Skewness is a statistic that
measures the asymmetry of a distribution. Given a sequence of values,
*x** _{i}*, the
sample skewness is:

You might recognize
*m** _{2}* as
the mean squared deviation (also known as variance);

Negative skewness indicates that a distribution “skews left”; that is, it extends farther to the left than the right. Positive skewness indicates that a distribution skews right.

In practice, computing the skewness of a sample is usually not a
good idea. If there are any outliers, they have a disproportionate
effect on
*g** _{1}*.

Another way to evaluate the asymmetry of a distribution is to look at the relationship between the mean and median. Extreme values have more effect on the mean than the median, so in a distribution that skews left, the mean is less than the median.

Pearson’s median skewness coefficient
is an alternative measure of skewness that explicitly captures the
relationship between the mean, *μ*, and the median,
*μ** _{1/2}*:

This statistic is robust, which means that it is less vulnerable to the effect of outliers. ...

Start Free Trial

No credit card required