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# stats::obliquity

Obliquity (skewness) of a data sample

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::obliquity(x1, x2, …)
stats::obliquity([x1, x2, …])
stats::obliquity(s, <c>)
```

## Description

stats::obliquity(x1, x2, …, xn) returns the obliquity (skewness)

,

where is the mean of the data xi.

The obliquity is a measure for the symmetry of a distribution. It is zero, if the distribution of the data is symmetric around the mean. Positive values indicate that the distribution function has a "longer tail" to the right of the mean than to the left. Negative values indicate a "longer tail" to the left.

The column index c is optional, if the data are given by a stats::sample object containing only one non-string column. Cf. Example 3.

External statistical data stored in an ASCII file can be imported into a MuPAD® session via import::readdata. In particular, see Example 1 of the corresponding help page.

## Examples

### Example 1

We calculate the obliquity of a data sequence:

`float(stats::obliquity(0, 7, 7, 6, 6, 6, 5, 5, 4, 1))`

Alternatively, data may be passed as a list:

`stats::obliquity([2, 2, 4, 6, 8, 10, 10])`

### Example 2

We create a sample:

`stats::sample([[a, 5, 8], [b, 3, 7], [c, d, 0]])`
```a  5  8
b  3  7
c  d  0
```

The obliquity of the second column is:

`stats::obliquity(%, 2)`

### Example 3

We create a sample consisting of one string column and one non-string column:

`stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])`
```"1996"  1242
"1997"  1353
"1998"  1142
```

We compute the obliquity of the second column. In this case this column does not have to be specified, since it is the only non-string column:

`float(stats::obliquity(%))`

## Parameters

 x1, x2, … The statistical data: arithmetical expressions. s A sample of domain type stats::sample. c An integer representing a column index of the sample s. This column provides the data x1, x2 etc.

## Return Values

Arithmetical expression. FAIL is returned, if the obliquity does not exist.