Samuelson's inequality
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 uncorrected sample standard deviations of their sample mean. == Statement of the inequality == If we let x ¯ = x 1 + ⋯ + x n n {\displaystyle {\overline {x}}={\frac {x_{1}+\cdots +x_{n}}{n}}} be the sample mean and s = 1 n ∑ i = 1 n ( x i − x ¯ ) 2 {\displaystyle s={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\overline {x}})^{2}}}} be the standard deviation of the sample, then x ¯ − s n − 1 ≤ x j ≤ x ¯ + s n − 1 for j = 1 , … , n .