What is the Empirical Rule?

Also known as the 68-95-99.7 rule. It states that for a normal distribution, nearly all data falls within 3 standard deviations of the mean.

What are the percentages?

68% within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs.

Only for symmetric, bell-shaped (normal) distributions.

Calculate ranges for 68%, 95%, and 99.7% of data in a normal distribution.

Mean (μ)

Average value

Standard Deviation (σ)

Spread of data

68% (±1σ)

85 to 115

Approximately 68% of the data falls within this range.

95% (±2σ)

70 to 130

Approximately 95% of the data falls within this range.

99.7% (±3σ)

55 to 145

Approximately 99.7% of the data falls within this range.

Frequently Asked Questions

How to Use

What it calculates

This empirical rule solves mathematical and statistical problems using standard formulas. 68-95-99.7 rule ranges.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Empirical Rule.

Explore More

Visualize quartiles and outliers.

Histogram and frequency table.

Distribution with original values.

Compare means of 3+ groups using F-test.

Calculate conditional probability P(A|B) using priors.

Probability on interval [0, 1].