Statistics Measures Matching

The question requires matching statistical measures of dispersion from List I with their correct definitions from List II.

Step 1: Analyze Coefficient of Variation (a)

Coefficient of Variation measures the relative variability by expressing the standard deviation as a percentage of the mean. The definition matching this concept is (iii) Variation of the distribution adjusted with mean in percentage. Mathematically, $CV = \frac{\sigma}{\mu} \times 100$.

Step 2: Analyze Standard Deviation (b)

Standard deviation ($\sigma$) is a fundamental measure of dispersion, calculated as the square root of the variance. The definition matching this is (i) Square root of the average of the squared deviation measured from mean. Mathematically, $\sigma = \sqrt{\frac{\sum(x_i - \mu)^2}{N}}$.

Step 3: Analyze Mean Deviation (c)

Mean Deviation is the average of the absolute differences between each data point and a measure of central tendency (mean or median). Definition (iv) Average of the absolute deviation of scores from a measure of central tendency correctly describes this measure.

Step 4: Analyze Quartile Deviation (d)

Quartile Deviation ($QD$), also known as semi-interquartile range, measures dispersion around the median. It is half the difference between the first ($Q_1$) and third ($Q_3$) quartiles ($QD = \frac{Q_3 - Q_1}{2}$). Definition (ii) Absolute measure of dispersion around median fits this concept.

Step 5: Final Matching

Based on the analysis, the correct matching is:

This corresponds to the option a-(iii), b-(i), c-(iv), d-(ii).