In statistics, the 68-95-99.7 rule — or three-sigma rule, or empirical rule — states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean.
About 68.27% of the values lie within 1 standard deviation of the mean. Similarly, about 95.45% of the values lie within 2 standard deviations of the mean. Nearly all (99.73%) of the values lie within 3 standard deviations of the mean.
In mathematical notation, these facts can be expressed as follows, where x is an observation from a normally distributed random variable, μ is the mean of the distribution, and σ is its standard deviation:
Read more about 68-95-99.7 Rule: Derivation, Uses, Higher Deviations
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“The world is filled with the proverbs and acts and winkings of a base prudence, which is a devotion to matter, as if we possessed no other faculties than the palate, the nose, the touch, the eye and ear; a prudence which adores the Rule of Three, which never subscribes, which never gives, which seldom lends, and asks but one question of any project,—Will it bake bread?”
—Ralph Waldo Emerson (1803–1882)