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VARP Function in Calligra Sheets: Population Variance

Statistical Intermediate Calligra Sheets

Compute whole-population variance in Calligra Sheets with VARP, worked squared-deviation examples, the n divisor and comparisons to sample VAR.

Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in Calligra Sheets. How formula examples are checked

Quick answer: VARP calculates population variance: the average squared difference between each valid numeric observation and the mean of the entire population. Its denominator is n. KDE documents VARP(6;7;8) ≈ 0.6666667 and VARP(12;5;7) ≈ 8.6667. For a sample estimate, use VAR, not VARP. [K1, K2, K3, K6, I1]

Validation, 2026-10-13: This guide is based on the official source and handbook. All outputs are independently derived predictions. No native Calligra execution is claimed.

Exact formula syntax, parameters and accepted values

=VARP(value1; [value2]; ...)
=VARP(A2:A9)
  • First argument (value1, required): numeric scalar, cell reference or numeric range. C++ registration setParamCount(1,-1) makes one formula argument sufficient, and setAcceptArray() permits array/range input. [K2]
  • Subsequent arguments (value2 etc., optional): additional numeric literals/references/ranges. Argument order does not change variance mathematically for valid numbers. No distinct optional population switch is registered. [K2, I1]
  • One or more actual observations: for a single numeric observation, population variance is zero by the mathematical formula. The func_variancep guard returns an internal value error when count==0; one-observation display remains a recommended native test. [K3, I1]
  • Type/precision: KDE’s handbook lists floating-point values/ranges; result is a floating-point variance in squared units (e.g. cm² for heights in cm). Numeric counting is source-verified; exact handling of strings/Booleans/errors is not natively observed. [K1, K3, K4]
  • Separator, defaults and locale: KDE’s English syntax uses ; and decimal .. There is no optional default argument to change the denominator; practical limits, translations and decimal/separator variants require verification on the installed build. [K1, K2]

Population variance formula, with μ = Σxᵢ/n:

VARP = Σ (xᵢ − μ)² / n

VAR divides by n−1 instead. STDEVP takes the square root of VARP and restores the original measurement units. The pinned func_variancep computes a squared-deviation numerator and divides it by count; the wrapper explicitly checks zero accepted observations. [K3, K4, I1]

Complete worksheet you can reconstruct from scratch

  1. In a new Calligra worksheet, put A1=Population measurement.
  2. Enter the following eight numeric cells A2:A9. They are the complete population for this example, not a sampling of something larger.
  3. Copy each formula into the stated H cell using the documented English punctuation; verify sufficient displayed digits.
  4. The outputs are calculated expectations, not evidence of a Sheets application test. [I1]
A cell Number A cell Number
A2 2 A6 5
A3 4 A7 5
A4 4 A8 7
A5 4 A9 9
Enter in Formula Independently expected result Meaning
H2 =VARP(A2:A9) 4 Population variance = 32/8.
H3 =VAR(A2:A9) 4.571428571429 Sample variance = 32/7.
H4 =AVERAGE(A2:A9) 5 Population mean.
H5 =STDEVP(A2:A9) 2 Population standard deviation = √4.
H6 =VARP(6;7;8) 0.666666666667 Official KDE example.
H7 =VARP(12;5;7) 8.666666666667 Official KDE example.
H8 =VARP(15;80;3) 1144.222222222222 Unevenly spread complete population.
H9 =VARP(-2;0;2) 2.666666666667 Negative data permitted mathematically.
H10 =VARP(40;60) 100 Two-member population, mean 50.
H11 =VARP(5;5;5) 0 No squared deviations.
H12 =STDEVP(A2:A9)^2 4 Independent relation with standard deviation.

Audit: The eight observations have mean 5, deviations −3,−1,−1,−1,0,0,2,4 and squared-deviation sum 9+1+1+1+0+0+4+16 = 32. Consequently VARP(A2:A9) = 32/8 = 4. VAR(A2:A9) = 32/7 ≈ 4.571428571429. Neither is a typographical error; the interpretation of the dataset determines the denominator. [I1, K3]

Advanced application 1 — reproduce VARP using transparent helper cells

In B1 type Squared deviation; in B2 enter =(A2-$H$4)^2 and copy through B9. The results, in sequence, must be 9, 1, 1, 1, 0, 0, 4, 16. [I1]

In H13, enter =SUM(B2:B9) to get 32. In H14, enter =COUNT(A2:A9) to get 8. In H15, enter =H13/H14 to get 4. [I1]

This method is helpful when auditing a complete inventory because every cell’s contribution is visible. Absolute $H$4 holds the mean reference fixed when copied; otherwise you may inadvertently compare observations against different cells. The numerator uses scalar squared-difference cells instead of relying on unverified array-evaluation shortcuts.

Advanced application 2 — convert or rescale an entire population

If all values are converted according to new_value = 2*old_value + 3, the population variance scales by 2²=4 and is unaffected by the additive 3. In D2 type =2*A2+3 and fill down to D9. Your calculated values are 7, 11, 11, 11, 13, 13, 17, 21. In H16 type =VARP(D2:D9), expecting 16; in H17 type =STDEVP(D2:D9), expecting 4. The standard deviation scales by 2, while the variance scales by 4. [I1]

This is particularly useful when transforming a complete population from one measurement unit to another (a multiplier on every value). Since variance’s units are squared, a conversion factor is squared as well. For instance a standard deviation of 2 metres corresponds to a variance of 4 m²; rescaling metres to centimetres multiplies the variance by 10,000, not 100. [I1]

Troubleshooting and boundaries

Input/issue Evidence-based expectation Unverified condition
Population with one numeric observation Math predicts variance = 0; count=1 passes the count==0 guard. Confirm actual native rendered result for VARP(10). [K3, I1]
No accepted numeric values Pinned func_variancep returns internal Value::errorVALUE() for count==0. Application-visible error string is not verified. [K3]
Variance differs from sample VAR Same squared deviations, n for VARP instead of n−1 for VAR. No native ambiguity about the mathematical operation on valid numeric data. [K1–K3]
Result seems disproportionately large Variance is in squared units; compare to STDEVP if original units are desired. Interpretation, not an observed error. [I1]
Blank/text/Boolean entries The false numeric counting path is used, but the entire front-end conversion pipeline was not exercised. Exact handling of each direct/indirect input. [K3, K4]
Unexpected error or displayed text Check leading =, locale punctuation, accidental text formatting and that A2:A9 are numeric. Specific Calligra locale and visible messages. [K1]
Function unavailable VARP is shipped as a registration in the examined statistical module. Installed platform/package/module may differ. [K2]
Many very large floating-point values Precision loss or overflow could make naively equivalent calculations diverge. Numeric edge cases not natively measured.

Pending native test cases: VARP(10), empty range, text-only range, mixed references, error cell, direct text or Boolean arguments, multiple-range arguments, localized separators, large magnitudes, tiny differences between large numbers, behavior on supported Linux/Flatpak builds. The source does not justify manufacturing a screenshot, error label or observed decimal display.

Version and compatibility — avoid accidental Excel assumptions

Calligra 26.08.2: VARP is explicitly registered to func_variancep and is not a synonym for VAR. Related names VAR and VARIANCE both use func_variance (sample divisor) and are covered together in the VAR guide. The official catalogue records no explicit alias for VARP. [K2, K3]

Excel: Microsoft documents modern VAR.P as population variance and legacy VARP for compatibility, but this says nothing about Calligra’s acceptance of a dotted name, old workbook import behavior or mixed-type coercions. The population/sample concept aligns mathematically, not necessarily in all implementation details. [M1]

Related: VAR — sample variance, STDEVP — population standard deviation, AVERAGE — mean. Every link is an official KDE documentation anchor checked as existing, without implying cross-platform runtime equivalence. [K1]

Source and execution boundaries

Version examined: Calligra 26.08.2, issued 2026-10-08, with C++ source pinned at commit 72123cc643f6625351139e7df294544255a1056f. The long-lived KDE handbook has an older displayed revision (2013-03-11); the version-pinned registration and engine define the behavior investigated here. Source presence is not evidence that a particular Linux distribution package, Flatpak, edition or platform successfully executes the formula. The official Calligra download page describes Linux distribution packages/Flatpak and Windows support as in progress. [K1–K5]

All outputs in the worksheet tables are independently calculated expectations, not recorded Calligra application results. The data are deliberately plain numeric constants to avoid unverified text, Boolean or date coercion. No screenshots, application runs, localized parser checks or import/export tests were conducted. [I1]

Official KDE handbook links inspected on 2026-10-13: AVERAGE — mean, COUNT — numeric items, SUM, SQRT, STDEV — sample standard deviation, STDEVP — population standard deviation, VAR — sample variance, VARIANCE — VAR-equivalent registration, VARP — population variance. [K1, K2]

References and evidence audit — accessed 2026-10-13