Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The function skewness of the subpackage stats[describe, ...] computes the moment coefficient of skewness of the given data. It is defined to be the third moment about the mean, divided by the third power of the standard deviation.

The skewness measures the degree to which a distribution is asymmetric. For a symmetric distribution, the skewness is zero. If a distribution has a longer tail to the left than to the right, it is said to have negative skewness. If the reverse is true, then the distribution has a positive skewness.

Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.

The computation of the skewness involves that of the standard deviation. Since, the definition of standard deviation varies according to whether it is computed for the whole population, or only for a sample, then so does the skewness vary. The parameter Nconstraint controls this behavior. For more information on this subject, refer to describe[standarddeviation].

There are other possibilities for the definition of the skewness, as can be seen in various books on statistics.

The command with(stats[describe],skewness) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{stats}\right)\:$

$\mathrm{describe}\left[\mathrm{skewness}\right]\left(\left[1\,4\,7\right]\right)$

$0$

$\mathrm{describe}\left[\mathrm{skewness}\right]\left(\left[1\,6\,7\right]\right)$

$-\frac{77\sqrt{62}}{961}$

$\mathrm{describe}\left[\mathrm{skewness}\right]\left(\left[1\,2\,7\right]\right)$

$\frac{77\sqrt{62}}{961}$