VARP in WPS Spreadsheet: Population Variance and Squared Units
Calculate variance for a complete numeric population, verify the divisor n and understand shifts, scaling and the difference from sample variance.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
VARP calculates population variance: the mean squared deviation from the mean of the supplied population. Use this interpretation when the values represent the entire population you intend to describe. Treating a sample as a population changes the statistic’s denominator and interpretation.
Syntax and clean-data scope
=VARP(number1, number2, ...)
The historical WPS lesson describes 1 through 30 arguments. That is its documented syntax-era limit, not a claim about every current build. The original examples use one fully numeric range, avoiding limits on the number of separate arguments and mixed-value coercion.
The formula image is sum((x−mean)^2)/n. It divides by the number of numeric observations n, rather than n−1. The output has squared measurement units.
Original worksheet example
Enter 2, 4, 6 in A2:A4 and use =VARP(A2:A4) in C2.
- The mean is 4.
- Deviations are −2, 0, 2.
- Squared deviations are 4, 0, 4, with total 8.
- Divide by three observations: expected population variance is 8/3, approximately 2.66666666666667.
The sample calculation would divide 8 by 2 and return 4. Those answers describe different estimators; do not select one merely because it is larger or smaller.
Independent controls
| Numeric range values | Formula | Expected population variance |
|---|---|---|
| 2, 4, 6 | =VARP(A2:A4) |
8/3 |
| 12, 14, 16 | =VARP(A2:A4) |
8/3 |
| 4, 8, 12 | =VARP(A2:A4) |
32/3 |
| 5, 5, 5 | =VARP(A2:A4) |
0 |
| −2, 0, 2 | =VARP(A2:A4) |
8/3 |
| 0, 2, 4, 6 | =VARP(A2:A5) |
5 |
The last case includes a genuine zero observation. Its mean is 3 and squared deviations total 20, giving 20/4=5. A blank cell is not an interchangeable way to encode that zero.
Advanced checks: translation and scaling
Adding 10 to every value shifts the mean by 10 but leaves each deviation unchanged. This explains the first two rows. Multiplying every observation by two multiplies squared deviations, and hence variance, by four. Thus converting measurement units changes variance quadratically.
For the first population, taking the square root of 8/3 gives a population standard deviation of approximately 1.6329931619 in the original units. The variance itself remains in squared units. Avoid comparing variances from differently scaled measurements without accounting for those units.
Documentation and troubleshooting
The WPS demonstration lists 19 observations and displays 2260.138504. Its population-divisor formula is visible beside the example. This is a historical vendor illustration, not a benchmark of precision for other input magnitudes.
The lesson says logical and text values are ignored and points to VARPA when they should be included. The examples here do not generalize that statement to every scalar/reference coercion path. No empty-range or error-cell result is invented. Check the range, intended population, numeric completeness and unit scale first.
AVERAGE supplies the mean concept and DEVSQ concerns the unnormalized squared-deviation sum. A modern dotted spelling is not treated as an automatically available alias of this documented legacy function.
Availability and evidence scope
The official WPS lesson is dated 2019-06-13 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.