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- Q249514 subject Q5639957.
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- Q249514 abstract "Template:ForIn probability theory, Chebyshev's inequality (also spelled as Tchebysheff's inequality, Russian: Нера́венство Чебышёва) 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 (or equivalently, at least 1−1/k2 of the distribution's values are within k standard deviations of the mean). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics. 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.In practical usage, in contrast to the 68-95-99.7% rule, which applies to normal distributions, under Chebyshev's inequality a minimum of just 75% of values must lie within two standard deviations of the mean and 89% within three standard deviations.The term Chebyshev's inequality may also refer to Markov's inequality, especially in the context of analysis.".
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- Q249514 comment "Template:ForIn probability theory, Chebyshev's inequality (also spelled as Tchebysheff's inequality, Russian: Нера́венство Чебышёва) 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 (or equivalently, at least 1−1/k2 of the distribution's values are within k standard deviations of the mean).".
- Q249514 label "Chebyshev's inequality".