VARPA Function

Excel Functions › Statistical

All versions Statistical

The Excel VARPA function calculates the variance of an entire population while also counting text and logical values — TRUE as 1, FALSE and text as 0 — unlike VAR.P, which ignores them.


Quick answer:
=VARPA({1,2,3,4,5,1}) population variance = 2.2222...

Syntax

=VARPA(value1, [value2], ...)
ArgumentDescription
value1RequiredThe first value, cell, or range that represents the whole population. Numbers, logical values, and text are all evaluated.
value2, ...OptionalUp to 254 additional values or ranges. TRUE counts as 1; FALSE and any text count as 0.

How to use it

VARPA treats your arguments as the complete population (not a sample), so it divides the sum of squared deviations by n rather than n−1. What sets it apart from VAR.P is how it handles non-numbers: VARPA includes them.

=VARPA({1,2,3,4,5,1}) // TRUE counted as 1 = 2.2222
=VAR.P({1,2,3,4,5}) // numbers only = 2

The two formulas above use the same five numbers, but VARPA adds a sixth value (a TRUE, shown here as its numeric equivalent 1), which pulls the mean and the variance. The rule of thumb:

Value typeVARPA counts it as
1Numberits value
2TRUE1
3FALSE0
4Text ("abc", "")0
5Empty cellignored

Which variance function? Use VAR.P for a full population of pure numbers, VAR.S for a sample, and VARPA only when you genuinely want text/logical cells scored as 0/1 instead of skipped.

Try it: interactive demo

Live demo

Pick a VARPA example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

What is the difference between VARPA and VAR.P?
VAR.P ignores text and logical values in a range; VARPA includes them, counting TRUE as 1 and FALSE or text as 0. With pure-number data the two return the same result.
Does VARPA use population or sample variance?
Population — it divides by n (the count of all evaluated values). For a sample estimate that divides by n−1, use VARA or VAR.S instead.
How are TRUE and FALSE treated by VARPA?
Logical TRUE is evaluated as 1 and FALSE as 0, so both become part of the population and affect the mean and variance.
Is VARPA a modern or legacy function?
VARPA has existed since early Excel versions and remains current — it was never replaced by a dotted name. (The pair without text handling is the modern VAR.P, formerly VARP.)

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Related functions: VAR.P · VAR.S · STDEVPA · VARA · AVERAGEA