Question

Coefficient of variation of two distribution are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means?

• A. 35, 22.85
• B. 22.85, 35.28
• C. 36, 22.85
• D. 35.28, 23.85

Answer 1

Answer: (A)

35, 22.85

Answer 2

${C.V. (1st\, distribution) = 60, \sigma_{1} = 21}$ ${C.V. (2nd \, distribution) = 70, \sigma_{2} = 16}$ Let $\bar{x_1}$ and $\bar{x_2}$ be the means of 1st and 2nd distribution, respectively, Then ${C.V. (1st\, distribution) = \frac{\sigma_{1}}{\bar{x_{1}}} \times 100 }$ $\therefore \:\: 60 = \frac{21}{\bar{x_{1}}} \times 100$ or $\bar{x_1} = \frac{21}{60} \times 100 = 35$ and ${C.V. (2nd \,distribution) = \frac{\sigma_{2}}{\bar{x_{2}}} \times 100}$ i.e., $70 = \frac{16}{\bar{x_2}} \times 100$ or, $\bar{x_2} = \frac{16}{70} \times 100 = 22.85$