COVARIANCE.S Function (Gnumeric)

• Introduced: Gnumeric 1.11.3 release notes explicitly record its addition.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Statistics plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. The tables and named advanced check use 1.12.57 ssconvert. Current 1.12.62 source was inspected; that release was not executed.

COVARIANCE.S returns sample covariance: Σ(xᵢ−x̄)(yᵢ−ȳ)/(m−1), where m is the number of retained numeric pairs. A positive result indicates positive joint variation in this dataset; a negative result indicates opposite variation. Covariance is measured in the product of the two variables’ units and is not bounded by −1 and 1. Versioned function help.

=COVARIANCE.S(array1,array2)

array1 and array2 are required, correspondingly ordered datasets. The original collections must have matching lengths. Positions containing text, logical values or blanks in either input are excluded as pairs; the remaining numeric values are not independently shifted together.

Current implementation.

Enter these values with the stated storage types. F5, G5, H7 and L3 are genuinely empty; do not type an empty string into them.

For F2:F4=2,4,6 and G2:G4=3,7,8, the means are 4 and 6. Cross-products are (−2)(−3)=6, 0×1=0 and 2×2=4. Their sum is 10; dividing by m−1=2 gives 5, matching the native result. Dividing by m=3 would instead give the population covariance 10/3.

Each row must describe the same observation in both columns. Sorting only one column can change the answer while leaving the formula syntactically valid. A covariance alone does not establish causation or a predictive model.

The missing-row examples deliberately use the same first dataset. K2:K4=3,“skip”,8 excludes the middle pair, leaving (2,3) and (6,8). Their sample covariance is 10. L has a blank at the same position and also gives 10. M2:M4=TRUE,7,8 excludes the first pair and gives 1 from (4,7),(6,8).

The native advanced symmetry check subtracts the covariance with its arguments reversed and returns zero. Independently, sample covariance of X with itself equals its sample variance: F2:F4 gives 4. A constant second dataset J2:J4 gives zero covariance, without requiring every first-column value to be equal.

The retained 1.12.57 and 1.12.62 worksheet callbacks have the same relevant argument guards and calculation dispatch. That source comparison does not establish execution or universal floating-point equivalence in the later build.

Fewer than two retained pairs and unequal original lengths produce #VALUE! in the tested build. Source errors propagate, as the explicit division-by-zero example shows. The help’s worked-example prose uses COVAR, a population function; it must not be reused unchanged for COVARIANCE.S. The examples here use the correct sample divisor m−1.

F5 is an actually empty cell. Errors below are the tested build’s results, not zero-valued mathematical answers.

• Current worksheet implementation
• Tested-version worksheet implementation
• Current paired-position collection
• Current sample covariance calculation

The retained workbook’s stale SUM cache and uncached SUM both recalculated correctly. Formula identities, typed inputs and native results were inspected. The importer reported unsupported style-extension elements; that warning is retained, and no all-formatting claim is made. GUI entry, other locales and later-release output were not tested.

COVAR, CORREL, VAR.