SKEW

The numerical values to compute the skew of. This can be a constant value, a column, a cell range, or an expression evaluating to any of the above. For the format definition of data, see the "Macro Function Parameters" section in the chapter in this guide for your IBM® product. There must be at least three values in data.

keyword

This optional keyword determines how the computation is performed over the input data range. Select one of the following:

ALL - Performs the computation on all cells in data (default)

COL - Performs the computation separately for each column of data

ROW - Performs the computation separately for each row of data

For more details on using keywords in IBM® Campaign, see Format Specifications.

For more details on using keywords in IBM® PredictiveInsight, see Format Specifications.

Description

SKEW calculates the skew of the distribution of all the cells in the specified data range. Skewness measures the degree of asymmetry of a distribution about its mean. A positive skew value indicates a distribution with an asymmetric tail leaning towards more positive values; a negative skew indicates a distribution with an asymmetric tail leaning towards more negative values. A zero skew value indicates that the distribution is symmetrical about its mean.

Skew is calculated as follows:

where nis the number of samples in the distribution, mean is the average, and σis the standard deviation of the distribution. A minimum of three data values must be provided to compute skew.

If the standard deviation σ =0, SKEW returns zero.

Examples

TEMP = SKEW(3) or TEMP = SKEW(3, ALL)

Creates a new column named TEMP containing the value zero.

TEMP = SKEW(MERGE(3, 7, 2))

Creates a new column named TEMP containing the value 0.14.

TEMP = SKEW(V1)

Creates a new column named TEMP containing a single value which is the skew of the contents of column V1.

TEMP = SKEW(V1:V3)

Creates a new column named TEMP containing a single value which is the skew of the contents of columns V1, V2, and V3.

TEMP = SKEW(V1[10:20])

Creates a new column named TEMP containing a single value which is the skew of the cells in rows 10-20 of column V1.

TEMP = SKEW(V1[1:5]:V4)

Creates a new column named TEMP containing a single value which is the skew of the cells in rows 1-5 of columns V1 through V4.

TEMP = SKEW(V1:V3, COL)

Creates three new columns named TEMP, VX, and VY. The single value in the TEMP column is the skew of the contents of column V1, the single value in the VX column is the skew of the contents of column V2, and the single value in the VY column is the skew of the contents of column V3.

TEMP = SKEW(V1[1:5]:V3,COL)

Creates three new columns named TEMP, VX, and VY, each containing a single value. The value in column TEMP is the skew of the cells in rows 1-5 of column V1, the value in column VX is the skew of the cells in rows 1-5 of column V2, and the value in column VY is the skew of the cells in rows 1-5 of column V3.

TEMP = SKEW(V1:V3, ROW)

Creates a new columns named TEMP where each cell entry is the skew of the corresponding row across columns V1, V2, and V3.

TEMP = SKEW(V1[10:50]:V3,ROW)

Creates a new column named TEMP, where the first 41 cells contain the skew of the values in rows 10-50 across columns V1 through V3. The other cells in TEMP are empty.

Related Functions

Function	Description
AVG or MEAN	Computes the arithmetic mean or average of a range of cells
KURTOSIS	Computes the kurtosis of a range of cells
STAT	Computes the first through fourth moments of the specified data range
VARIANCE	Computes the variance of a range of cells