## Empirical or 68-95-99.7 Rule Calculation

The empirical rule is a statistical rule that describes the distribution of a data set in terms of its mean and standard deviation. It states that for a normally distributed data set:

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.

To use the empirical rule to calculate these values, you will need to know the mean and standard deviation of your data set. Once you have these values, you can use the following formulas:

To calculate the range of values within one standard deviation of the mean: mean +/- 1 * standard deviation

To calculate the range of values within two standard deviations of the mean: mean +/- 2 * standard deviation

To calculate the range of values within three standard deviations of the mean: mean +/- 3 * standard deviation

For example, if the mean of a data set is 100 and the standard deviation is 15, then:

Approximately 68% of the data falls within the range of 85 to 115 (100 +/- 1 * 15).

Approximately 95% of the data falls within the range of 70 to 130 (100 +/- 2 * 15).

Approximately 99.7% of the data falls within the range of 55 to 145 (100 +/- 3 * 15).

I hope this helps! Let me know if you have any other questions.