Sample Excess Kurtosis Calculator
Calculate adjusted excess kurtosis for a numeric sample.
How the sample excess kurtosis calculator works
Excess kurtosis compares a sample’s fourth standardized moment with the normal-distribution reference, which is defined as zero after subtracting three. This calculator uses the finite-sample Fisher correction rather than the simple population moment. Positive values indicate greater tail weight or outlier propensity by this measure; negative values indicate a flatter, lighter-tailed pattern relative to normal.
The default evenly spaced sample 1, 2, 3, 4, 5 has mean 3 and symmetric deviations. Applying the adjusted sample formula gives the verified excess kurtosis minus 1.2. That negative result reflects the short bounded sequence’s lighter tails compared with an ideal normal distribution, not an error caused by subtracting the normal reference.
Reading sample excess kurtosis calculator results privately
At least four observations and nonzero variance are required. Small-sample kurtosis is noisy even with bias correction, and a single value does not distinguish sharp central peaks from heavy tails. Some sources report ordinary kurtosis with normal reference three rather than excess kurtosis with reference zero, creating an exact difference of three. This sample excess kurtosis calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why is normal excess kurtosis zero?
Excess kurtosis subtracts three from ordinary kurtosis so the normal distribution becomes the zero reference.
Does positive kurtosis always mean a sharper peak?
No. The fourth moment is strongly tied to tail weight and outliers; peak shape alone is an incomplete interpretation.
Is the sample excess kurtosis calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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