Empirical Rule Calculator

The Empirical Rule Calculator is an online tool that enables quick & accurate calculations based on the empirical rule, making your calculations simple.

Updated at:May 22, 2024

What is the Empirical Rule?

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

  • Approximately 68% of the data falls within one standard deviation (╧â) of the mean (╬╝).
  • Approximately 95% of the data falls within two standard deviations (2╧â) of the mean.
  • Approximately 99.7% of the data falls within three standard deviations (3╧â) of the mean.
How do I use the Empirical Rule Calculator?

To use the Empirical Rule Calculator, input the mean (μ) and standard deviation (σ) of your data set. The calculator will then compute the ranges for 68%, 95%, and 99.7% of the data based on these inputs.

input values are required for the calculator:

  • The mean (╬╝) of your data set.
  • The standard deviation (╧â) of your data set.
Why is my standard deviation required to be greater than 0?

The standard deviation (σ) measures the amount of variation or dispersion in a set of values. A standard deviation of 0 would imply that all data points are identical, which is not useful for statistical analysis.

Can this calculator be used for data that is not normally distributed?

The Empirical Rule specifically applies to data that follows a normal distribution. If your data is not normally distributed, the results from this calculator may not be accurate.

How do I interpret the results from the Empirical Rule Calculator?

The calculator provides the ranges within which approximately 68%, 95%, and 99.7% of the data fall. For example, if the mean is 50 and the standard deviation is 5, the 68% range will be from 45 to 55, the 95% range will be from 40 to 60, and the 99.7% range will be from 35 to 65.