VAR Function in Apple Numbers: Sample Variance and Examples

=VAR(value, value…)

There is no population/sample switch argument: VAR itself is for a sample; for the entire population, Apple documents the separate VARP function. Apple’s definition computes squared deviations from the sample mean and divides by one less than the number of values (n−1). [A1]

Important type distinction: Apple’s VAR page explicitly lists number and date/time values, but does not explicitly list duration. Its STDEV page does list duration. Do not infer that VAR accepts all STDEV data types, or paste an Excel-based type claim, without an Apple-native check. This tutorial uses numeric data only. [A1, A2]

This tutorial is based on Apple Formulas and Functions Help, documentation edition 15.4, with the function page accessed 2026-10-12. The edition label identifies the help material, not a proven minimum release of Numbers on every device. Apple provides separate release information for Mac; if you must support a particular historical app version, check that release’s availability before deploying this formula. [A1, R1]

All input examples use cells in one Numbers table, with ranges such as B2:B9. Numbers spreadsheets can contain multiple tables on a sheet; when sourcing another table, select its cells through the formula editor so Numbers constructs the table- or sheet-qualified reference. Do not paste Excel’s Sheet!A1 form and assume it means the same thing in Numbers. [R1, R2]

Locale: These formulas use English function names, . for decimal fractions and , between function arguments. If the system uses a comma decimal separator, Apple instructs using semicolons between arguments when formulas are typed manually. Colons identifying ranges, such as B2:B9, stay colons. Function-name capitalization is not significant. [R1]

Verification labels: Documentation-checked expected output means Apple published that exact example. Independently calculated expected output means the mathematical result was checked outside Numbers. Neither is an observation from running Apple Numbers; native Apple Numbers execution and screenshots were not available in this review.

1. Create a Numbers table named QualitySamples with row 1 as a header: A1 Batch, B1 Reading.
2. Enter these numeric readings exactly; use a separate result cell, such as D2, to avoid including the result in the input range.

=VAR(B2:B9)

Independently calculated expected result: 4.571428571428571. The average of the eight readings is 5; their squared deviations sum to 32. The sample formula is 32 / (8−1) = 32/7. This computation was reproduced independently with Python statistics.variance, not observed in Apple Numbers. [A1, C1]

Useful cross-check formulas

These are mathematical/documentation-based expectations; these formulas were not executed natively. Locale adaptation for more than one argument: =VAR(3;7) when a comma is used as decimal separator. [A1, A2, R1, C1]

Sample data: If eight readings were selected from a longer production process, VAR estimates the process’s variation using the n−1 correction. Apple characterizes this as sample (unbiased) variance. [A1]

Population data: If the eight readings are the entire population you want to describe, dividing by n is appropriate; Apple’s function for that is VARP. With the example data VAR(B2:B9) is expected 4.5714, while the population variance is 4. Choosing VAR or VARP should reflect the sampling design, not a preference for a larger or smaller number. [A1, C1]

Relation to standard deviation: To report dispersion in the original unit rather than its square, use STDEV. The mathematical relationship for numeric samples is STDEV(data) = SQRT(VAR(data)), explicitly stated by Apple. [A1, A2] When values are all identical the variance is zero, but zero variance alone says nothing about sample representativeness.

Check against Apple’s own worked dataset

Apple documents first-column test scores 75, 100, 40, 80, 90 and reports =VAR(A1:A5) as 520. The corresponding sample standard deviation is sqrt(520) ≈ 22.8035085019828. This separate example is checked directly against Apple’s published function guide. [A1, A2]

1. Fewer than two valid values: Apple’s reference requires a minimum of two. A single-reading range cannot estimate n−1 sample variance. This guide does not claim a particular displayed Numbers error code. [A1]
2. Wrong data type: VAR’s documented accepted types are numbers and dates/times, all of one type. Do not assume duration support because a different function lists durations. [A1]
3. Imported numeric-looking text: ensure column B cells are numeric rather than text. Apple’s VAR page does not fully establish every mixed-contents or Boolean coercion outcome, so do not rely on unspecified conversion rules. [A1]
4. Different answer from VARP: one divides by n−1 and the other by n. The results should differ unless the variance is zero; they answer different sampling questions. [A1]
5. Unexpectedly high variance: inspect units, transcription errors and outliers; a squared deviation gives a far-out reading disproportionately more weight.
6. Circular-reference risk: don’t include your own formula result in the selected input range.
7. Formatting: displaying a few decimal digits rounds the visible output; that is not evidence of a different underlying sample variance.
8. Excel compatibility: Microsoft’s modern function is VAR.S; Apple’s VAR is a sample-variance function. Microsoft documents text and logical-value handling for Excel separately. Use their respective official help and test any imported workbook rather than assuming identical error or coercion rules. [X1]

• STDEV returns sample standard deviation.
• VARP returns population variance.
• AVERAGE returns the arithmetic mean.
• Apple VAR reference [A1].
• Apple STDEV reference [A2].
• Apple Functions overview — separator/notation rules [R1].
• Apple Numbers release history [R2].
• Microsoft VAR.S reference [X1]; Excel-specific, not Numbers source evidence.

Sources checked 2026-10-12. A1/A2/R1/R2 identify Apple’s documentation, C1 independently calculated arithmetic, X1 Microsoft’s Excel help. No native execution has taken place.

The formulas were not executed in a native Numbers app on Mac, iPad, iPhone or iCloud.com. Recheck display formatting, locale entry, data typing, empty/error cells, table references and older release support in the target installation. Test representative examples in the target app before relying on the worksheet. Do not use this tutorial as a substitute for reviewing the data collection method or domain-specific analysis assumptions.