Documentation/Calc Functions/SKEWP
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Function name:
SKEWP
Category:
Statistical Analysis
Summary:
Calculates a measure of the skewness of a distribution using a population 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:
SKEWP(Number 1 [; Number 2 [; … [; Number 255]]])
Returns:
Returns a real number, which is the estimated population skewness of the distribution.
Arguments:
Number 1, Number 2, ..., Number 255 give the set of real numbers from which the population 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 SKEWP 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 SKEWP reports a parameter list error (Err:504).
- Text in cells and empty cells are ignored.
- If there are less than three supplied numbers, then SKEWP reports a #DIV/0! error.
- If the standard deviation of the supplied numbers is equal to zero, then SKEWP reports an invalid argument error (Err:502).
Additional details:
- The formula for SKEWP is:
- [math]\displaystyle{ skewness\:=\:\frac{1}{n}\sum_{i=1}^{n}\left( \frac{x_i-\bar{x}}{\sigma}\right)^3 }[/math]
- where
- [math]\displaystyle{ n }[/math] is the population size
- [math]\displaystyle{ x_i }[/math] is the i-th data point
- [math]\displaystyle{ \bar{x} }[/math] is the mean of the population
- [math]\displaystyle{ \sigma }[/math] is the standard deviation of the population.
- For more information on skewness, visit Wikipedia's Skewness page.
Examples:
| Formula | Description | Returns |
|---|---|---|
| =SKEWP(A1:A5) where cells A1:A5 contain the values 1, 3, 4, 5, and 9 respectively. | Here the function estimates a positive population skewness. | 0.593600459637472 |
| =SKEWP(1; 3; 4; 5; 7) | Here the function estimates a zero population skewness, indicating a symmetric distribution. | 0 |
| =SKEWP({1; 2; 4; 5; 6}) | Here the function estimates a negative population skewness. | -0.157987551437596 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
SKEW.P since v.2013.