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I have 2 non-normal population datasets where the median is a better measure of central tendency.

To compare the spread of these 2 populations, can I calculate the coefficient of variation (CV) with population median and standard deviation σ? Or, is CV only applicable to sample mean and standard deviation?

Population 1:

  • Median = 2,556; Mean = 2,797; σ = 1,910

Population 2:

  • Median = 2,954; Mean = 3,436; σ = 1,959
Harper
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2 Answers2

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A more appropriate way to estimate CV of skewed data would be, what may be termed as the "Quartile based Coefficient of Variation" [or QCV]

QCV = [(Q3 - Q1) / Q2] x 100

where Q1, Q2, Q3 are the first, second and the third quartiles. Note that the second quartile is the median.

Subhash Chandra
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  • This is a different measure. It's not, in general, a good estimator of SD/mean. For skewed data, the median isn't usually a good estimator of the mean and the IQR isn't expected to equal the SD. Naturally rules of thumb, including fudge factors, might be developed for some circumstances, but if you have to work with the CV too this loses its point. Note further that as with the CV, this measure may work very poorly if zeros or negative values are present. More generally, if this is a helpful measure the usual implication is that you are better off on logarithmic scale. – Nick Cox Jan 14 '19 at 15:43
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Here is an interesting option "Coefficient of Quartile Variation"

$$CQV = \left(\frac{Q_3-Q_1}{Q_3+Q_1}\right)\times 100$$

Reference: https://cran.r-project.org/web/packages/cvcqv/vignettes/cqv_versatile.html

Thiago Pires
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  • how does this answer the question? it doesn't even use median – StupidWolf Jan 10 '21 at 06:10
  • It is interesting and relevant to the discussion. The link cites several sources, so has some support, unlike the Q2-based calculation.

    I agree that it is a real shame is that Q3+Q1 is used, rather than Q2, although maybe something can be done with a factor of x2 'correction' by someone with a better grounding in stats than me.

     – Big Old Dave Mar 29 '22 at 13:48