SUMSQ in WPS Spreadsheet: Add Squared Values and Check Residual Magnitudes

• Introduced: documented by 2019-06-19 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated. This is documentation evidence, not an installed-build guarantee.
• Scope: exact supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=SUMSQ(number1,[number2],...)

The official WPS lesson permits numeric values, arrays, names and numeric-cell references. Its formal text says 1–30 arguments, while its walkthrough says 1–225. Those conflicting limits are not converted into a universal current-build maximum here; all examples use only a few arguments or one small range.

The same walkthrough loosely mentions calculating a square root, but the formal definition is the sum of squares. A separate SQRT call is needed when a square root of that sum is intended. This guide follows the explicit definition and independently checked arithmetic.

Enter numeric -3, 4, 0, 2 in A2:A5:

=SUMSQ(A2:A5)

Expected result: 29. The contributions are 9, 16, 0 and 4. The sign of -3 disappears when it is squared; zero remains a numeric observation even though it contributes nothing to the total.

The ordinary sum is three, whose square is nine. Thus =SUM(A2:A5)^2 has expected result 9, not 29. Squaring and summing do not commute because squaring a sum introduces cross-products.

=SUMSQ(3,4)
=SQRT(SUMSQ(3,4))

Expected results are 25 and 5. The second is the Euclidean length of a vector with perpendicular components three and four, while the first is its squared length.

For the four-component source in A2:A5, the square root of SUMSQ has expected value approximately 5.385164807. Keep the squared quantity and its square root labeled separately; their units differ.

Create observed values 10, 12, 8 in C2:C4 and predicted values 9, 14, 8 in D2:D4. In E2 enter =C2-D2 and fill down. The residuals are 1, -2, 0.

=SUMSQ(E2:E4)

Expected sum of squared residuals: 5. The raw residual sum is -1, so adding residuals alone can hide opposing directions. Squaring makes the nonzero deviations contribute positively.

Dividing by the three complete paired observations gives a mean square of approximately 1.666666667. Taking its square root gives approximately 1.290994449. This is an explicitly defined root-mean-square residual, not an automatic statistical degrees-of-freedom correction.

For numeric observations 2, 4, 6, the arithmetic mean is four. Their deviations from that mean are -2, 0, 2, whose SUMSQ is 8.

The uncentered SUMSQ is instead 56, from 4+16+36. Centering materially changes the quantity being measured. If the three values are the entire population under study, dividing the centered sum by three gives population variance 8/3, approximately 2.666666667.

A sample-estimation problem can require a different denominator. SUMSQ does not decide which statistical model or correction is appropriate; make that choice explicit before interpreting the result.

Multiplying every value in A2:A5 by two gives -6, 8, 0, 4 and expected SUMSQ 116, four times 29. Negating every original value leaves expected SUMSQ at 29.

These identities follow from squaring each input. Equal sums of squares do not mean equal source vectors: the original and its negative have different signed values but the same total squared magnitude.

The dated WPS source does not resolve its conflicting argument-count statements or a complete text, blank, error and overflow matrix. The examples use explicit numeric inputs and do not claim another application’s range-coercion rules.

Preserve paired row alignment when constructing residuals. A correct SUMSQ over incorrectly paired differences is still the wrong error measure. Keep original values and helper differences visible, and round only the report rather than the intermediate residuals.

• WPS Academy: SUMSQ lesson, 2019-06-19 (Chinese; Windows Personal scope).
• Editorial testing standards.

The cited WPS product lesson was read directly. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.