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Documentation/Calc Functions/DEVSQ

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Function name:

DEVSQ

Category:

Statistical Analysis

Summary:

Calculates the sum of the squared deviations from the mean of the specified data set.

Syntax:

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

Returns:

Returns a non-negative real number, which is the sum of the squared deviations from the mean of the specified data set.

Arguments:

Number 1, Number 2, ..., Number 255 give the data set containing the values to contribute to the calculation. 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 DEVSQ 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.

  • If any argument is a text string in quotation marks, then DEVSQ reports a parameter list error (Err:504).
  • DEVSQ includes numbers, dates/times, and logical values in its calculation.
  • DEVSQ ignores empty cells and text strings in cells.
  • If there are no supplied numbers, then DEVSQ reports a #DIV/0! error.
  • If only one value is supplied, then DEVSQ returns 0.

Additional details:

  • DEVSQ ignores any text in cells or empty cells. If you suspect wrong results, look for text within the supplied data range(s). To highlight text content within a data range, use Calc's View ▸ Value Highlighting feature.
  • The formula for DEVSQ is:
[math]\displaystyle{ \text{DEVSQ}~=~\sum_{i=1}^{n}\left ( x_{i}\:-\:\bar{x} \right )^2 }[/math]
where
  • xi are the values in the data set
  • is the mean of the values in the data set
  • n is the number of values in the data set.
  • The value returned by DEVSQ is related to the variance of the data set, except that the value returned by DEVSQ has not been divided by n (population variance) or n-1 (sample variance).

Examples:

Formula Description Returns
=DEVSQ(A1:A5) where cells A1:A5 contain the values 1, 2, 3, 4, and 5 respectively. Here the function calculates the sum of the squared deviations from the mean for the five integer numbers given The same result is obtained from the formulas =DEVSQ(A1; A2; A3; A4; A5) and =DEVSQ({1, 2, 3}; {4, 5}) 10
=DEVSQ(1.5; -2.0; 0.0; -4.2) Here the function calculates the sum of the squared deviations from the mean for the four real numbers given. 18.3675

Related LibreOffice functions:

VAR

VARA

VARP

VARPA

ODF standard:

Section 6.18.20, part 2

Related (or similar) Excel functions:

DEVSQ