Chebyshev's inequality

• Chebyshev inequality, Tchebycheff inequality, Tchebycheff's inequality

From the surname of Russian mathematician Pafnuty Chebyshev (1821–1894), the discoverer.

Chebyshev's inequality

1. (statistics) 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:

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

• Chebyshev's sum inequality