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Coefficient of Variation: Definition, example, Formula

The standard deviation is an absolute measure of dispersion and hence can not be used for comparing variability of 2 data sets with different means.

Therefore, such comparisons are done by using a relative measure of dispersion called coefficient of variation (CV).


CV = \(\frac{σ}{μ}\)


where σ is the standard deviation and μ is the mean of the data set. 

CV is often represented as a percentage,


CV % =\( \frac{σ}{μ}\times 100\)


When comparing data sets, the data set with larger value of CV% is more variable (less consistent) as compared to a dataset with lesser value of CV%.

 

For example:


μσCV%

Data set 1

5

1

20%

Data set 2

20

2

10%

   

Although σ = 2 for data set 2 is more than σ = 1 for data set 1, data set 2 is actually less variable compared to data set 1, as can be seen by the fact that data set 2 has a CV % of 10%, while data set 1 has a CV % of 20%.


So comparison of variability between 2 or more data sets (with different means) should be done by comparing CV % and not by comparing standard deviations.


Coefficient of Variation Practice Problems

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