This empirical rule calculator helps you determine the percentage of data within one, two, and three standard deviations from the mean in a normal distribution.
Empirical Rule Calculator
The Empirical Rule, also known as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% falls within two standard deviations.
- Approximately 99.7% falls within three standard deviations.
How to Use the Calculator
To use this calculator, input the mean (average) and standard deviation of your data set into the fields provided and press the “Calculate” button. The calculator will display the ranges for 68%, 95%, and 99.7% intervals based on your inputs.
How It Calculates the Results
The calculator computes the ranges based on the mean and standard deviation by adding and subtracting the calculated standard deviations from the mean:
- Mean ± 1 standard deviation for the 68% interval.
- Mean ± 2 standard deviations for the 95% interval.
- Mean ± 3 standard deviations for the 99.7% interval.
Limitations
Note that this calculator assumes your data follows a normal distribution. It may not provide accurate results for data sets that do not fit this pattern. Additionally, the calculator requires that the standard deviation is a positive value and that all inputs must be numeric.