Chebyshev's inequality

English

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Etymology

From surname of Pafnuty Chebyshev, the discoverer.

Noun

Chebyshev's inequality (uncountable)

1. (statistics) The theorem that in any data sample with finite variance, the probability of any random variable X lying within an arbitrary real k number of standard deviations of the mean is 1 / k2, i.e. assuming mean μ and standard deviation σ, the probability Pr is:
$\Pr(\left|X-\mu\right|\geq k\sigma)\leq\frac{1}{k^2}$