Coefficient of Variation

Standard deviation is measured in the same unit as the data (kg, cm, ₹, months, etc.), so it cannot be used, by itself, to compare the variability of two data sets that are in different units, or that have very different means even within the same unit. The coefficient of variation (C.V.) removes this limitation by expressing the standard deviation as a percentage of the mean: $\text{C.V.} = 100 \times \frac{\sigma}{\bar{x}}$ Because C.V. is a pure, unit-free percentage, it lets two or more distributions be compared for relative variability directly. A distribution with a smaller C.V. is said to be more homogeneous or compact, and more consistent; a distribution with a larger C.V. is said to be more heterogeneous, i.e. more variable.

Worked Example (Ex.1): Three batsmen Varad, Viraj and Akhilesh have mean runs $\bar{x}_1=50,\bar{x}_2=52,\bar{x}_3=21$ and standard deviations $\sigma_1=11,\sigma_2=16,\sigma_3=5$. $\text{C.V.}_1 = 100\times11/50=22$, $\text{C.V.}_2=100\times16/52\approx30.77$, $\text{C.V.}_3=100\times5/21\approx23.81$. Since Varad's C.V. is the smallest, he is the most consistent player. When deciding whom to select: by consistency, Varad (smallest C.V.) should be chosen; but by expected score, the player with the highest mean, Viraj, would be chosen instead — the two criteria can point to different answers. …