68-95-99.7 rule

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for 68.27 % of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45 %; and three standard deviations (light, medium, and dark blue) account for 99.73 %.

The 68-95-99.7 rule, or three sigma rule, or empirical rule, states that for a normal distribution, almost all values lie within 3 standard deviations of the mean.

About 68% of the values lie within 1 standard deviation of the mean (or between the mean minus 1 times the standard deviation, and the mean plus 1 times the standard deviation). In statistical notation, this is represented as: μ ± σ.

About 95% of the values lie within 2 standard deviations of the mean (or between the mean minus 2 times the standard deviation, and the mean plus 2 times the standard deviation). The statistical notation for this is: μ ± 2σ.

Almost all (actually, 99.7%) of the values lie within 3 standard deviations of the mean (or between the mean minus 3 times the standard deviation and the mean plus 3 times the standard deviation). Statisticians use the following notation to represent this: μ ± 3σ.

This rule is often used to quickly get a rough estimate of something's probability, given its standard deviation.

[edit] External links

• "A description and illustration using Java Applets by Balasubramanian Narasimhan"