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- Chebyshevs_inequality abstract "In 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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- Chebyshevs_inequality wikiPageWikiLink 68–95–99.7_rule.
- Chebyshevs_inequality wikiPageWikiLink Absolute_value.
- Chebyshevs_inequality wikiPageWikiLink Andrey_Markov.
- Chebyshevs_inequality wikiPageWikiLink Banach_space.
- Chebyshevs_inequality wikiPageWikiLink Cantellis_inequality.
- Chebyshevs_inequality wikiPageWikiLink Carl_Friedrich_Gauss.
- Chebyshevs_inequality wikiPageWikiLink Category:Articles_containing_proofs.
- Chebyshevs_inequality wikiPageWikiLink Category:Probabilistic_inequalities.
- Chebyshevs_inequality wikiPageWikiLink Category:Probability_theory.
- Chebyshevs_inequality wikiPageWikiLink Category:Statistical_inequalities.
- Chebyshevs_inequality wikiPageWikiLink Chebyshevs_sum_inequality.
- Chebyshevs_inequality wikiPageWikiLink Chebyshev–Markov–Stieltjes_inequalities.
- Chebyshevs_inequality wikiPageWikiLink Concave_function.
- Chebyshevs_inequality wikiPageWikiLink Concentration_inequality.
- Chebyshevs_inequality wikiPageWikiLink Convex_conjugate.
- Chebyshevs_inequality wikiPageWikiLink Convex_function.
- Chebyshevs_inequality wikiPageWikiLink Cornish–Fisher_expansion.
- Chebyshevs_inequality wikiPageWikiLink Covariance_matrix.
- Chebyshevs_inequality wikiPageWikiLink Cumulant.
- Chebyshevs_inequality wikiPageWikiLink Dimension.
- Chebyshevs_inequality wikiPageWikiLink Dip_test.
- Chebyshevs_inequality wikiPageWikiLink Dirac_delta_function.
- Chebyshevs_inequality wikiPageWikiLink Eatons_inequality.
- Chebyshevs_inequality wikiPageWikiLink Eli_Upfal.
- Chebyshevs_inequality wikiPageWikiLink Exchangeable_random_variables.
- Chebyshevs_inequality wikiPageWikiLink Expected_value.
- Chebyshevs_inequality wikiPageWikiLink Extended_real_number_line.
- Chebyshevs_inequality wikiPageWikiLink Francesco_Paolo_Cantelli.
- Chebyshevs_inequality wikiPageWikiLink Fréchet_space.
- Chebyshevs_inequality wikiPageWikiLink Function_(mathematics).
- Chebyshevs_inequality wikiPageWikiLink Geoffrey_Grimmett.
- Chebyshevs_inequality wikiPageWikiLink Hermite–Hadamard_inequality.
- Chebyshevs_inequality wikiPageWikiLink Hilbert_space.
- Chebyshevs_inequality wikiPageWikiLink Indicator_function.
- Chebyshevs_inequality wikiPageWikiLink Interval_(mathematics).
- Chebyshevs_inequality wikiPageWikiLink Irénée-Jules_Bienaymé.
- Chebyshevs_inequality wikiPageWikiLink J._B._S._Haldane.
- Chebyshevs_inequality wikiPageWikiLink Jensens_inequality.
- Chebyshevs_inequality wikiPageWikiLink Kantorovich_inequality.
- Chebyshevs_inequality wikiPageWikiLink Kolmogorovs_inequality.
- Chebyshevs_inequality wikiPageWikiLink Kurtosis.
- Chebyshevs_inequality wikiPageWikiLink Law_of_large_numbers.
- Chebyshevs_inequality wikiPageWikiLink Le_Cams_theorem.
- Chebyshevs_inequality wikiPageWikiLink Markovs_inequality.
- Chebyshevs_inequality wikiPageWikiLink Maurice_Kendall.
- Chebyshevs_inequality wikiPageWikiLink Mean.
- Chebyshevs_inequality wikiPageWikiLink Measurable_function.
- Chebyshevs_inequality wikiPageWikiLink Measure_(mathematics).
- Chebyshevs_inequality wikiPageWikiLink Median.
- Chebyshevs_inequality wikiPageWikiLink Michael_Mitzenmacher.
- Chebyshevs_inequality wikiPageWikiLink Mizar_system.
- Chebyshevs_inequality wikiPageWikiLink Mode_(statistics).
- Chebyshevs_inequality wikiPageWikiLink Monotonic_function.
- Chebyshevs_inequality wikiPageWikiLink Multidimensional_Chebyshevs_inequality.
- Chebyshevs_inequality wikiPageWikiLink Multivariate_random_variable.
- Chebyshevs_inequality wikiPageWikiLink Normal_distribution.
- Chebyshevs_inequality wikiPageWikiLink Pafnuty_Chebyshev.
- Chebyshevs_inequality wikiPageWikiLink Paley–Zygmund_inequality.
- Chebyshevs_inequality wikiPageWikiLink Pareto_distribution.
- Chebyshevs_inequality wikiPageWikiLink Pettis_integral.
- Chebyshevs_inequality wikiPageWikiLink Probability_distribution.
- Chebyshevs_inequality wikiPageWikiLink Probability_theory.
- Chebyshevs_inequality wikiPageWikiLink Rademacher_distribution.
- Chebyshevs_inequality wikiPageWikiLink Random_variable.
- Chebyshevs_inequality wikiPageWikiLink Real_number.
- Chebyshevs_inequality wikiPageWikiLink Samuelsons_inequality.
- Chebyshevs_inequality wikiPageWikiLink Semivariance.
- Chebyshevs_inequality wikiPageWikiLink Skewness.
- Chebyshevs_inequality wikiPageWikiLink Standard_deviation.
- Chebyshevs_inequality wikiPageWikiLink Standard_score.
- Chebyshevs_inequality wikiPageWikiLink Strong_order_two.
- Chebyshevs_inequality wikiPageWikiLink Symmetric_probability_distribution.
- Chebyshevs_inequality wikiPageWikiLink Transpose.
- Chebyshevs_inequality wikiPageWikiLink Unimodality.
- Chebyshevs_inequality wikiPageWikiLink United_States_Environmental_Protection_Agency.
- Chebyshevs_inequality wikiPageWikiLink Vakhania.
- Chebyshevs_inequality wikiPageWikiLink Variance.
- Chebyshevs_inequality wikiPageWikiLink Vysochanskij–Petunin_inequality.
- Chebyshevs_inequality wikiPageWikiLink Walters_conjecture.
- Chebyshevs_inequality wikiPageWikiLinkText ""higher moments versions"".
- Chebyshevs_inequality wikiPageWikiLinkText ""vector versions"".
- Chebyshevs_inequality wikiPageWikiLinkText "Bienaymé–Chebyshev inequality".
- Chebyshevs_inequality wikiPageWikiLinkText "Cantelli".
- Chebyshevs_inequality wikiPageWikiLinkText "Chebyshev".
- Chebyshevs_inequality wikiPageWikiLinkText "Chebyshev's inequality".
- Chebyshevs_inequality wikiPageWikiLinkText "Chebyshev's inequality#An application: distance between the mean and the median".
- Chebyshevs_inequality wikiPageWikiLinkText "Chebyshev's inequality#Variant: One-sided Chebyshev inequality".
- Chebyshevs_inequality wikiPageWikiLinkText "Chebyshev's_inequality".
- Chebyshevs_inequality wikiPageWikiLinkText "median-mean inequality".
- Chebyshevs_inequality date "May 2012".
- Chebyshevs_inequality id "p/c021890".
- Chebyshevs_inequality reason "articles should be reasonably self contained, more explanation needed".
- Chebyshevs_inequality title "Chebyshev inequality in probability theory".
- Chebyshevs_inequality wikiPageUsesTemplate Template:!.