1. What is the Empirical Rule?

The Empirical Rule (68-95-99.7 Rule) states that for a normal distribution:

• ≈68% of data falls within ±1 standard deviation from the mean
• ≈95% within ±2 standard deviations
• ≈99.7% within ±3 standard deviations

2. How Does the Calculator Work?

The calculator generates a normal distribution curve based on your input mean (μ) and standard deviation (σ), then shades the areas corresponding to ±1σ, ±2σ, and ±3σ.

3. Importance of the Empirical Rule

The Empirical Rule provides a quick way to estimate the spread of data in a normal distribution, useful in statistics, quality control, and risk assessment.

4. Using the Calculator

Enter the mean and standard deviation of your normal distribution. The calculator will display the percentage ranges and generate a visual representation.

5. Frequently Asked Questions (FAQ)

Q1: When is the Empirical Rule applicable?
A: Only for perfectly normal distributions. Many real-world distributions are approximately normal.

Q2: What if my data isn't normally distributed?
A: The Empirical Rule percentages won't hold. Consider other methods like Chebyshev's inequality.

Q3: Why are the percentages fixed?
A: These are mathematical properties of the normal distribution curve.

Q4: Can I use this for sample data?
A: Yes, if you know the sample mean and standard deviation, and the distribution is normal.

Q5: How accurate is the Empirical Rule?
A: The percentages are exact for theoretical normal distributions.