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> the median and percentiles are a more relevant and intuitive number to think about

A good example of this is when people say "more than half of drivers say they are above average drivers! Idiots!" Of course that's perfectly possible if most drivers are basically fine and some are really really bad. For example, 99.99% of people have greater than the average number of legs.

The correct impossible statement would be if more than half of drivers are better than the median driver.




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