Empirical Rule Calculator (68%, 95%, 99.7%)

The Empirical Rule Calculator helps you easily determine the ranges in which your data points fall, according to the empirical rule (68%, 95%, 99.7%). By entering the mean and standard deviation of your data set, the calculator provides the ranges within one, two, and three standard deviations from the mean, making it easier to understand the distribution of your data.

Empirical Rule Formula

For a normal distribution:

• 68% of data lies within 1 standard deviation of the mean.
• 95% of data lies within 2 standard deviations of the mean.
• 99.7% of data lies within 3 standard deviations of the mean.

Empirical Rule Definition

The Empirical Rule, or 68-95-99.7 rule, describes the spread of data in a normal distribution. It highlights that:

• Approximately 68% of data falls within one standard deviation of the mean.
• Roughly 95% falls within two standard deviations.
• About 99.7% lies within three standard deviations.

This rule simplifies the process of predicting data behavior in a normal distribution, aiding in identifying outliers and understanding the likelihood of different outcomes.

Empirical Rule Example

To calculate the empirical rule:

1. Determine the standard deviation. Calculate the average deviation from the mean for your data set.
2. Apply the empirical rule. Use the above formula to determine the data ranges for 68%, 95%, and 99.7% confidence levels.

FAQ

• What is the Empirical Rule? It states that for a normal distribution, 68%, 95%, and 99.7% of data lies within 1, 2, and 3 standard deviations from the mean, respectively.