Chebyshev's inequality definition

Chebyshev's inequality

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Chebyshev's inequality

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:

$\Pr(\left|X-\mu\right|\geq k\sigma)\leq\frac{1}{k^2}$