Enter the mean and standard deviation of a normal distribution to find the value ranges covering 68%, 95%, and 99.7% of your data.
The empirical rule — also called the 68-95-99.7 rule — describes how data is distributed in a normal (bell-shaped) distribution. It tells you what percentage of values fall within 1, 2, and 3 standard deviations of the mean.
The empirical rule is a statistical rule that applies to data following a normal distribution. It states that almost all of the data will fall within three standard deviations of the mean, distributed as follows:
68% range = μ ± 1σ | 95% range = μ ± 2σ | 99.7% range = μ ± 3σThe empirical rule gives a quick way to understand the spread of normally distributed data without needing a full probability table. It's widely used to spot unusual values: a data point beyond 3 standard deviations from the mean occurs in less than 0.3% of cases, making it a strong candidate for an outlier.
It's another name for the empirical rule: 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations, for a normal distribution.
No, it only applies to data that is approximately normally distributed (a symmetric, bell-shaped curve). For skewed or non-normal data, the percentages will not hold, and you should use Chebyshev's inequality instead.
Because 99.7% of normally distributed data falls within 3 standard deviations of the mean, a value beyond that range is very unusual (less than 0.3% probability) and is often treated as a potential outlier.
The empirical rule gives quick approximate percentages for whole standard deviation bands (1, 2, 3σ). A z-score gives the exact number of standard deviations any individual value is from the mean, which can then be converted to a precise probability using a normal distribution table.