2.5. Measures of dispersion (variability/spread)

Descriptive statistics tries to describe data. It does this by tables and diagrams, or by representing the data by some form of measurement. The most commonly form of measurement to describe data, are the measurements of central tendency. However, measures of central tendency do not give a very clear picture of the data and are therefore (or should be) accompanied by a measure of dispersion.

To put it bluntly: if your head is in a burning oven and your feet are in a refrigerator, on average you will be doing just fine. Another statistical joke that makes the point is that three hunters go deer hunting. One shoots two meter to the left of the deer, the other shoots two meter to the right. The third shouts: yippie on average we got him! Measures of dispersion provide information about how varied the numbers were. Did the people agree with each other? Were there many differences? etc.

For nominal variables dispersion is often not calculated. One measurement is the Variation Ratio (VR) (normally credited to Freeman (1965)), which is the percentage of cases that do not fall in the modal category. It is one of many types of Qualitative Variation. On Wikipedia a long list of other Qualitative Variation coefficients can be found.

References
Freeman, L. C. (1965). Elementary applied statistics: for students in behavioral science. New York: Wiley.