# How do I calculate the average coefficient of variation?

I'm a biochemist and I usually compare the variability of my measurements in terms of coefficient of variation (CV) since I can "visualize" the deviations more easily in terms of percentages deviation from my mean value. Now, I measured an analyte 20 times in a sample in one month, and again 20 times the second month. Now I'd like to calculate the mean CV of those two sets of measurements. I know I can get a pooled sd and then maybe get the arithmetic mean of two means to calculate at the end mean or pooled CV, but I suppose I cannot do that, true? Can I just get mean CV (add, and divide by two?). Statisticians are usually in terms of squares, adding and square-rooting sd-s or variances, am I right? And for what is worth, I suppose also that if I combine all data in one set, I'd probably get different sd and CV?

• I've added the obvious tag, on which there are several good answers (interested party!). stats.stackexchange.com/questions/118497/… is one discussion. – Nick Cox Nov 23 '18 at 10:41
• Do you have actual data ? Combining data of two samples and combining the statistic of say two separate samples is a distinct issue. Pooling of raw data from two samples may give a different coeff. of variation - probabably more representative. – Subhash C. Davar Nov 23 '18 at 13:59

I don't see any special value to averaging coefficients of variation (CVs).

Ideally your CV is consistent across datasets or groups or variables in which case you can underline that fact by citing a narrow range.

Conversely, if your CV is not at all consistent an average is not informative and how to get it a secondary issue. A wider issue is that the CV is a ratio, SD/mean, and ratios are often volatile and not easily or comfortably averaged. Otherwise put, the point you make that average CVs could be calculated in different ways shows up that the notion of average CV is not well defined.

In the great majority of cases where I have seen coefficient of variation used:

1. The implication is that you should be working on logarithmic scale.

2. Or it is not really helping.

Sample data that is real or realistic for you would allow a more specific answer.

In short, getting very different results is likely to be a sign that the data need closer analysis. Ignoring the difference by averaging is going in the wrong direction.

• Thank you Nick for the answer. Yes, indeed, you are right about averaging CVs when they are not so different, as they are mostly in my case, is not a big advantage. I was merely trying to "do it the right way", but I cannot find any logic in my head that would appreciate more one way or the other. My SDs and means are mostly similar, on one or two occasions I have noticeable differences (I'm measuring set or analytes in my samples) - still clinically irrelevant. That's why I wanted to do it properly, statistically correct because I don't know of any reasons/limitations to either way. – Jelena Nov 23 '18 at 11:07
• You need to think in terms of the right model for the data, not reducing puzzling descriptive statistics to yet more descriptive statistics. The problem could be almost anything, e.g. an outlier or outliers in one dataset not another; CV being an unsuitable reduction any way; a need to think on some quite different scale or using quite different summary statistics. – Nick Cox Nov 23 '18 at 11:11
• Thank you for the tag, I'm reading it right now, interesting stuff... Happy to learn some more! – Jelena Nov 23 '18 at 12:10