Empirical Rule Calculator
Enter the mean and standard deviation of approximately normal data to see intervals covering 68%, 95%, and 99.7% of observations.
68% interval
(85.000, 115.000)
Approximately 68% of observations fall within 1 standard deviation of the mean.
95% interval
(70.000, 130.000)
Approximately 95% of observations fall within 2 standard deviations of the mean.
99.7% interval
(55.000, 145.000)
Approximately 99.7% of observations fall within 3 standard deviations of the mean.
How to Use This Calculator
- Provide the population or sample mean and standard deviation of a roughly normal dataset.
- Reference the intervals to describe typical and extreme observations.
- Use the 95% interval for quick back-of-the-envelope estimates of uncertainty.
Formula
68%: μ ± 1σ
95%: μ ± 2σ
99.7%: μ ± 3σ
The empirical rule holds precisely for normal distributions and approximately for bell-shaped, symmetric datasets.
Frequently Asked Questions
Does the empirical rule apply to skewed data?
Not reliably. Skewed distributions deviate from the 68-95-99.7% breakdown; use quantiles instead.
How do I verify normality?
Inspect histograms, Q-Q plots, or perform normality tests (Shapiro–Wilk, Anderson–Darling).
Can I use sample statistics?
Yes. The rule is often applied to sample means and standard deviations as approximate descriptors.