VAR.P Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel VAR.P function calculates the variance of an entire population — the average squared deviation from the mean, dividing by n rather than n−1.


Quick answer:
=VAR.P({1,2,3,4,5,6,7,8,9,10}) population variance = 8.25

Syntax

=VAR.P(number1, [number2], ...)
ArgumentDescription
number1RequiredThe first value or range representing the whole population.
number2, ...OptionalUp to 254 additional values or ranges.

How to use it

Use VAR.P when your data covers the complete population — every member, not a sample. It divides the sum of squared deviations by n.

=VAR.P({1,2,3,4,5,6,7,8,9,10}) // population variance = 8.25

If your numbers are only a sample drawn from a larger population, use VAR.S instead — it divides by n−1 to correct for the smaller spread a sample tends to show. The square root of VAR.P is STDEV.P.

=SQRT(VAR.P({1,2,3,4,5,6,7,8,9,10})) // = STDEV.P ≈ 2.872

VAR.P vs VAR.S: population (VAR.P) divides by n; sample (VAR.S) divides by n−1. VAR.P is always the smaller of the two for the same data. VAR.P replaces the legacy VARP.

Try it: interactive demo

Live demo

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Result:

Practice workbook

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Frequently asked questions

When should I use VAR.P instead of VAR.S?
Use VAR.P when your data represents the entire population. Use VAR.S when the data is a sample drawn from a larger group you want to make inferences about.
Why does VAR.P divide by n and VAR.S by n minus 1?
Dividing a sample by n−1 (Bessel's correction) compensates for the fact that a sample tends to under-represent the true spread. A full population needs no such correction, so VAR.P uses n.
Does VAR.P ignore text and logical values?
Yes — like VAR.S, it skips text, logical values, and empty cells in a referenced range. To include logicals and text as numbers, use VARPA instead.
How is VAR.P different from the old VARP?
They compute the identical result; VAR.P is the modern name introduced in Excel 2010. VARP remains in the Compatibility category for backward compatibility.

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Related functions: VAR.S · STDEV.P · STDEV.S · VARA · VARPA · AVERAGE