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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.
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma 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.
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
Add a calculator widget to the page. Like a spreadsheet you can refer to other widgets in the same page. Template parameters [Edit template data] Parameter Description Type Status id id The id for this input. This is used to reference it in formula of other calculator templates String required type type What type of input box Suggested values plain number text radio checkbox passthru hidden ...
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If is the total of a sample of size n from some population in which the mean is μ and the standard ... 0.9974, characteristic of the 68–95–99.7 rule. ...