Empirical Rule Calculator

Calculate standard deviation ranges (68-95-99.7 rule).

68% of Data falls between (μ ± 1σ) --

95% of Data falls between (μ ± 2σ) --

99.7% of Data falls between (μ ± 3σ) --

Understanding the Empirical Rule

The Empirical Rule (also known as the 68-95-99.7 rule) is a shorthand used in statistics to describe normal distributions. It states that:

68% of data falls within 1 standard deviation of the mean.
95% of data falls within 2 standard deviations of the mean.
99.7% of data falls within 3 standard deviations of the mean.

When to Use It

This rule only applies to data that is normally distributed (shaped like a symmetrical bell curve). It allows you to quickly estimate where most of your data lies without complex calculations.

Example: IQ Scores

IQ scores are designed to have a Mean of 100 and a Standard Deviation of 15. Applying the rule:

68% of people have an IQ between 85 and 115.
95% of people have an IQ between 70 and 130.
99.7% of people have an IQ between 55 and 145.