The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical guideline that describes data distribution in a normal distribution. The rule states that for a normal distribution:

  • About 68% of the data falls within one standard deviation of the mean.
  • About 95% of the data falls within two standard deviations of the mean.
  • About 99.7% of the data falls within three standard deviations of the mean.

In other words, if a data set follows a normal distribution, we can expect that most of the data fall within a certain range of values around the mean. The empirical rule is a useful tool for understanding the spread of data and identifying outliers.