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
Famous quotes containing the word rule:
“Great statesmen seem to direct and rule by a sort of power to put themselves in the place of the nation over which they are set, and may thus be said to possess the souls of poets at the same time they display the coarser sense and the more vulgar sagacity of practical men of business.”
—Woodrow Wilson (1856–1924)