For approximately normal data, the empirical rule describes coverage within one, two and three standard deviations.
Empirical Rule Calculator
Form
Results
0
Table of Contents
1
What is Empirical Rule?
2
How to Use This Calculator
- Enter or select Mean, Standard deviation.
- Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
- Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
3
Formula Used
Intervals: μ ± σ; μ ± 2σ; μ ± 3σ
4
Variables Explained
| Input | What it means |
|---|---|
| Mean | The arithmetic average or stated population mean used as a reference. |
| Standard deviation | The spread of individual observations around their mean, in the data’s original units. |
5
Worked Example
Mean 100 and standard deviation 15 give 85–115 for the roughly 68% interval.
6
Why Use This Calculator?
Sketch approximate coverage intervals when a normal model is reasonable.
7
Common Mistakes
- The 68–95–99.7 pattern is not reliable for strongly skewed or multimodal data.
8
Frequently Asked Questions
Does a calculated statistic prove a conclusion?
A statistic describes the supplied data under stated assumptions. Sampling design, missing observations and the suitability of the model still determine what can reasonably be concluded.
Should I include every observation?
Use the observations required by your study design and state any exclusion rule. Removing values only because they change the answer can bias the analysis.
9
Sources & References
Mini Calculator provides online calculators for multiple niches including mathematical, financial, Health, informative, Chemistry, physics, statistics, and conversions. You can use any calculator for free without any limits.