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In [[statistics]], the '''quartile coefficient of dispersion''' is a descriptive statistic which measures [[Statistical dispersion|dispersion]] and which is used to make comparisons within and between data sets. | |||
The statistic is easily computed using the first (''Q''<sub>1</sub>) and third (''Q''<sub>3</sub>) [[quartile]]s for each data set. The quartile coefficient of dispersion is:<ref>{{cite doi|10.1016/j.csda.2005.05.007}}</ref> | |||
: <math>{Q_3 - Q_1 \over Q_3 + Q_1}.</math> | |||
Consider the following two data sets: | |||
: Data set A: 2, 4, 6, 8, 10, 12, 14. | |||
:: ''n'' = 7, range = 12, mean = 8, median = 8, ''Q''<sub>1</sub> = 4, ''Q''<sub>3</sub> = 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, ''Q''<sub>1</sub> = 2, ''Q''<sub>3</sub> = 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. | |||
==References== | |||
{{reflist}} | |||
{{DEFAULTSORT:Quartile Coefficient Of Dispersion}} | |||
[[Category:Statistical deviation and dispersion]] | |||
[[Category:Statistical ratios]] | |||
{{statistics-stub}} | |||
Revision as of 21:02, 24 October 2013
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]
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.
References
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