Chebyshev's Inequality

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.


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