In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, the quartile coefficient of dispersion is a descriptive statistic which measures dispersion

Statistical dispersion

In statistics, statistical dispersion is variability or spread in a variable or a probability distribution...

 and which is used to make comparisons within and between data sets.

The statistic is easily computed using the first (Q₁) and third (Q₃) quartile

Quartile

In descriptive statistics, the quartiles of a set of values are the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled...

s for each data set. The quartile coefficient of dispersion is

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.