Empirical Rule Calculator (68-95-99.7 Rule)
The Empirical Rule (also known as the 68-95-99.7 rule) states that for a normal distribution:
- Approximately 68% of data falls within 1 standard deviation of the mean
- Approximately 95% of data falls within 2 standard deviations of the mean
- Approximately 99.7% of data falls within 3 standard deviations of the mean
Input Parameters
The center of your distribution
Measures the spread of your data
Calculate probabilities for this value
Results
Standard Deviation Ranges
| Range | Values | % of Data | Contains Values | 
|---|---|---|---|
| μ ± 1σ | 68.27% | ||
| μ ± 2σ | 95.45% | ||
| μ ± 3σ | 99.73% | 
Z-Score Analysis
| Z-Score for X: | |
| P(X < x): | |
| P(X > x): | 
Custom Range Analysis
| Range: | |
| P(lower ≤ X ≤ upper): | |
| % of total area: | 
