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Documentation/Calc Functions/VAR

From The Document Foundation Wiki

Function name:

VAR

Category:

Statistical Analysis

Summary:

Calculates the sample variance of a set of numbers.

Syntax:

VAR(Number 1 [; Number 2 [; … [; Number 255]]])

Returns:

Returns a non-negative real number, which is the sample variance of the supplied numbers.

Arguments:

Number 1, Number 2, ..., Number 255 give the set of real numbers for which the sample variance is to be calculated. Each argument may be a value or an expression, a reference to a single cell, a reference to a cell range, the name of a named or database range, or an inline array.

Note that although VAR can accept up to 255 arguments, each argument could specify a range of cells. This means that the number of real numbers processed could be many more than 255.

The following conditions (including errors) may be encountered:

  • If any argument is a string in quotation marks, then VAR reports a parameter list error (Err:504).
  • Text in cells and empty cells are ignored.
  • If less than two numbers are supplied, then VAR reports a #DIV/0! error.

Additional details:

  • Calc's VAR and VAR.S functions perform identical calculations. The requirements for VAR are specified in ODF 1.2; VAR.S is provided for interoperability with Microsoft Excel.
  • The formula for the sample variance ([math]\displaystyle{ s^2 }[/math]) is:
[math]\displaystyle{ s^2\:=\:\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^2 }[/math]
where
  • [math]\displaystyle{ n }[/math] is the size of the sample
  • [math]\displaystyle{ x_{i} }[/math] is the i-th value in the sample
  • [math]\displaystyle{ \bar{x} }[/math] is the sample mean
  • For more information on variances, visit Wikipedia's Variance page.

Examples:

Formula Description Returns
=VAR(A1:A5) where cells A1:A5 contain the values 1, 2, 3, 4, and 5 respectively. Here the function calculates the sample variance of the five values in the specified cells. 2.5
=VAR(3; 4; 5; 6; 2; 3; 1) Here the function calculates the sample variance of the seven values passed as individual arguments. 2.95238095238095
=VAR({3, 4, -5, 6.05, 2, 3, -1.5}) Here the function calculates the sample variance of the seven values passed in an inline array. 13.7991666666667

Related LibreOffice functions:

AVERAGE

AVERAGEA

STDEV

STDEV.P

STDEV.S

STDEVA

STDEVP

STDEVPA

VAR.P

VAR.S

VARA

VARP

VARPA

ODF standard:

Section 6.18.82, part 2

Related (or similar) Excel functions:

VAR