Enter the standard deviation and mean of your data set into the calculator to determine the values that fall within the empirical rule.
- Standard Deviation Calculator
- Statistical Significance Calculator
- Confidence Interval Calculator (1 or 2 means)
- Post Test Probability Calculator
Empirical Rule Formula
The following equation is used to calculate the total values of data within the 3 sets of the empirical rule.
- 68% of data within 1 standard deviation
- 95% of data within 2 standard deviations
- 99.7% of data within 3 standard deviations
Empirical Rule Definition
The empirical rule is the analysis of a data set to determine which values of data fall within 3 subsets of data. These subsets are 68%, 95%, and 99.7% of data. So for example, if a data set has a mean of 5 and a standard deviation of 1, then 68% of the data would fall between 4 and 6. (5-1= 4 and 5+1 = 6).
Empirical Rule Example
How to calculate the empirical rule?
- First, determine the standard deviation.
Calculate the average value of the standard deviation of the data set.
- Next, determine the empirical rule values.
Using the formula above, calculate the empirical rule values.
The empirical rule states that 68% of data lies within 1 standard deviation, 95% of data lies within 2 standard deviations, and 99.7% of data lies within 3 standard deviations.