Empirical Rule Calculator
Calculate the percentage of data within 1, 2, or 3 standard deviations from the mean using the empirical rule (68-95-99.7 rule).
Published by:
isCalculator Editorial Team
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How to use this tool?
Follow these steps to use the Empirical Rule Calculator:
- Enter the Mean (μ): Type the average value of your normal distribution (e.g., 100).
- Enter the Standard Deviation (σ): Type the standard deviation (must be greater than zero, e.g., 15).
- Click "Calculate": Press the button to compute the ranges.
Results: The calculator shows the data ranges for:
- 68% of data: within 1 standard deviation (mean ± σ)
- 95% of data: within 2 standard deviations (mean ± 2σ)
- 99.7% of data: within 3 standard deviations (mean ± 3σ)
Note: This rule applies only to normal distributions. Inputs can be any real numbers (no specific units required).
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Frequently Asked Questions
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.
Enter the mean and standard deviation of your normally distributed dataset, then click Calculate. The tool will show the ranges covering 68%, 95%, and 99.7% of the data.
No, the empirical rule only applies to data that follows a normal (bell-shaped) distribution. For non-normal distributions, Chebyshev's inequality may be used instead.
