68–95–99.7 rule

（重定向自Three sigma rule）

For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.

Prediction interval (on the y-axis) given from the standard score (on the x-axis). The y-axis is logarithmically scaled (but the values on it are not modified).

Diagram showing the cumulative distribution function for the normal distribution with mean (µ) 0 and variance (σ2) 1.

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of one, two and three standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively. 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:

单词	Three sigma rule
释义	Three sigma rule 英语百科 68–95–99.7 rule （重定向自Three sigma rule） In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of one, two and three standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively. 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:
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