This empirical rule calculator is often employed to calculate the share of values that fall within a specified number of ordinary deviations from the mean. It also plots a graph of the results. Simply enter the mean (M) and variance (SD), and click on the “Calculate” button to get the statistics.

### The Empirical Rule

The Empirical Rule, which is additionally referred to as the three-sigma rule or the 68-95-99.7 rule, represents a high-level guide which will be wont to estimate the proportion of a traditional distribution which will be found within 1, 2, or 3 standard deviations of the mean. consistent with this rule, if the population of a given data set follows a traditional , bell-shaped distribution in terms of the population mean (M) and variance (SD), then the subsequent is true of the data:

An estimated 68% of the info within the set is positioned within one variance of the mean; i.e., 68% lies within the range [M – SD, M + SD].

An estimated 95% of the info within the set is positioned within two standard deviations of the mean; i.e., 95% lies within the range [M – 2SD, M + 2SD].

An estimated 97.7% of the info within the set is positioned within three standard deviations of the mean; i.e., 99.7% lies within the range [M – 3SD, M + 3SD].

#### Example

Let’s say the many an exam follow a bell-shaped distribution that features a mean of 100 and a typical deviation of 16. What percentage of the people that completed the exam achieved a score between 68 and 132?

Solution: 132 – 100 = 32, which is 2(16). As such, 132 is 2 standard deviations to the proper of the mean. 100 – 68 = 32, which is 2(16). This suggests that a score of 68 is 2 standard deviations to the left of the mean. Since 68 to 132 is within 2 standard deviations of the mean, 95% of the exam participants achieved a score of between 68 and 132.

To calculate the Empirical rule use this calculator!