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%.](/Images/godic/202502/16/Empirical_Rule1315.PNG")
![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).](/Images/godic/202502/16/Standard_score_and_prediction_interval1315.png")
![Diagram showing the cumulative distribution function for the normal distribution with mean (µ) 0 and variance (σ2) 1.](/Images/godic/202502/16/Cumulative_distribution_function_for_normal_distribution,_mean_0_and_sd_11315.png")
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: