There is a popular anecdote along these lines that comes from the 1950's US Air force. https://www.thestar.com/news/insight/2016/01/16/when-us-air-force-discov

There is a popular anecdote along these lines that comes from the 1950's US Air force. https://www.thestar.com/news/insight/2016/01/16/when-us-air-force-discovered-the-flaw-of-averages.html https://www.thestar.com/news/insight/2016/01/16/when-us-air-... The scientists also expected that a sizable number of pilots would be within the average range on all 10 dimensions. But even Daniels was stunned when he tabulated the actual number. Zero. Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions. Using their definition of "average range", which is the middle 30% (in height, waist circumference, etc), we should expect to find one such individual for every 1/0.3^10 = 169,351 people on average.