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How Deviant Can You Be?

Paul A. Samuelson
Journal of the American Statistical Association
Vol. 63, No. 324 (Dec., 1968), pp. 1522-1525
DOI: 10.2307/2285901
Stable URL: http://www.jstor.org/stable/2285901
Page Count: 4
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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 $\sqrt{N - 1}$ 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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