The sample mean and variance for the *jth*
variable xj
are defined in the standard fashion as

(171)

and

(172)

**Uncorrected
univariate skewness.** The *uncorrected univariate skewness
*for variable xj
is defined as

(173)

**Corrected univariate skewness. **The
uncorrected estimate is biased. The following *corrected univariate
skewness *is an unbiased estimate when the distribution is normal.

(174)

The asymptotic variance of these measures is
6/*N*, which is used to standardize the uncorrected skewness to produce
the "normalized" skewness printed by the program.