The Empirical Rule Formula Calculator is a statistical tool used to determine the distribution of data points in a normal distribution based on the mean and standard deviation. Also known as the 68-95-99.7 rule or the three-sigma rule, the Empirical Rule states that for a normal distribution:

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

This calculator helps users quickly determine these ranges without manual calculations, making it invaluable for statisticians, researchers, and students working with normally distributed data.

How to use the Empirical Rule Formula Calculator?

1. Enter the Mean (μ

Input the average value of your dataset in the “Mean (μ)” field. This represents the central tendency of your data.

2. Enter the Standard Deviation (σ)

Input the standard deviation of your dataset in the “Standard Deviation (σ)” field. This represents the spread or dispersion of your data points from the mean.

3. Click “Calculate”

After entering both values, click the “Calculate” button. The calculator will show three ranges, each corresponding to the 68%, 95%, and 99.7% rules:

• The range for 68% of the data (within one standard deviation)
• The range for 95% of the data (within two standard deviations)
• The range for 99.7% of the data (within three standard deviations)

Each result includes a brief interpretation to help you understand its significance.

By providing quick and accurate calculations, this Empirical Rule Formula Calculator simplifies the process of understanding and applying the 68-95-99.7 rule to real-world data analysis tasks.