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: |