# SKEW

## Purpose:

Calculates the skewness of a series.

## Syntax:

SKEW(series, bias)

series

-

A series. The z value.

bias

-

Optional. An integer, the bias calculation. Valid methods are:

 0: compute unbiased estimate (default) 1: compute biased estimate

## Returns:

A scalar, the skewness of the series.

## Example:

W1: {3, 4, 5, 2, 3, 4, 5, 6, 4, 7}

W2: {skew(w1)}

W3: {skew(w1, 1)}

W2 == {0.359453}, the unbiased or population skew.

W3 == {0.303193}, the biased skew.

## Remarks:

Skewness is the third standardized moment defined as: where μ3 is the third moment about the mean and σ is the standard deviation.

The biased or sample skew is computed as: where the arithmetic mean is defined as: The unbiased or population skew is computed as: By default, SKEW calculates the unbiased or population skewness as used in SAS, SPSS, and Excel. To calculate the biased skew, set the bias flag to 1.

Skewness characterizes the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values. Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values.

For multi-column data, SKEW returns the skewness of each column.