The standard deviation is proportional to the mean - , e.g. a mean with 20 may have a std. of 2 (10%). If this is compared to the same std. but a mean of 10, the std. of 2 would correspond to 20%. When you have hug differences in means and want to compare their variation, it would be better to take the coefficient of variation, because it normalizes the standard deviation with respect to the mean. 

Best Susanne

Hello Richardas...

This information about Gini Index or Gini Coefficient is new to me. But it does look like a really promising way to represent data inequality. It definitely warrants more attention. 

Thanks  

I would like to add one more point. Sometimes it is not clear whether obtained std. is significant or not. For example, for some data 0.2 could be a huge std. whereas in some other case even 5 is not that bad (ex: out of 100 marks in a test).  It is safer to use CV when you don't know much about the data (except the mean). CV is basically a relative std. which you can calculate in percentage and would make sense easily. 

the coefficient of variation is something useless. check our new paper

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...

In some cases, the coefficient of variation and the RSD are the same thing. However, the RSD cannot be negative while the Coefficient of Variation can be positive or negative. This is because the two formulas differ in a minor way: the Coefficient of Variation divides by the mean while the RSD divides by the absolute value of the mean.

Hi everyone and thank you for the interesting discussion!

I would be happy if someone could refer me to papers which had detemined coefficient of variation cutofffs/acceptable levels, in any field. I study the medical practice variation field and use the coefficient of variation method, and therefore searching for accepatable levels.

Thanks in advance,

Sagi

CV is an index of deviation, somehow standardized with respect to the mean. It has no unit. SD is the root of variance. The main merit of it is the identical unit with the original data. In this case, SD is preferable.

With regard to the question asked:

"I am trying to compare the inter-annual variability of a model and an observation system. So I was wondering which of the two statistics would be best to compare the inter-annual variability of the two datasets, either inter-annual standard deviation of the coefficient of variation".

Does heteroscedasticity enter into the above given answers? If so, how?

I am not familiar with the distinction proposed by Kashyap Thummar between CV and RSD. CV is very widely used without any restriction that it be positive. On what authority do you propose this distinction?