Empirical Rule Calculator

The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical principle that states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Use the Empirical Rule when you have data that follows a normal (bell-shaped) distribution. It's useful for understanding data spread, identifying outliers, and making predictions about where most of your data points should fall.

If your data doesn't closely match the 68-95-99.7 percentages, it may indicate that your data is not normally distributed. This could mean your data is skewed, has multiple peaks, or follows a different distribution pattern.

Compare the actual percentages in your data to the expected 68%, 95%, and 99.7%. If they're close, your data likely follows a normal distribution. Large differences suggest non-normal data or the presence of outliers.

Population standard deviation divides by N (total count), while sample standard deviation divides by N-1 (degrees of freedom). This calculator uses population standard deviation. For small samples, consider using sample standard deviation instead.

While you can input any numeric data, the Empirical Rule is most meaningful for data that follows a normal distribution. For skewed or non-normal data, the percentages may not match the expected values.

Outliers are data points that fall outside the expected ranges. According to the Empirical Rule, only about 0.3% of data should fall beyond 3 standard deviations from the mean in a normal distribution.

The Empirical Rule provides approximate percentages. In practice, real data may vary slightly from these exact percentages even for normal distributions. The rule is most useful as a general guideline for understanding data spread.

Z-scores measure how many standard deviations a data point is from the mean. The Empirical Rule corresponds to z-scores of ±1 (68%), ±2 (95%), and ±3 (99.7%). This calculator shows the actual ranges and percentages for your data.

Yes! The Empirical Rule is commonly used in quality control to identify when processes are out of control. Data points falling outside the expected ranges may indicate process changes or defects that need attention.