Chebyshev's inequality

English

Alternative forms

• Chebyshev inequality, Tchebycheff inequality, Tchebycheff's inequality

Etymology

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

Proper noun

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:

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

Related terms

• Chebyshev's sum inequality

Translations

theorem

• Catalan: desigualtat de Txebixov f
• Chinese:

  Mandarin: 切比雪夫不等式 (Qièbǐxuěfū bùděngshì)

• Czech: Čebyševova nerovnost f
• Finnish: Tšebyšovin epäyhtälö
• French: inégalité de Tchebychev f
• German: tschebyscheffsche Ungleichung f, Tschebyscheff-Ungleichung f
• Italian: disuguaglianza di Čebyšëv f
• Portuguese: desigualdade de Chebyshev f
• Russian: нера́венство Чебышёва n (nerávenstvo Čebyšóva)
• Spanish: desigualdad de Chebyshov f