1. ANATOMY OF THE EMPIRICAL RULE
(also known as the Rule)
The Empirical Rule applies to a specific type of distribution called a bell-shaped distribution (Normal Distribution) as shown below.
The Empirical Rule states that for a bell-shaped distribution, approximately:
68.26% of the observations lie within one standard deviation of the mean.
95.44% of the observations lie within two standard deviations of the mean.
99.74% of the observations lie within three standard deviations of the mean.
NOTE: For distributions of any shape there is a more general rule, Chebyshev’s theorem. It states that at least 75% of all scores will fall within 2 standard deviations above and below the mean; and at least 89% of all scores will fall within 3 standard deviations of the mean.
68.26%
95.44%
99. 74%