What is the Empirical Rule?

The Empirical Rule, also known as the 68-95-99.7 rule or the Three-Sigma Rule, is a statistical principle used to describe the distribution of data in a normal distribution (bell curve). It states that:

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

This rule is widely used in statistics, data analysis, and quality control to understand the spread of data and identify outliers.

How to Use the Empirical Rule Calculator?

1. Enter the Mean (μ)

• Type the average value of your dataset into the “Mean (μ)” field.
• This represents the central tendency of your data.
• Use decimal points if necessary (e.g., 75.5).

2. Enter the Standard Deviation (σ)

• Input the standard deviation of your dataset into the “Standard Deviation (σ)” field.
• This measure represents the spread or variability of your data.
• Use decimal points if needed (e.g., 12.3).

3. Click “Calculate”

After entering both values, click the “Calculate” button.

The calculator will show three ranges, each corresponding to a different percentage of data:
a) 68% range (±1σ): This shows the interval containing approximately 68% of the data.
b) 95% range (±2σ): This displays the interval containing about 95% of the data.
c) 99.7% range (±3σ): This presents the interval containing roughly 99.7% of the data.

Each range is presented with its lower and upper bounds.

By following these steps, users can effectively utilize the Empirical Rule Calculator to gain insights into their data distribution, set expectations for data ranges, and make informed decisions based on statistical principles.