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: Understand measures of dispersion.
Measures of dispersion describe the spread or variability of data. They are broadly classified into:
Absolute measures and
\[ \text{Relative measures}. \]

Step 2: Recall absolute measures of dispersion.
Absolute measures are expressed in the same units as the data. Examples include:
Range, Mean Deviation, Quartile Deviation, Standard Deviation
Thus:
Range is an absolute measure.
Mean Absolute Deviation is an absolute measure.
Quartile Deviation is also an absolute measure.

Step 3: Recall relative measures of dispersion.
Relative measures are unit-free ratios used for comparison between datasets.
The coefficient of variation is defined as
\[ CV=\frac{\sigma}{\bar{x}}\times100 \] where
\[ \sigma=\text{standard deviation} \] and
\[ \bar{x}=\text{mean}. \]
Since it is dimensionless, it is a relative measure of dispersion.

Step 4: Analyze the options.

(A) Range: Absolute measure. Incorrect.

(B) Mean Absolute Deviation about Mean: Absolute measure. Incorrect.

(C) Coefficient of Variation: Relative measure. Correct.

(D) Quartile Deviation: Absolute measure. Incorrect.

Step 5: Final conclusion.
Therefore, the relative measure of dispersion is
\[ \boxed{\text{Coefficient of Variation}} \]