Documentation/Calc Functions/VARPA

    From The Document Foundation Wiki

    Function name:

    VARPA

    Category:

    Statistical Analysis

    Summary:

    Calculates the population variance of a set of numbers.

    VARPA is a variant of the VARP function. The main difference between the two is that VARP ignores cells containing text, whereas VARPA treats text values as the number 0.

    Syntax:

    VARPA(Number 1[; Number 2[; ...[; Number 255]]])

    Returns:

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

    Arguments:

    Number 1, Number 2, ..., Number 255 give the set of real numbers for which the population 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 VARPA 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:

    • Text strings are treated as the number 0.
    • Empty cells are ignored.
    • If no numbers are supplied, then VARPA reports a #DIV/0! error.
    • If only one number is supplied, then VARPA returns 0.

    Additional details:

    • The formula for the population variance ([math]\displaystyle{ \sigma^2 }[/math]) is:
    [math]\displaystyle{ \sigma^2\:=\:\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\mu)^2 }[/math]
    where
    • [math]\displaystyle{ n }[/math] is the size of the population
    • [math]\displaystyle{ x_{i} }[/math] is the i-th value in the population
    • [math]\displaystyle{ \mu }[/math] is the population mean
    • For more information on variances, visit Wikipedia's Variance page.

    Examples:

    Formula Description Returns
    =VARPA(A1:A6) where cells A1:A5 contain the values 1, 2, 3, 4, and 5 respectively, with cell A6 empty. Here the function calculates the population variance of the five values in cells A1:A5, ignoring the empty cell A6. 2
    =VARPA(A1:A6) where cells A1:A5 contain the same values as in the previous example, with cell A6 containing the string "Calc functions". Here the function calculates the population variance of the five values in cells A1:A5 and the value 0 allocated for the text string in cell A6. Note that the formula =VARPA(1; 2; 3; 4; 5; 0) returns the same value. 2.91666666666667
    =VARPA(3; 4; 5; 6; 2; 3; 1; "LibreOffice") Here the function calculates the population variance of the first seven values passed as individual arguments, along with the value 0 allocated for the text string in the final argument. Note that the formula =VARPA(3; 4; 5; 6; 2; 3; 1; 0) returns the same value. 3.5
    =VARPA({3, 4, -5, 6.05, 2, 3, -1.5}) Here the function calculates the population variance of the seven values passed in an inline array. 11.8278571428571

    Related LibreOffice functions:

    AVERAGE

    AVERAGEA

    STDEV

    STDEV.P

    STDEV.S

    STDEVA

    STDEVP

    STDEVPA

    VAR

    VAR.P

    VAR.S

    VARA

    VARP

    ODF standard:

    Section 6.18.85, part 2

    Related (or similar) Excel functions:

    VARPA