Quartile coefficient of dispersion

In statistics, the quartile coefficient of dispersion is a descriptive statistic which measures dispersion and which is 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. The quartile coefficient of dispersion is

${Q_3 - Q_1 \over Q_3 %2B Q_1}.$

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 quartile coefficient of dispersion of data set A is 2.7 times as great (0.5 / 0.18) as that of data set B.