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:^[1]

${\displaystyle {Q_{3}-Q_{1} \over Q_{3}+Q_{1}}.}$

Example

Consider the following two data sets:

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

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.

See also

• Coefficient of variation

References

1. Bonett, D. G. (2006). "Confidence interval for a coefficient of quartile variation". Computational Statistics & Data Analysis. 50 (11): 2953–2957. doi:10.1016/j.csda.2005.05.007.