Chebyshev's Rule

Chebyshev's Rule is a non-parametric analog of the Empirical Rule. It gives us a lower limit on what proportion of a distribution can be found within k standard deviations of the mean, whether that distribution is Normal or not.

Put simply, it says that within any distribution, the proportion of that distribution that can be found within k standard deviations of its mean is at least

$$1-\frac{1}{k^2}$$

Note: It is necessary that $k > 1$, as otherwise, the rule produces a negative proportion -- which makes no sense at all.