Q.Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is
(A) 0
(B) 1
(C) 1.5
(D) 2.5

Concept: Coefficient of variation (CV) is the ratio of standard deviation ($\sigma$) to the mean ($\bar{x}$), expressed as a percentage:

Step 1: For the first distribution: $CV_1 = 50$, $\bar{x}_1 = 30$

Step 2: For the second distribution: $CV_2 = 60$, $\bar{x}_2 = 25$ …

The coefficient of variation is a relative measure of dispersion — it tells you how large the standard deviation is compared to the mean. This is especially useful when comparing variability across datasets with different units or scales. Here, we are given the CV and the mean for two distributions, and we need the difference in their standard deviations.

The formula is straightforward:

Where $\sigma$ is the standard deviation and $\bar{x}$ is the arithmetic mean. Rearranging gives $\sigma = \frac{CV \times \bar{x}}{100}$.

Let’s apply it step by step.

1. First distribution: $CV_1 = 50$, $\bar{x}_1 = 30$

2. Second distribution: $CV_2 = 60$, $\bar{x}_2 = 25$

3. Difference: $\sigma_1 - \sigma_2 = 15 - 15 = 0$ …