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In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
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The relation between and are given by the following table, where the values for DRMS and 2DRMS (twice the distance root mean square) are specific to the Rayleigh distribution and are found numerically, while the CEP, R95 (95% radius) and R99.7 (99.7% radius) values are defined based on the 68–95–99.7 rule
English: This histogram demonstrates the empirical rule, also known as the 68–95–99.7 rule. Note that the areas of histogram bars are not proportional to the stated probabilities, unless by an incredible coincidence.
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as for "three sigma rule", idk, this sounds as if it was a rule dealing with a 3-sigma case, while "68-95-99.7" is actually a list of cases of n sigma, with a modest n=1..3. The page title actually helped me remember "68-95-99.7" by now, but as 4 or 5 sigma also occur in everyday considerations, I keep having to look it up anyway.
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Its practical usage is similar to the 68–95–99.7 rule, which applies only to normal distributions. Chebyshev's inequality is more general, stating that a minimum of just 75% of values must lie within two standard deviations of the mean and 88.89% within three standard deviations for a broad range of different probability distributions .