Empirical Rule

Applies to normal distributions.

• The probability of area between the mean and $\pm 1$ standard deviation is 0.68.
• The probability of area between the mean and $\pm 2$ standard deviations is 0.95.
• The probability of area between the mean and $\pm 3$ standard deviations is 0.997.

Chebyshev’s Theorem

For any $k\gt 1$, at least $1-\frac{1}{k^2}$ of the values lie within $k\sigma$ of the mean.