Chebyshev's Inequality

For any dataset, regardless of the shape of the distribution, at least 100(1-(1/(k^2)))% of the data elements will lie within k standard deviations of the mean, where k>1. That is, at least 100(1-(1/(k^2)))% of the data will lie between μ-k σ and μ+k σ for k>1, where μ is the mean and σ is the standard deviation of the distribution. This Demonstration illustrates the minimal percentage of data elements found within k standard deviations of any dataset's mean.

THINGS TO TRY

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DETAILS

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

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Contributed by: Craig Bauling

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