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:
“When any practice has become the fixed rule of the society in which we live, it is always wise to adhere to that rule, unless it call upon us to do something that is actually wrong. One should not offend the prejudices of the world, even if one is quite sure that they are prejudices.”
—Anthony Trollope (1815–1882)