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:

Example

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 1.5 56% 2 75% 3 89% 4 94%

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