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!