KURT in WPS Spreadsheet: Corrected Sample Excess Kurtosis

=KURT(number1, number2, ...)

The article says 1 through 30 arguments, while its actual function-dialog image says 1 through 255. This source conflict does not establish a universal current argument ceiling. All original examples use one fully numeric range, with at least four nonconstant observations.

The lesson calls the statistic “peakedness” or flatness relative to normality. Treat that as a limited description: fourth moments also depend strongly on tails and unusual observations. A single kurtosis number does not fully characterize the visual peak or establish normality.

For n observations, mean m and sample standard deviation s, the displayed WPS equation is:

n*(n+1)/((n−1)*(n−2)*(n−3))*sum(((x−m)/s)^4) − 3*(n−1)^2/((n−2)*(n−3)).

Enter 1, 2, 3, 4 in A2:A5 and use =KURT(A2:A5) in C2.

1. Mean m = 2.5; squared deviations sum to 5.
2. Sample variance is 5/3, so s squared is 5/3.
3. Fourth-power deviations sum to 10.25. Divide by s to the fourth power, 25/9, to get standardized fourth-power sum 3.69.
4. The first coefficient is 10/3 and the correction term is 13.5.
5. The independent result is 12.3 − 13.5 = −1.2.

Using a population standard deviation or simply subtracting three from an uncorrected moment would produce a different statistic.

Shifting every observation changes the mean but leaves centered deviations unchanged. Scaling changes deviations and standard deviation together, leaving this dimensionless statistic unchanged. Unlike skewness, reversing signs does not reverse kurtosis because fourth powers are even.

The sample 1, 1, 1, 5 yields 4, showing how a single separated value can affect the fourth-power sum. It does not prove that the underlying population has a particular tail law. With small samples, the estimate can vary substantially when an observation changes.

A value near zero is not a complete normality test, and a negative value does not mean negative variance. Keep the raw data, sample size and other summaries beside the result. DEVSQ helps explain the squared-deviation component; AVERAGE explains the center.

The vendor example uses nine prices 7.8, 6.7, 10.23, 12.25, 13.79, 15.28, 18.33, 21.58 and 23.12, displaying −1.140741971. The formula image confirms that s is the sample standard deviation.

The lesson documents #DIV/0! for fewer than four data points or zero sample standard deviation. It distinguishes direct logical/numeric-text arguments from values inside references, but this guide does not rely on mixed-value coercion. Numeric zeros are genuine observations; blanks and error cells require separate handling. Original controls avoid those cases and do not infer a modern dotted alias or a population-kurtosis contract.

The official WPS lesson is dated 2019-06-10 and explicitly labels WPS Office for Windows Personal. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.

The complete lesson and its formula images and walkthrough were inspected on October 18, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.