Zoho Sheet DVARP Function: Population Variance

Zoho’s official DVARP entry was retrieved on October 15, 2026. It documents the current rolling web service, not an original introduction release or last functioning version; both historical endpoints remain unknown. Mobile/offline parity is unverified. The additional calculations below are independent mathematical expectations, not native Zoho Sheet output.

DVARP(database; field; criteria)

All three arguments are documented. The first range includes headers and records. The field is a quoted column label or a reference to the header cell. The criteria range contains a header and its condition. The criteria column can differ from the measurement field.

The formulas follow Zoho’s semicolon syntax. Use your workbook’s locale separator where necessary. Keep the field explicit rather than assuming another product’s optional arguments or numeric field-index conventions.

Create Measures and enter A1:C7 exactly as below. Measurement values are numeric. Put Group in E1 and Red in E2; put Group in G1 and Blue in G2.

E1:E2 selects rows 2,4,5,7, while G1:G2 selects rows 3,6. Use these formulas on Measures:

In I1 enter Group and leave I2 physically empty. =DVARP(A1:C7;"Measure";I1:I2) gives 16.888888889 under Zoho’s documented blank-below-header rule. The entire population for this calculation is the selected field within the stated database, not every cell in the worksheet.

Red’s mean is 4. Its deviations are −2,0,0,2 and squared deviations 4,0,0,4, totaling 8. For a population calculation, divide by n = 4, giving variance 8/4 = 2. This produces the displayed population variance.

Taking the square root gives population standard deviation √2 ≈ 1.414213562. Variance 2 and standard deviation 1.414213562 are different quantities and should not share an unlabeled result column.

Duplicate Measures and change only C7 from 6 to 10. Red becomes 2,4,4,10, with mean 5 and squared-deviation total 36. DVARP becomes 9.000000000. Blue remains 4.000000000. This shows the effect of one more distant observation without changing group membership.

In another original copy, add 100 to every Red measurement: 102,104,104,106. The result remains 2.000000000, because translating all observations shifts the mean equally and preserves deviations.

In a third original copy multiply those Red measurements by 10: 20,40,40,60. The result becomes 200.000000000. Variance scales by the square of the factor, so a unit conversion by ten multiplies variance by one hundred. Convert the whole dataset consistently rather than mixing units within a field.

Red has mean 4 and variance 2. Blue has mean 12 and variance 4. A count-weighted average of those two within-group variances is (4×2+2×4)/6 = 2.666666667. It is not the full six-record variance, approximately 16.888888889.

The full dataset has mean 40/6. Its total squared-deviation sum is 101.333333333, while the within-group squared-deviation sums total only 16. The difference, 85.333333333, comes from the separation between group means. This decomposition explains why averaging group variances cannot reconstruct total variance without accounting for different centers.

A population with one known numeric observation has mathematical variance and standard deviation zero; an empty population has no defined mean or variance. Exact native error tokens for every small or empty selection are not specified by the checked entry, so these mathematical limits are not presented as observed Zoho output.

The page lists general name, type and reference errors, but does not provide a full coercion table for text, booleans, blank cells or embedded errors. The worked table uses only numeric observations and ordinary text group labels. Do not silently turn missing measurements into zero: zero changes both the center and the spread.

If a result differs, check the database boundary, header names, criteria range and actual selected values before changing the formula. Inspect whether the intended statistic is sample or population, variance or standard deviation. A square-root mismatch often indicates the wrong statistic; a difference by n/(n−1) in variance suggests the wrong denominator.

The related official database catalog distinguishes these operations. Common names in other products do not establish matching error handling, coercion or version support. No cross-product import test was performed.