Empirical Rule Calculator

How to Calculate the Empirical Rule

The empirical rule is calculated using three ranges:

1. First Range = [mean - standard deviation, mean + standard deviation]


2. Second Range = [mean - 2 * standard deviation, mean + 2 * standard deviation]


3. Third Range = [mean - 3 * standard deviation, mean + 3 * standard deviation]

Why the Empirical Rule is Important

The empirical rule helps forecast data points and identify trends, making it valuable in data analysis and statistics.

Understanding Your Results

After using the empirical rule calculator, you will get three different lines of results.

• 68% of data - The first line of your results is telling you 68% of your data points should fall within the given range. These values are within one standard deviation of the mean.


• 95% of data - The second line of your results is telling you 95% of your data points should fall within the given range. These values are within two standard deviation of the mean.


• 99.7% of data - The third line of your results is telling you 99.7% of your data points should fall within the given range. These values are within three standard deviation of the mean.

How to Use This Calculator

1. Enter the value of the mean.


2. Enter the standard deviation.


3. Hit calculate and instantly get your answer!

Calculation Example

Let's say you are a teacher and you wanted to use the empirical rule on your student's latest test scores. The mean was 90 and carried a standard deviation of 3. Using the three formulas, we find that 68% of the data should fall between 87 and 93, 95% of the data should be between 84 and 96, while 99.7% of the scores are between 81 and 99.