# Chebyshev's inequality

## English

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