COVARIANCE.P in WPS Spreadsheet: Population Covariance from Matched Observations
Calculate population covariance with the n divisor, preserve observation pairs and interpret units rather than treating covariance as a percentage.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: Use =COVARIANCE.P(A2:A5,B2:B5) for population covariance of two aligned numeric series. With x values 1, 2, 3, 4 and y values 2, 4, 4, 6, the independent expected result is 1.5. Use the population definition when the rows represent the population you intend to describe.
Exact syntax and arguments
=COVARIANCE.P(array1,array2)
Both arguments are required; neither has a default. Each supplies one variable’s observations. WPS describes integer cell ranges and also permits numeric arrays, names and references. The worked data deliberately use integer inputs. Each row must identify the same observation in both columns. Equal range sizes alone do not establish meaningful pairing: sorting only one column destroys the original pairs.
The population calculation sums (x − mean_x) × (y − mean_y) over pairs and divides by n. The result has x-units multiplied by y-units. It is not restricted to −1 through 1 and should not normally be formatted as a percentage.
Build a small, auditable example
| Cell | Value | Cell | Value |
|---|---|---|---|
| A2 | 1 | B2 | 2 |
| A3 | 2 | B3 | 4 |
| A4 | 3 | B4 | 4 |
| A5 | 4 | B5 | 6 |
Put =COVARIANCE.P(A2:A5,B2:B5) in F2. Independent expected F2: 1.5.
The means are 2.5 and 4. The four centered products are 3, 0, 0 and 3. Their sum is 6, divided by four observations. This hand calculation makes a sample/population mistake easy to detect: dividing by three would give 2, a different statistic.
Advanced example: compare changes of measurement scale
Enter C2:C5 as 102, 104, 104, 106 and D2:D5 as 20, 40, 40, 60. Keep your results elsewhere, such as F3:F5.
| Formula | Independent expectation | Interpretation |
|---|---|---|
=COVARIANCE.P(A2:A5,C2:C5) |
1.5 | Adding 100 to y does not change centered deviations |
=COVARIANCE.P(A2:A5,D2:D5) |
15 | Multiplying y by 10 multiplies covariance by 10 |
=COVARIANCE.P(A2:A5,A2:A5) |
1.25 | Covariance of x with itself is its population variance |
These are mathematical controls for fully numeric matched observations, not native precision benchmarks. A larger covariance after changing units does not mean a stronger association. For a scale-free linear measure, see CORREL.
Errors, data cleaning and interpretation
The WPS lesson documents #N/A for unequal numbers of data points and #DIV/0! when an array is empty. It says text, logical values and empty referenced cells are ignored, while zeros are counted. That wording does not settle the alignment of every mixed-type pair. Filter or clean both columns together, keep valid zeros, and confirm the remaining observation count.
Constant numeric y produces zero covariance. Zero covariance also need not mean no relationship: for x = −1, 0, 1 and y = 1, 0, 1, the independent covariance is zero even though y = x squared. Positive or negative covariance describes the supplied pairings; it does not prove causation.
The official example’s extracted table has corrupted entries, so its displayed 5.2 is not reused as an auditable example. The new dataset above avoids silently repairing the vendor table. COVAR covers a related population statistic, but the inspected sources do not establish a universal alias or a build-by-build replacement relationship. Keep the exact dotted spelling when this is the function your workbook requires.
Availability, version history and evidence
The official WPS COVARIANCE.P lesson was published 2020-09-02 and labels its applicable edition WPS Office for Windows Personal. The lesson was checked on October 19, 2026. This establishes a documented-by date, not the release in which the function first appeared. No numeric build, last supported version or retirement date is established. Mac, Linux, web, mobile and global-English edition parity are unverified.
Original expected results here are independent calculations or explicitly labelled test expectations, not native WPS execution. No WPS screenshot or installed-build test is claimed. Formula separators and displayed decimal precision can depend on the target setup; verify the exact function name in that installation before distributing a workbook.