Empirical Rule Calculator
Use this unified calculator to apply the Empirical Rule (68-95-99.7 rule) to both ungrouped (raw) data and grouped (frequency distribution) data. The empirical rule describes the distribution of data in a bell-shaped (normal) distribution.
Quick Start
| Empirical Rule Calculator | |
|---|---|
| Data Type | Ungrouped (Raw Data) Grouped (Frequency Distribution) |
| Enter the X Values (Separated by comma,) | |
| Type of Frequency Distribution | DiscreteContinuous |
| Enter the Classes for X (Separated by comma,) | |
| Enter the frequencies (f) (Separated by comma,) | |
| Results | |
| Number of Observations (n): | |
| Mean of X values: (x̄) | |
| Standard Deviation (SD): | |
| 68% of Data falls between: | |
| 95% of Data falls between: | |
| 99.7% of Data falls between: | |
The Empirical Rule (68-95-99.7 Rule)
For bell-shaped (approximately normal) distributions:
- 68% of data falls within ±1 standard deviation of the mean
- 95% of data falls within ±2 standard deviations of the mean
- 99.7% of data falls within ±3 standard deviations of the mean
Formulas
Range Calculations:
- 68% range: x̄ ± 1σ = [x̄ - σ, x̄ + σ]
- 95% range: x̄ ± 2σ = [x̄ - 2σ, x̄ + 2σ]
- 99.7% range: x̄ ± 3σ = [x̄ - 3σ, x̄ + 3σ]
Where:
- x̄ = mean
- σ = standard deviation
When to Use
✓ Data appears approximately normal/bell-shaped ✓ Quick estimation of data spread ✓ Identifying unusual values (outliers) ✓ Quality control in manufacturing
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