Quartile coefficient of dispersion

In statistics, the quartile coefficient of dispersion is a descriptive statistic used to make comparisons within and between data sets. The statistic is easily computed using the first (Q1) and third (Q3) quartiles for each data set. Consider the following two data sets:


 * Data set A: 2, 4, 6, 8, 10, 12, 14


 * n = 7, range = 12, mean = 8, median = 8, Q1 = 4, Q3 = 12


 * coefficient of dispersion = 0.5


 * Data set B: 1.8, 2, 2.1, 2.4, 2.6, 2.9, 3


 * n = 7, range = 1.2, mean = 2.4, median = 2.4, Q1 = 2, Q3 = 2.9


 * coefficient of dispersion = 0.18

The formula for the coefficient of dispersion is


 * $${Q_3 - Q_1 \over Q_3 + Q_1}.$$

The dispersion or spread within data set A is 2.7 (0.5/0.18) times as great as that of data set B. To put this in perspective, imagine that data set A represents executive salaries in company A. Data set B, on the other hand, represents average executive salaries in companies competing with or similar to company A. Unless company A's performance (however you choose to measure performance) is significantly greater than average, this data can be used as a basis for arguing that company A's executives are over-compensated.

Note also that company A's most senior executives receive considerably more than average.

The coefficient of dispersion is an easily computed statistic which allows meaningful comparisons to be made from comparative data sets.