Documentation/Calc Functions/VARPA
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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:
ODF standard:
Related (or similar) Excel functions:
VARPA