Empirical Rule Calculator – 68–95–99.7
Find intervals within one, two and three standard deviations of a normal distribution.
Formula
μ ± σ ≈ 68%; μ ± 2σ ≈ 95%; μ ± 3σ ≈ 99.7%
Lower 1σ ≈ (100)-(15) · Upper 1σ ≈ (100)+(15) · Lower 2σ ≈ (100)-2×(15) · Upper 2σ ≈ (100)+2×(15) · Lower 3σ ≈ (100)-3×(15) · Upper 3σ ≈ (100)+3×(15)
How to use
- Enter the mean.
- Enter a positive standard deviation in the same unit.
- Read the lower and upper limits of each interval.
Examples
- μ=100, σ=15: about 95% lies from 70 to 130.
Frequently asked questions
When does the rule apply?
To normal distributions; it is an approximation for roughly bell-shaped data.
Are the percentages exact?
No. They are rounded normal-distribution probabilities.
Does it prove my data are normal?
No. You must assess the distribution separately.
Sources
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