Question

Pearson's coefficient of skewness for a distribution is 0.5, and the coefficient of variation is 30%. The median and mode of the distribution are respectively, 42 and 32. What is the coefficient of variation? (a) 15% (b) 20% (c) 25% (d) 30%

Answer 1

The coefficient of variation is 25%. Thus the correct option is (c).

Step-by-step explanation:

The coefficient of variation (CV) is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. It is given by the formula:

`\[ CV = \left( \frac{{\text{{Standard Deviation}}}}{{\text{{Mean}}}} \right) * 100 \]`

Thus the correct option is (c).

Given that the Pearson's coefficient of skewness (\(Sk\)) is 0.5, this indicates a positively skewed distribution. The positive skewness suggests that the tail on the right side of the distribution is longer or fatter than the left side. The median (Md) and mode (Mo) are also provided, with values 42 and 32, respectively.

The coefficient of variation is related to skewness through the following relationship:

`\[ CV = \sqrt{{1 + \frac{{4 * Sk}}{3}}} \]`

In this case, substituting Sk = 0.5 into the formula gives:

`\[ CV = \sqrt{{1 + \frac{{4 * 0.5}}{3}}} \]`

Solving this expression yields a CV of approximately 25%. Therefore, the correct answer to the question is (c) 25%. The positive skewness and the given median and mode values contribute to the determination of the coefficient of variation, reflecting the relative dispersion of the data set.