Sample Kurtosis Calculator
Excess kurtosis describes tail weight and peakedness relative to a normal distribution under a particular estimator. This calculator applies an adjusted sample estimator.
How to use this calculator
- Enter at least four numeric observations; constant samples are rejected.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by kurtosis calculator calculator
Adjusted excess kurtosis uses the fourth central moment with a finite-sample correction and subtracts the normal-reference adjustment.
- Adjusted excess kurtosis uses the fourth central moment with a finite-sample correction and subtracts the normal-reference adjustment.
- Kurtosis can be unstable with small samples and extreme values. It is not a stand-alone test of normality.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
A seven-observation sample is entered as semicolon-separated values to estimate adjusted excess kurtosis.
The tool calculates the sample mean and second and fourth central moments before applying the finite-sample formula.
Zero is the normal-reference value for excess kurtosis, under this estimator.
Understanding the result
Excess kurtosis describes tail weight and peakedness relative to a normal distribution under a particular estimator. This calculator applies an adjusted sample estimator.
Kurtosis can be unstable with small samples and extreme values. It is not a stand-alone test of normality.
Important notes
Kurtosis can be unstable with small samples and extreme values. It is not a stand-alone test of normality.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
Can excess kurtosis be negative?
Yes. A negative result indicates lighter tails than the normal-reference value under this statistic.
Does high kurtosis always mean a sharp peak?
No. It is strongly influenced by tail behavior and extreme observations.
How should I interpret this result?
Kurtosis can be unstable with small samples and extreme values. It is not a stand-alone test of normality.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
- Z-Score — Learn what a z-score measures and how it describes a value relative to a mean and standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.