Obliquity (skewness) of a data sample

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


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


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.


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:



x1, x2, …

The statistical data: arithmetical expressions.


A sample of domain type stats::sample.


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.

See Also

MuPAD Functions

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