How Deviant Can You Be?

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Abstract
For a finite universe of N items, it is proved no one can lie more than standard deviations away from the mean. This is an improvement over the result given by Tchebycheff's inequality: and a similar improvement is possible when speaking of how far from the mean any odd-number r out of N observations can lie. However, the relative inefficiency of Tchebycheff's inequality as applied to a finite universe does go to zero as N goes to infinity.

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