KURT in Excel: Sample Excess Kurtosis and Outlier Sensitivity

=KURT(number1, [number2], ...)

The reference permits 1–255 arguments; an argument can supply multiple observations through a range. Direct logical values and numeric text can be counted, while text, logical values and blanks inside references are ignored. Numeric zero remains an observation. Error arguments and unconvertible direct text cause errors. Fewer than four counted observations, or zero sample spread, produce documented #DIV/0!. Microsoft’s syntax and data rules

For reproducibility, use a clean numeric column and explicitly check its count. Replacing a missing measurement with zero changes the dataset; leaving it blank changes the number of counted observations. Neither choice is merely formatting.

Enter A2:A5 as 2, 4, 6 and 8, one number per cell. In B2 enter:

=KURT(A2:A5)

The independent expectation is −1.2. Here is the calculation, so the result does not depend on an unexplained example value:

• n = 4 and mean = 5.
• Deviations are −3, −1, 1 and 3.
• Sum of squared deviations is 20; sample variance s² = 20/3.
• Sum of fourth powers is 164.
• The standardized fourth-power sum is 164/(20/3)² = 3.69.

Using Q = sum[((xi − mean)/s)^4], the documented estimator is:

K = n(n+1)Q / ((n−1)(n−2)(n−3))
    − 3(n−1)^2 / ((n−2)(n−3))

Thus K = (10/3)×3.69 − 13.5 = −1.2. The sample standard deviation in the denominator is essential. Substituting the population standard deviation changes the statistic.

Translation leaves deviations unchanged. Multiplying every observation by the same nonzero scale multiplies fourth powers and squared variance by matching factors, so the standardized result is unchanged. These invariances make useful checks when a measurement changes units.

For 2, 4, 6 and 20, the mean becomes 8, squared deviations total 200, and fourth powers total 22,304. The standardized fourth-power sum is 5.0184. Applying the same n=4 adjustment gives 3.228. Changing one observation from 8 to 20 therefore changes the statistic from −1.2 to 3.228.

This is a sensitivity illustration, not a rule that the value 20 is erroneous. Inspect provenance, units and the measurement process before deciding how to handle it. A fourth-moment summary cannot distinguish a valid extreme measurement from a transcription problem. Report the sample size and examine the observations alongside the statistic; a very small dataset can be particularly unstable.

Positive and negative excess kurtosis summarize aspects of the fourth moment relative to a normal benchmark. Treating the sign as a complete description of a histogram’s peak, or as a universal risk classification, loses important information. Two datasets can share kurtosis while differing substantially elsewhere.

A2:A4 containing 2, 4, 6 has only three observations and has the documented #DIV/0! outcome. Four copies of 5 have zero spread and the same documented outcome. Adding duplicate records to meet the minimum changes the data and is not a statistical repair.

Use COUNT and STDEV.S to inspect count and sample spread. SKEW concerns asymmetry, whereas KURT uses an even power and is unchanged by reflecting every value through zero. Neither function replaces a plot or a justified sampling model.

Microsoft’s dedicated reference, checked October 18, 2026, lists Excel for Microsoft 365 on Windows and Mac, Excel 2024 on Windows and Mac, Excel 2021 on Windows and Mac, Excel 2019 and Excel 2016. This is the documented product scope, not a record of execution on those releases. First introduction and last functioning build are unknown; the product list does not establish either. The reference continues to document this function; it does not establish a retirement date.

The examples here are independently calculated or explicitly identified as documented expectations. No Excel application or other spreadsheet engine was run, and no native screenshots are supplied. Very large, ill-conditioned or locale-sensitive inputs require separate validation.

Official KURT reference.