Statistics Empirical Rule

The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical principle that states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

In other words, if a dataset is approximately normally distributed, then:

68% of the data is within one standard deviation of the mean (i.e. mean ± 1 standard deviation)

95% of the data is within two standard deviations of the mean (i.e. mean ± 2 standard deviations)

99.7% of the data is within three standard deviations of the mean (i.e. mean ± 3 standard deviations)

The Empirical Rule is a useful tool for understanding the distribution of data and for identifying outliers. However, it is important to note that the rule is only applicable for approximately normally distributed data, and it may not hold for other types of distributions.