The standard deviation percentages, often associated with the empirical rule (or 68-95-99.7 rule), describe how much of the data in a normal distribution falls within certain standard deviations from the mean.
Understanding the Empirical Rule
The empirical rule provides a quick estimate of the spread of data in a normal distribution based on its standard deviation. Here's a breakdown:
- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations of the mean.
- 99.7% of the data falls within 3 standard deviations of the mean.
Standard Deviation Percentages in a Table
| Standard Deviations from the Mean | Percentage of Data |
|---|---|
| +/- 1 | 68% |
| +/- 2 | 95% |
| +/- 3 | 99.7% |
Practical Application
Let's say the average height of adult women is 5'4" (64 inches) with a standard deviation of 2.5 inches.
- 68% of women are between 61.5 inches (64 - 2.5) and 66.5 inches (64 + 2.5).
- 95% of women are between 59 inches (64 - 5) and 69 inches (64 + 5).
- 99.7% of women are between 56.5 inches (64 - 7.5) and 71.5 inches (64 + 7.5).
Important Considerations
- This rule only applies to approximately normal distributions (bell-shaped curves).
- These percentages are approximations, not exact values.
In summary, the standard deviation percentages within a normal distribution are approximately 68%, 95%, and 99.7% for 1, 2, and 3 standard deviations from the mean, respectively.
