Question

The coefficient of variation of the two frequency distributions is 60% and 40% respectively. Both series have the same mean = 15. What is their standard deviation?

• A. \( \sigma_1 = 2 \) and \( \sigma_2 = 3 \)
• B. \( \sigma_1 = 9 \) and \( \sigma_2 = 6 \)
• C. \( \sigma_1 = 3 \) and \( \sigma_2 = 7 \)
• D. \( \sigma_1 = 16 \) and \( \sigma_2 = 6 \)

Hint:

To calculate the standard deviation from the coefficient of variation, simply multiply the CV by the mean and divide by 100.

Answer 1

The Correct Option is A

Step 1: The coefficient of variation (CV) is given by: \[ \text{CV} = \frac{\sigma}{\mu} \times 100 \] Where \( \sigma \) is the standard deviation and \( \mu \) is the mean. Since both distributions have the same mean of 15, we can write the equations for each distribution: For the first distribution: \[ 60 = \frac{\sigma_1}{15} \times 100 \quad \Rightarrow \quad \sigma_1 = \frac{60 \times 15}{100} = 9 \] For the second distribution: \[ 40 = \frac{\sigma_2}{15} \times 100 \quad \Rightarrow \quad \sigma_2 = \frac{40 \times 15}{100} = 6 \] Thus, the standard deviations for the two distributions are \( \sigma_1 = 9 \) and \( \sigma_2 = 6 \), corresponding to option (B).