DEVSQ Function in Calligra Sheets: Sum of Squared Deviations

=DEVSQ(value1; [value2]; ...)
=DEVSQ(A2:A9)
=DEVSQ(21;33;54;23)

• value1: required numeric observation, numeric cell reference, or range/array of observations. The C++ registration specifies setParamCount(1,-1) and accepts arrays, so one formula argument may contain multiple observations. The XML handbook spells the variable-argument pattern DEVSQ(value; value;...). [K1–K3]
• value2 and later: optional additional numeric arguments/references/ranges. There is no optional divisor, sampling mode, mean, or rounding argument. The registration does not set a finite fixed upper bound; this is not proof that every installation accepts arbitrarily many arguments. [K2]
• Output: one numeric squared-deviation sum for valid finite numeric inputs. Squared units apply: measurements in centimetres produce a result measured in cm². [K1, I1]
• Input conventions: KDE’s English examples separate arguments with semicolons (;) and use a decimal point, with ranges written A2:A9. Parser changes under other locales have not been executed or confirmed. Brackets here document optional arguments; do not type the brackets into formulas. [K1]
• No default mean: the function computes its own arithmetic mean over its accepted inputs. Its inspected wrapper passes the computed mean to an engine arrayWalk operation named devsq. Text, error-cell and Boolean coercion within that helper still requires native verification. [K3]

For numbers x1…xn with mean m = SUM(x)/n, the defining calculation is:

DEVSQ = (x1-m)^2 + (x2-m)^2 + ... + (xn-m)^2

Unlike sample variance VAR, it does not divide by n−1; unlike population variance VARP, it does not divide by n. For well-formed numeric datasets, DEVSQ = VAR*(n−1) = VARP*n. These relationships are independent mathematical identities, not observations from Calligra at runtime. [K1, K3, I1]

1. In a new sheet, enter A1 = Measurement and the following eight values in A2:A9 as numbers. Do not include a total or heading inside that range.
2. Put H1 = Audit formulas and enter the formulas in H2:H13, keeping their destinations outside A2:A9.
3. Increase displayed decimal places for the sample variance, and confirm that changing one A cell recalculates related formulas when tested in a native application; the numbers printed below are the independently calculated expectations. [I1]

Audit the 32 by hand: the values have mean 5. Subtract 5 to obtain −3,−1,−1,−1,0,0,2,4. Squaring yields 9,1,1,1,0,0,4,16, adding to 32. In this dataset the population standard deviation is sqrt(32/8)=2 and sample standard deviation is sqrt(32/7)≈2.1380899353. [I1]

Set B1 = Deviation and C1 = Squared deviation. Put =A2-$H$3 in B2 and copy through B9, then put =B2^2 in C2 and copy through C9. For A2:A9, the expected B values are −3,−1,−1,−1,0,0,2,4; the expected C values are 9,1,1,1,0,0,4,16. In H14, enter =SUM(C2:C9) → 32. In H15, enter =H14/H4 → 4; in H16, enter =H14/(H4-1) → 4.571428571429. [I1]

The absolute $H$3 locks the mean while copying formulas; without it, the reference will move and the per-row comparison becomes invalid. A manual audit is useful when reviewing an outlier or checking whether text or missing data changed the set of accepted observations. It is not a substitute for checking native coercion behavior.

Place D2:D5 = 2,4,4,4 and E2:E5 = 5,5,7,9. The independent results are:

Why 14 differs from 32: each group uses its own mean (3.5 and 6.5), whereas the combined observations use one overall mean of 5. This identity matters for grouping, ANOVA preparation and quality-control comparisons. Do not add within-group DEVSQ values and label them the total ungrouped variation. [I1]

Native validation still required: zero/one/multiple observations, a range versus literal arguments, blank/text/Boolean cells, nested arrays and cell errors, locale separators, large numeric ranges, and function availability in a real installation. No native screenshots, parser executions or error-label claims are supplied here.

KDE registers DEVSQ as a distinct function in the 26.08.2 statistical module; DEVSQA is separately registered and uses a different deviation walk (devsqa) that needs its own type-specific review. These names describe distinct function variants. [K2, K3]

Microsoft’s Excel documentation also defines DEVSQ, but uses comma-separated syntax in its English examples and specifies Excel-specific argument and type-handling behavior. That document is evidence about Excel only, not proof that Calligra duplicates every Excel coercion rule or accepts a specific XLSX round-trip. The calculation is mathematically comparable for the numeric-only examples here. [M1, I1]

Version examined: KDE Gear/Calligra 26.08.2 (official announcement 2026-10-08) with source pinned at commit 72123cc643f6625351139e7df294544255a1056f. KDE’s Calligra download page points primarily to Linux distribution packages and Flatpak and says Windows support is under development. The registration confirms a shipped source implementation, not a native execution test on Linux/Windows. [K2–K5]

KDE documentation (opened 2026-10-13): AVERAGE — mean, COUNT — numeric observations, SUMSQ — squared sum, VAR — sample variance, VARP — population variance, STDEV — sample standard deviation, and STDEVP — population standard deviation.

• [K1] KDE function handbook, DEVSQ meaning, semicolon syntax, numeric type and the 684.75 example: https://docs.kde.org/stable_kf6/en/calligra/sheets/functions.html#DEVSQ.
• [K2] Version-pinned KDE registration, setParamCount(1,-1), setAcceptArray, DEVSQ versus DEVSQA: https://github.com/KDE/calligra/blob/72123cc643f6625351139e7df294544255a1056f/sheets/functions/statistical.cpp#L160-L171.
• [K3] Pinned KDE implementation, func_devsq and func_devsqa, mean and array-walk calls: https://github.com/KDE/calligra/blob/72123cc643f6625351139e7df294544255a1056f/sheets/functions/statistical.cpp#L1084-L1104.
• [K4] Pinned KDE statistical XML, documented syntax, example and declared number parameters: https://github.com/KDE/calligra/blob/72123cc643f6625351139e7df294544255a1056f/sheets/functions/statistical.xml.
• [K5] Release and platform references, KDE Gear 26.08.2 (2026-10-08) and Calligra downloads: https://kde.org/announcements/gear/26.08.2/ · https://calligra.org/download/.
• [M1] Microsoft Excel DEVSQ documentation, comparison only: https://support.microsoft.com/en-us/excel/functions/devsq-function.
• [I1] Independent arithmetic, 2026-10-13: Python statistics mean/variance and a separate centered-squares identity were used to check table values and rounding. Not native Calligra execution.