Empirical or 68-95-99.7 Rule Calculation
The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical concept that is used to describe the distribution of data in a normal distribution. The rule states that:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
This means that in a normal distribution, most of the data falls within a certain range of values around the mean. For example, if a dataset has a normal distribution with a mean of 50 and a standard deviation of 10, then approximately:
- 68% of the data falls between 40 and 60.
- 95% of the data falls between 30 and 70.
- 99.7% of the data falls between 20 and 80.
The Empirical Rule is a useful concept in statistics because it allows you to make predictions about the distribution of data based on the mean and standard deviation. It is often used in quality control and process improvement to monitor the distribution of data and identify potential issues. It can also be used to compare datasets and determine whether they have similar or different distributions.
