# VARPA function

This article describes the formula syntax and usage of the VARPA function in Microsoft Excel.

## Description

Calculates variance based on the entire population.

## Syntax

VARPA(value1, [value2], ...)

The VARPA function syntax has the following arguments:

• Value1, value2, ...    Value1 is required, subsequent values are optional. 1 to 255 value arguments corresponding to a population.

## Remarks

• VARPA assumes that its arguments are the entire population. If your data represents a sample of the population, you must compute the variance by using VARA.

• Arguments can be the following: numbers; names, arrays, or references that contain numbers; text representations of numbers; or logical values, such as TRUE and FALSE, in a reference.

• Logical values and text representations of numbers that you type directly into the list of arguments are counted.

• Arguments that contain TRUE evaluate as 1; arguments that contain text or FALSE evaluate as 0 (zero).

• If an argument is an array or reference, only values in that array or reference are used. Empty cells and text values in the array or reference are ignored.

• Arguments that are error values or text that cannot be translated into numbers cause errors.

• If you do not want to include logical values and text representations of numbers in a reference as part of the calculation, use the VARP function.

• The equation for VARPA is : where x is the sample mean AVERAGE(value1,value2,…) and n is the sample size.

## Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

 Strength 1345 1301 1368 1322 1310 1370 1318 1350 1303 1299 Formula Description R esult =VARPA(A2:A11) Variance of breaking strengths for all the tools, assuming that only 10 tools are produced (entire population). 678.84 =VAR(A2:A11) This example uses the VAR function, which assumes a sample of the population, and returns a different result. 754.27
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