There are four ways distributions can be compared.  Two were mentioned last week–central tendency and dispursion.  Central tendency talks about the average value.  Dispursion reflect the distribution’s variability.

The other two are skewness and kurtosis.

Skew (or skewness) is a measure of lack of symmetry.  Skew occurs when one end (or tail) of the distribution sticks out farther than the other.  Like this:

In this picture, the top image is that of positive skew and the bottom picture is negative skew.

Skew can happen when data are clustered at one end of a distribution like in a test that is too easy or too hard.  When the mean is is a larger number (i.e., greater) than the median, the distribution is positively skewed.  When the median is is a larger number (i.e., greater)  than the mean, the distribution is negatively skewed.

The other characteristic of a distribution is kurtosis.

Kurtosis refers to the overall shape of the distribution relative to its peak.  Distributions can be relatively flat, or platykurtic, or they can be relatively peaked, or leptokurtic.  This drawing provides a mnemonic to remember those terms:

A normal distribution, the bell curve, is called mesokurtic.

These terms are used to describe a distribution in a report or presentation.  When all four characteristics of a distribution are described, central tendency, dispursion, skew, and kurtosis, the reader has a clear picture of the data base.  From that point, frequencies and percentages can be reported.  Then statistical tests can be performed and reported as well.