Coefficient of variation

Let $Q=\{q_1,\ldots,q_n\}$ ($n\in\mathbb N$, $n>1$) a collection of elements and $d:\,Q\times Q \longrightarrow \mathbb R^+$ a distance between a pair of elements (as a measure of similarity). Assume that all elements in $Q$ are different according to $d$. I define the dispersion in $Q$ as

$$\sigma^2 =\frac{1}{n-1} \displaystyle\sum_{i=1}^n\left(\mu_c-d(q_c,q_i)\right)^2,$$

where $q_c$ is a centroid in $Q$ and $\mu_c$ is the average of distances between the centroid and the other objects.

Then, I normalize this measure in the interval $[0,1]$ as the coefficient of variation:

$$D=\frac{\sigma}{\mu_c}.$$

My question is if this is well-defined.

I think that it is because $\mu_c$ is strictly positive (distances are positive, all elements are pair-wise different and there must be at least two elements in $Q$). My doubt is that in the Wikipedia they say that it should be computed only for data measured on a ratio scale, and I don't really understand what that means.

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