VAR.S Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel VAR.S function estimates the variance of a population from a sample — the sum of squared deviations divided by n−1.


Quick answer:
=VAR.S({1,2,3,4,5,6,7,8,9,10}) sample variance ≈ 9.167

Syntax

=VAR.S(number1, [number2], ...)
ArgumentDescription
number1RequiredThe first value or range in the sample.
number2, ...OptionalUp to 254 additional values or ranges.

How to use it

VAR.S is the everyday variance: use it when your numbers are a sample from a larger population. It divides by n−1 (Bessel's correction) so the estimate isn't biased low.

=VAR.S({1,2,3,4,5,6,7,8,9,10}) // sample variance ≈ 9.167

For the same data VAR.S is always a little larger than the population VAR.P, because dividing by the smaller n−1 inflates the result. Its square root is the sample standard deviation STDEV.S.

=SQRT(VAR.S({1,2,3,4,5,6,7,8,9,10})) // = STDEV.S ≈ 3.028

Which one? If you have every data point (the whole population), use VAR.P. If your data is a sample standing in for something bigger, use VAR.S. VAR.S replaces the legacy VAR.

Try it: interactive demo

Live demo

Pick a VAR.S example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

When should I use VAR.S?
Use VAR.S when your data is a sample drawn from a larger population — the usual case in surveys and experiments. Use VAR.P only when you have the entire population.
Why is VAR.S larger than VAR.P for the same data?
VAR.S divides by n−1 while VAR.P divides by the larger n. A smaller denominator yields a larger value, which corrects the tendency of a sample to underestimate true spread.
Does VAR.S handle text and logical values?
It ignores text, logical values, and empty cells inside a referenced range. To count logicals and text as numbers, use VARA instead.
How is VAR.S different from the old VAR?
They are computationally identical; VAR.S is the modern name added in Excel 2010. The legacy VAR still works and lives in the Compatibility category.

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