What is the Standard Deviation Rule (68-95-99.7 Rule)?
The Standard Deviation Rule, also known as the Empirical Rule, is a statistical concept that applies to normal distributions. It states:
- Approximately 68% of data falls within 1 standard deviation of the mean (μ ± σ)
- Approximately 95% of data falls within 2 standard deviations of the mean (μ ± 2σ)
- Approximately 99.7% of data falls within 3 standard deviations of the mean (μ ± 3σ)
How to Use This Calculator
- Enter the mean (μ) of your dataset
- Enter the standard deviation (σ) of your dataset
- Click the "Calculate" button to see the probabilities
Example Usage
Suppose you have a dataset with a mean of 100 and a standard deviation of 15:
- You would expect approximately 68% of values to fall between 85 (100-15) and 115 (100+15)
- Approximately 95% of values to fall between 70 (100-2×15) and 130 (100+2×15)
- Approximately 99.7% of values to fall between 55 (100-3×15) and 145 (100+3×15)
Practical Applications
This rule is widely used in statistics, quality control, finance, and many other fields to understand data distributions and make predictions. It helps in:
- Identifying outliers in data
- Understanding the spread of measurements
- Making predictions about future observations
- Setting control limits in quality control