Empirical or 68-95-99.7 Rule Calculation
The 68-95-99.7 rule, also known as the empirical rule or three-sigma rule, is a statistical guideline that describes the percentage of data that fall within a few standard deviations from the mean in a normal distribution. The rule states the following:
About 68% of the data falls within one standard deviation of the mean.
Approximately 95% falls within two standard deviations.
Approximately 99.7% falls within three standard deviations.
If you have a dataset with a normal distribution, you can use a calculator to determine the ranges within one, two, and three standard deviations from the mean. Here's a simple way to calculate it:
- Within one standard deviation: mean ± standard deviation
- Within two standard deviations: mean ± 2 * standard deviation
- Within three standard deviations: mean ± 3 * standard deviation
For example, if the mean (average) of your data is 50 and the standard deviation is 10, then:
- Within one standard deviation: 50 ± 10 = 40 to 60 (68% of the data falls within this range).
- Within two standard deviations: 50 ± 2 * 10 = 30 to 70 (95% of the data falls within this range).
- Within three standard deviations: 50 ± 3 * 10 = 20 to 80 (99.7% of the data falls within this range).
This rule is particularly useful for understanding the distribution of data in statistics and identifying outliers. Keep in mind that the 68-95-99.7 rule applies for the normal distribution, and the actual distribution of your data may differ.
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