Significance of CV and Variance values in social science research and methods of their interpretation.
In general, these are different statistics. Coefficient of variation is the ratio of the standard deviation to the mean, and the variance is the square of the standard deviation.
Some useful guidance on the former here: https://influentialpoints.com/Training/Coefficient_of_variation_Use_and_misuse.htm
Put simply there are two key aspects to describing a distribition
1 the central tendency or middle
2 the spread or the degree of variation around the middle.
The problem with the variance (and the standard deviation) is that can be seen as a combination of these two elements in that is is affected by the units of measurement for the variable being studied. The coefficient of variation purports to be a measure of spread that is dimensionless.
So if you assessing income inequality of two countries with different monetary systems you would want the coefficient of variation.
This project is in part about developing a measure of inequality that uses a Poisson multilevel model to get at the spread taking account of the mean.
https://www.researchgate.net/project/Modelling-segregation-methodological-developments
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