1. What is the Empirical Rule?

The Empirical Rule, also known as the 68-95-99.7 Rule, describes the percentage of values that lie within a band around the mean in a normal distribution with a width of one, two, or three standard deviations.

2. How Does the Calculator Work?

The calculator uses the Empirical Rule formula:

Where:

• μ — Mean of the distribution
• σ — Standard deviation of the distribution

Explanation: The rule applies to perfectly normal distributions. Real-world data may vary slightly.

3. Applications of the Empirical Rule

Details: The Empirical Rule is used in statistics for quick estimates of data spread, quality control, and identifying outliers in normally distributed data.

4. Using the Calculator

Tips: Enter the mean and standard deviation of your normally distributed data. The calculator will show the ranges containing 68%, 95%, and 99.7% of values.

5. Frequently Asked Questions (FAQ)

Q1: When is the Empirical Rule not applicable?
A: The rule only applies to perfectly normal distributions. Skewed or non-normal distributions will have different percentages.

Q2: What percentage falls outside 3 standard deviations?
A: Only about 0.3% of values fall outside ±3σ in a perfect normal distribution.

Q3: Can this be used for sample data?
A: Yes, if the sample is large enough and normally distributed, you can use sample mean and standard deviation.

Q4: How accurate is the Empirical Rule?
A: It's exact for theoretical normal distributions but may vary slightly with real-world data.

Q5: What's the difference between Empirical Rule and Chebyshev's Theorem?
A: Chebyshev's Theorem applies to all distributions (not just normal) but gives less specific bounds.