Chebyshev's Inequality

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For any dataset, regardless of the shape of the distribution, at least of the data elements will lie within standard deviations of the mean, where . That is, at least of the data will lie between and for , where is the mean and is the standard deviation of the distribution. This Demonstration illustrates the minimal percentage of data elements found within standard deviations of any dataset's mean.

Contributed by: Craig Bauling (March 2011)
Open content licensed under CC BY-NC-SA



M. Sullivan III, Statistics: Informed Decisions Using Data, New Jersey: Pearson, 2010.

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