High Quality Content by WIKIPEDIA articles! In statistics, Samuelson's inequality, named after the economist Paul Samuelson, also called the Laguerre–Samuelson inequality, after the mathematician Edmond Laguerre, states that every one of any collection x1, ..., xn, is within ?(n ? 1) standard deviations of their mean. In other words, if we let overline{x} = frac{x_1+cdots+x_n}{n} be the mean and s = sqrt{frac{1}{n} sum_{i=1}^n (x_i - overline{x})^2 } be the standard deviation, then overline{x} - ssqrt{n-1} le x_i le overline{x} + ssqrt{n-1}qquad text{for }i = 1,dots,n. Equality holds on the left if and only if the n ? 1 smallest of the n numbers are equal to each other, and on the right iff the n ? 1 largest ones are equal. Samuelson's inequality may be considered a reason why studentization of residuals should be done externally.

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