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Documentation/Calc Functions/SKEW

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Function name:

SKEW

Category:

Statistical Analysis

Summary:

Calculates a measure of the skewness of a distribution using a sample set of numbers. Skewness is a measure of the symmetry or asymmetry of the distribution. Positive values indicate a distribution with a tail inclining to the positive side, and negative values a distribution with a tail inclining to the negative side.

Syntax:

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

Returns:

Returns a real number, which is the estimated sample skewness of the distribution.

Arguments:

Number 1, Number 2, ..., Number 255 give the set of real numbers from which the sample skewness 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 SKEW can accept up to 255 arguments, each argument could specify a range of cells. This means that many more than 255 real numbers could be processed.

The following conditions (including errors) may be encountered:

  • If any argument is a string in quotation marks, then SKEW reports a parameter list error (Err:504).
  • Text in cells and empty cells are ignored.
  • If there are less than three supplied numbers, then SKEW reports a #DIV/0! error.
  • If the standard deviation of the supplied numbers is equal to zero, then SKEW reports an invalid argument error (Err:502).

Additional details:

  • The formula for SKEW is:
[math]\displaystyle{ skewness\:=\:\frac{n}{(n-1)(n-2)}\sum_{i=1}^{n}\left( \frac{x_i-\bar{x}}{s}\right)^3 }[/math]
where
  • [math]\displaystyle{ n }[/math] is the number of data points in the sample
  • [math]\displaystyle{ x_i }[/math] is the i-th data point
  • [math]\displaystyle{ \bar{x} }[/math] is the mean of the sample
  • [math]\displaystyle{ s }[/math] is the standard deviation of the sample
  • For more information on skewness, visit Wikipedia's Skewness page.

Examples:

Formula Description Returns
=SKEW(A1:A5) where cells A1:A5 contain the values 1, 3, 4, 5, and 9 respectively. Here the function estimates a positive sample skewness. 0.884887319483005
=SKEW(1; 3; 4; 5; 7) Here the function estimates a zero sample skewness, indicating a symmetric distribution. 0
=SKEW({1; 2; 4; 5; 6}) Here the function estimates a negative sample skewness. -0.235513936408806

Related LibreOffice functions:

SKEWP

ODF standard:

Section 6.18.67, part 2

Related (or similar) Excel functions:

SKEW