The Empirical Rule

The Empirical Rule gives us a rule of thumb for approximating the proportion of a Normal distribution that falls within 1, 2, or 3 standard deviations of its mean.

Also called the 68-95-99.7 rule in some texts, for what will soon be obvious reasons, the Empirical Rules states that approximately

  • 68% of a Normal distribution can be found within 1 standard deviation of its mean
  • 95% of a Normal distribution can be found within 2 standard deviations of its mean
  • 99.7% of a Normal distribution can be found within 3 standard deviations of its mean

These approximations can, of course, be used in conjunction with the symmetry of a Normal distribution to approximate a few more proportions (such as the proportion of the distribution in the yellow, red, and blue vertical bands as shown below)