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

Solution:

Given, coefficient of variation, C₂ = 50 and coefficient of variation, C₂= 60 ${\bar{x}}_{1} = 30 and {\bar{x}}_{2} = 25$

$\begin{array}{ll} ∵ & C = \frac{σ}{\bar{x}} \times 100 \\ ∴ & 50 = \frac{σ_{1}}{30} \times 100 \\ \Rightarrow & σ_{1} = 15 and 60 = \frac{σ_{2}}{25} \times 100 \\ \Rightarrow & σ_{2} = 15 \\ ∴ & Required difference, σ_{1} - σ_{2} = 15 - 15 = 0 \end{array}$

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