Measure of dispersion for dataset with zero mean I'm testing a machine learning algorithm which, until now used coefficient of variation in order to relative measure dispersion among different attributes in a given dataset. 
Now that I need to test it thoroughly on larger dataset, it's critical to do something about the possibility of a zero mean, which would immediately breaks down coefficient of variation (cv), and hence the algorithm. Please note that the distributions are not essentially Gaussian, and are often skewed when they are. Also, the measure of dispersion needs to be dimensionless.
I searched the web a bit to find ways to 'normalize' cv in some manner, or to even find an alternative to cv. I tried inter-quartile range(iqr), but there was a significant drop in performance when I migrate from cv to iqr. 
Is there any other dispersion measure that returns similar values to that of cv? If not, is there any principled way to 'normalize' coefficient of variance?
 A: You have really pointed out one of the limitations of the coefficient of variation as a dispersion measure. However, I have one alternative measure of dispersion to recommend regarding this problem of getting the zero mean. although it has not been peer-reviewed, I am certain that STATISTICAL MIRRORING (Abdullahi, 2020) could be an appropriate alternative.
For instance, suppose you have a dataset: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
The mean, standard deviation, and coefficient of variation equal to 0, 3.3166, and #DIV/0! respectively. But, using statistical mirroring, you would get an answer to be -100% (i.e, the spread around the mean is perfectly equal and opposite direction as a mirror image of each other) and 0.00% (i.e, little dispersion around the mean) for the meanic proximity and meanic deviation respectively.
Reference:
Abdullahi, K.B. Optinalytic (Statistical) Mirroring: A New Novel Approach of Measure of Dispersion. Preprints 2019, 2019110268 (doi: 10.20944/preprints201911.0268.v1).
Or you can wait for a more detail explanation about statistical mirroring by following the up-coming version of the Preprint.
Sincerely,
