# Documentation/Calc Functions/SKEWP

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).

• The formula for SKEWP is:
$\displaystyle{ skewness\:=\:\frac{1}{n}\sum_{i=1}^{n}\left( \frac{x_i-\bar{x}}{\sigma}\right)^3 }$
where
• $\displaystyle{ n }$ is the population size
• $\displaystyle{ x_i }$ is the i-th data point
• $\displaystyle{ \bar{x} }$ is the mean of the population
• $\displaystyle{ \sigma }$ is the standard deviation of the population.

## 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

SKEW.P