Chebyshev's inequality

English

Alternative forms

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Etymology

From the surname of Russian mathematician Template:W (1821–1894), the discoverer.

Proper noun

1. Template:Lb The theorem that in any data sample with finite variance, the probability of any random variable X that lies k or more standard deviations away from the mean is no more than 1/k², i.e. assuming mean μ and standard deviation σ, the probability is:

   $\mathrm{Pr}(|X-\mu |\ge k\sigma )\le \frac{1}{k^2}$

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