Q.The monthly returns (in %) of two mutual funds over the past year have the following mean and standard deviation: Fund A: mean $=12\%$, SD $=3\%$; Fund B: mean $=15\%$, SD $=6\%$. Which fund's returns are more consistent (less variable)?

$CV=\dfrac{\sigma}{\bar{x}}\times100=\dfrac{3}{10}\times100=30\%$.

The coefficient of variation expresses the standard deviation as a percentage of the mean: …

$\text{CV}=\dfrac{\sigma}{\bar{x}}\times 100=\dfrac{5}{20}\times 100=25\%$.

Step 1 — the coefficient of variation is the relative measure

$\text{CV}=\dfrac{\sigma}{\bar{x}}\times 100$

…

$C.V.=\dfrac{\sigma}{\bar{x}}\times100=\dfrac{15}{75}\times100=20\%$.

The coefficient of variation measures relative dispersion:

$C.V.=\frac{\sigma}{\bar{x}}\times100.$

…

A relative measure is dimensionless; ₹10 has units ⇒ not relative.

Relative measures of dispersion (coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, coefficient of variation) are formed by dividing one quantity in the same units by another, so the units cancel and the result is a pure number such as $0.22$, $0.33$ or $0.44$.

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The blank is Variation.

The coefficient of variation (C.V.) is a relative (unit-free) measure of dispersion defined as

$C.V. = \frac{\sigma}{\bar{x}} \times 100,$ …