In probability theory, Chebyshev's inequality (also spelled as Tchebysheff's inequality, Нера́венство Чебышева) guarantees that in any probability distribution,"nearly all" values are close to the mean — the precise statement being that no more than 1/k2 of the distribution's values can be more than k standard deviations away from the mean. The inequality has great utility because it can be applied to completely arbitrary distributions (unknown except for mean and variance), for example it can be used to prove the weak law of large numbers.
The term Chebyshev's inequality may also refer to the Markov's inequality, especially in the context of analysis.
Read more about Chebyshev's Inequality: History, Statement, Example, Sharpness of Bounds, Finite Samples, Sharpened Bounds, Unimodal Distributions, Bounds For Specific Distributions, Zero Means, Haldane's Transformation, Chernoff Bounds, Integral Chebyshev Inequality
Famous quotes containing the word inequality:
“However energetically society in general may strive to make all the citizens equal and alike, the personal pride of each individual will always make him try to escape from the common level, and he will form some inequality somewhere to his own profit.”
—Alexis de Tocqueville (1805–1859)