Chebyshev’s Inequality

Chebyshev’s Inequality is used to describe the percentage of values in a distribution within an interval centered at the mean.

It states that for a distribution, the percentage of observations that lie within k standard deviations is atleast 1 – 1/k2

This is illustrated below:


The following table shows the minimum number of observations that lie within a certain number of standard deviations of the mean.

Standard Deviations% of observations

An important feature of Chebyshev’s Inequality is that it works with any kind of distribution.

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