Coefficient of Variation

Standard deviation is measured in the same unit as the original data — rupees, marks, kilograms — which makes it impossible to fairly compare the relative variability of two data sets recorded in different units (say, a factory's output in tonnes versus its revenue in lakhs of rupees), or even two series in the same unit but with very different average sizes (a standard deviation of ₹5 means something quite different for an average price of ₹20 than for an average price of ₹2,000).

The Coefficient of Variation (CV) solves this the same way every other coefficient in this chapter does — by expressing the absolute measure as a percentage of the mean, producing a dimensionless number directly comparable across series of any unit or scale:

A lower CV means more consistent (less variable) data relative to its own average; a higher CV means comparatively more spread out. This is exactly why CV is the standard tool for comparing the consistency of two things whose averages differ — the steadiness of returns from two investment options, the reliability of two machines' daily output, or the consistency of sales performance across two branches of a firm — a comparison a bare standard deviation cannot make fairly whenever the two things being compared have different average sizes. A series with the higher average is not automatically the more (or less) variable one until its CV is actually worked out; the chapter's worked examples deliberately include a case where the higher-average series turns out to be the less consistent one. …