeah ok my comment was unclear. My quote from the OP isn't false and the "no" in capitals is over the top and wrong. Yet the airline story does show that the mean (a bag of means of different factors) can be used -- is often used, wrongly -- to construct an average standard (or ideal) specimen. That specimen is then used as a reference, yet it doesn't exist. Also 1/ The normal distribution without a standard deviation tells us little about where a specimen lies in a given population; 2/ A normal distribution is often assumed when next to nothing is known about the actual distribution, and that's an even bigger problem, especially in social sciences.