⛰️ Kurtosis Calculator
Calculate excess kurtosis to assess tail heaviness relative to a normal distribution.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate excess kurtosis to assess tail heaviness relative to a normal distribution.
| Concept | Formula or rule |
|---|---|
| Kurtosis Calculator | Excess kurtosis = adjusted fourth standardized moment − 3 |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: A normal distribution has excess kurtosis near 0.
✓ Positive suggests heavier tails; negative suggests lighter tails.
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Calling kurtosis only peakedness
Modern interpretation emphasizes tail weight and outlier propensity.
Modern interpretation emphasizes tail weight and outlier propensity.
⚠️
Forgetting the minus 3 convention
Some software reports kurtosis around 3 for normal data; others report excess kurtosis around 0.
Some software reports kurtosis around 3 for normal data; others report excess kurtosis around 0.
⚠️
Trusting tiny samples
Fourth moments are unstable with few observations.
Fourth moments are unstable with few observations.
Practice Questions
1. What is normal excess kurtosis?
Answer: 0
2. Does positive kurtosis imply positive skew?
Answer: No.
3. Which moment is used for kurtosis?
Answer: The fourth standardized moment.
Frequently Asked Questions
What does positive excess kurtosis mean?▾
Heavier tails than a normal distribution.
What does negative excess kurtosis mean?▾
Lighter tails than a normal distribution.
Can kurtosis be affected by outliers?▾
Very strongly.