Question

Which one of the following is a relative measure of dispersion?

• A. Range
• B. Mean Absolute Deviation about Mean
• C. Coefficient of Variation
• D. Quartile Deviation

Hint:

Coefficient of Variation is useful for comparing variability between datasets having different units or different means.

Answer 1

The Correct Option is C

Step 1: Know the two families.
Spread can be shown two ways. An absolute measure carries the same unit as the data, like rupees. A relative measure is just a ratio, so it has no unit.

Step 2: Look for a unit in each option.
Range, mean absolute deviation and quartile deviation all carry the same unit as the data. So they are absolute measures.

Step 3: Check the coefficient of variation.
It is defined as
\[ CV=\frac{\sigma}{\bar{x}}\times100 \]
Here $\sigma$ and $\bar{x}$ have the same unit, so the unit cancels and only a pure number is left.

Step 4: Conclude.
Being unit free, the coefficient of variation is the relative measure.
\[ \boxed{\text{Coefficient of Variation}} \]