SKEW.P in Excel: Population Skewness and Standardized Third Moments

• Introduced: the Microsoft function catalogue marks SKEW.P as an Excel 2013 addition; an exact first build or preview date is not established here.
• 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.P reference. Documentation and independently modeled examples; no native Excel execution or broader platform certification.

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

Microsoft’s dedicated reference lists 1–254 number arguments, names, arrays or references. That is the documented argument scope, not a native-tested limit in this guide. A single reference can contain many observations.

The official equation is the sum of ((x−mean)/sigma)^3, divided by the population count N. Sigma is the population standard deviation. Substituting the sample standard deviation changes the answer.

Microsoft still requires at least three data points and nonzero spread. The mathematical third moment can be discussed in other cases, but that does not override the function’s documented restrictions.

Enter 1,1,4 in A2:A4.

=SKEW.P(A2:A4)

Expected result: approximately 0.707106781. The mean is 2, the squared deviations total 6, population variance is 2, and population standard deviation is the square root of 2.

The cubed standardized deviations total approximately 2.121320344. Dividing by all three observations gives 0.707106781. The larger observation contributes a positive tail.

On the same values, SKEW gives approximately 1.732050808. Neither value is a rounding correction to the other: they use different standardized formulas.

=SKEW.P(1,2,3)

Expected result: 0. The mean is 2, and the negative and positive cubed deviations cancel.

The population is not constant. A constant list 5,5,5 has standard deviation zero, so the function instead returns the documented #DIV/0! error. Do not replace that error with zero skewness and call the two datasets equivalent.

For the reflected population −1,−1,−4, expected skewness is approximately −0.707106781. Reflecting the sign reverses asymmetry without changing its magnitude.

For A2:A4 from the first fixture, put these formulas in D2:D4:

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

Expected values are 2, approximately 1.414213562, and 3. In B2 enter and fill through B4:

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

Then calculate:

=SUM(B2:B4)/D4

The result is approximately 0.707106781. These helpers apply to a clean numeric population; they do not silently resolve errors or coercion choices.

If STDEV.S is mistakenly substituted in D3, the same average of cubed standardized deviations becomes approximately 0.384900179. That is neither the correct SKEW.P nor the correctly adjusted SKEW result. Changing only one part of a statistical formula can create a third, unintended statistic.

Repeating the entire population gives 1,1,4,1,1,4. Its mean and population standard deviation remain unchanged. Both the cubed standardized-deviation sum and the count double, so SKEW.P remains approximately 0.707106781.

Selective repetition can change the shape. For numeric 0,0,0,4, population mean is 1, variance is 3, and expected SKEW.P is approximately 1.154700538. The single higher observation now accounts for one quarter of the records instead of one third.

These controls distinguish preserving a distribution’s relative frequencies from adding weight to selected observations. A table of distinct values alone is not enough to reproduce a frequency-weighted population statistic.

The populations 101,101,104 and 10,10,40 both retain the first fixture’s population skewness, approximately 0.707106781. Adding a constant and multiplying by a positive constant leave standardized asymmetry unchanged.

Multiplying by a negative constant reverses the sign. This is useful when a metric is recoded from a gain to a loss, but the reporting label must explain the changed direction.

For the same clean numeric data with n greater than two, multiplying SKEW.P by SQRT(n*(n-1))/(n-2) gives the adjusted sample SKEW model. At n=3 the multiplier is approximately 2.449489743, giving 1.732050808. The conversion requires identical included observations.

Microsoft says reference text, logical values and physically empty cells are ignored; numeric zeros are included. A reference containing numbers 1,1,4, text "4", TRUE and a physically empty cell therefore retains the three numeric observations for this model.

Direct logical values and direct numeric text are documented as counted. Do not assume moving them from reference cells into the argument list leaves the result unchanged.

The page documents #DIV/0! for fewer than three points or zero spread. It refers to sample standard deviation in that error sentence, but separately specifies population standard deviation in the equation; either convention is zero for a constant dataset. The examples follow the explicit population equation.

The source also names #NUM! for invalid values and #VALUE! for invalid types without a complete case matrix. Specific classifications for ambiguous mixed inputs remain unverified here. No native error tests were run.

Use STDEV.P to report population spread alongside skewness. Neither low nor zero skewness proves normality, validates an observation or establishes a causal explanation for a tail.

• Microsoft SKEW.P 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.