SKEW in Excel: Sample Skewness, Tail Direction and Data Checks

• Introduced: first introduction version is not established by the official history reviewed; the current product list is not a launch record.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official SKEW reference. Documentation and independently modeled examples; no native Excel execution or broader platform certification.

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

Microsoft documents 1–255 arguments and permits arrays or references. Multiple observations may come from one range argument.

The official equation uses the sample standard deviation s and the factor n/((n−1)(n−2)). It multiplies that factor by the sum of cubed standardized deviations, ((x−mean)/s)^3.

This is not SKEW.P, which uses the population standard deviation and averages the cubed standardized deviations. Keep the convention in a report’s label, particularly for small datasets where the results differ substantially.

Enter 1,1,4 in A2:A4.

=SKEW(A2:A4)

Expected result: approximately 1.732050808. The mean is 2 and deviations are −1,−1,2. Their squared sum is 6, so sample variance is 3 and sample standard deviation is the square root of 3.

The cubed standardized deviations sum to approximately 1.154700538. The sample adjustment is 3/((3−1)(3−2))=1.5, producing the final result.

The larger value 4 creates the positive tail in this fixture. The result is dimensionless; it is not an extra 1.73 units added to the average.

For numeric 1,2,3, deviations from the mean cancel in the cubed sum, so:

=SKEW(1,2,3)

Expected result: 0. The sample still has nonzero spread. Zero skewness is different from a constant sample, where the standardized equation cannot be evaluated.

Reflect the first dataset through zero, giving −1,−1,−4. Its skewness is approximately −1.732050808. Reflection changes the sign of the third moment while leaving the magnitude of standard deviation unchanged.

Using A2:A4 from the first example, place these formulas in D2:D4:

=AVERAGE(A2:A4)
=STDEV.S(A2:A4)
=COUNT(A2:A4)

D2 is 2, D3 is approximately 1.732050808 and D4 is 3. In B2 enter and fill through B4:

=((A2-$D$2)/$D$3)^3

Then calculate:

=D4/((D4-1)*(D4-2))*SUM(B2:B4)

The expected result is approximately 1.732050808, matching the independent model. This helper calculation is scoped to a clean numeric sample with at least three observations and nonzero standard deviation. It is not an error-cleaning formula.

Adding 100 to the first numeric sample gives 101,101,104. Multiplying the original values by 10 gives 10,10,40. Both retain skewness approximately 1.732050808: translation cancels in deviations, and positive scaling cancels during standardization.

Repeating the whole original sample gives 1,1,4,1,1,4. The population’s standardized third moment remains the same, but the sample-size adjustment changes. Expected SKEW is now approximately 0.968245837, not 1.732050808.

Repeated records therefore do not preserve this sample statistic merely because they preserve the relative frequencies. Check whether duplicates represent genuine additional observations before interpreting the estimate.

For the original n=3 dataset, SKEW.P is approximately 0.707106781. Multiplying it by SQRT(n*(n-1))/(n-2) gives the corresponding sample-adjusted SKEW. For n=6, that factor is smaller.

Microsoft documents that text, logical values and empty cells in a reference are ignored, while numeric zeros are included. A range containing numeric 1,1,4, text "4", TRUE and a physically empty cell therefore has the same numeric comparison sample as the first example.

Direct logical arguments and direct text representations of numbers are documented as counted. Moving an input from a reference into the argument list can therefore change the calculation; do not assume the two forms have identical type handling.

A numeric zero is a real observation. For 0,0,0,4, the expected SKEW is 2. Removing the zeros leaves only one accepted observation and triggers the documented insufficient-data condition.

Microsoft explicitly documents #DIV/0! for fewer than three data points or zero sample standard deviation. Thus numeric 1,2 and 5,5,5 are invalid examples for this calculation, for different reasons.

Error arguments and text that cannot be translated numerically cause errors; a complete mixed-error reference matrix was not tested here. Inspect input problems before suppressing errors in a report.

Skewness alone does not identify a data-entry mistake, establish a probability model or prove a sample is representative. Combine it with AVERAGE, MEDIAN, an observation count and an inspection of the underlying values. Zero skewness is not a proof of a normal distribution.

• Microsoft SKEW reference.
• Editorial testing standards.

Expected results are independent statistical/arithmetic models or explicitly documented rules, not captured native output. Examples use English function names and comma separators. Datasets and reporting policies are fictional.