The 68-95-99.7 rule, also known as the empirical rule, is a statistical rule used to remember the percentage of values that lie within an interval estimate in a normal distribution. The rule is based on the mean and standard deviation of a dataset, and it states that:
- 68% of the data falls within one standard deviation of the mean.
- 95% of the data falls within two standard deviations of the mean.
- 99.7% of the data falls within three standard deviations of the mean.
The rule is used to quickly estimate the probability of an observation being within a certain range, given its standard deviation, if the population is assumed to be normal. It is also used as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal. The empirical rule is widely used in empirical research, such as when calculating the probability of a certain data point occurring, or for forecasting outcomes when some data is missing.
