1. What is Kurtosis?

Kurtosis is a statistical measure that describes the degree to which a probability distribution is concentrated in the tails compared to a normal distribution. It measures the "tailedness" of the distribution as the fourth standardized moment.

2. How Does the Calculator Work?

The calculator uses the kurtosis formula:

Where:

• \( x_i \) — Individual data values
• \( \mu \) — Mean of the data
• \( \sigma \) — Standard deviation of the data
• \( n \) — Number of data points

Explanation: Kurtosis measures the fourth standardized moment about the mean, indicating whether data are heavy-tailed or light-tailed relative to a normal distribution.

3. Importance of Kurtosis Calculation

Details: Kurtosis helps identify outliers and understand the risk profile of data distributions. High kurtosis indicates heavy tails and more outliers, while low kurtosis indicates light tails and fewer outliers.

4. Using the Calculator

Tips: Enter numerical data values separated by commas. The calculator will compute the mean, standard deviation, and kurtosis automatically. Ensure you have at least 4 data points for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What does kurtosis value indicate?
A: Normal distribution has kurtosis ≈ 3. Values > 3 indicate heavy tails (leptokurtic), values < 3 indicate light tails (platykurtic).

Q2: What is excess kurtosis?
A: Excess kurtosis = kurtosis - 3. This centers the normal distribution at 0, making interpretation easier.

Q3: When is high kurtosis problematic?
A: High kurtosis in financial data indicates higher risk of extreme events. In quality control, it may suggest process instability.

Q4: What are typical kurtosis ranges?
A: Most distributions range from 1 to 10. Values outside this range are rare and may indicate data issues.

Q5: How does sample size affect kurtosis?
A: Small samples may give unreliable kurtosis estimates. For accurate results, use at least 20-30 data points.