High Quality Content by WIKIPEDIA articles! In probability theory, Chebyshev's inequality (also known as Tchebysheff's inequality, Chebyshev's theorem, or the Bienayme–Chebyshev inequality) guarantees that in any data sample or probability distribution, "nearly all" the values are "close to" the mean value — 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), and is a step in the proof of the weak law of large numbers.

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