In probability theory , Chebyshev's inequality guarantees that, for a wide class of probability distributions , "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.

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