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Q.

Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is

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a

0

b

1

c

1.5

d

2.5

answer is A.

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Detailed Solution

Here, $(CV)_{1} = 50, (CV)_{2} = 60, {\bar{x}}_{1} = 30 and {\bar{x}}_{2} = 25$

$\begin{array}{l} ∴ (CV)_{1} = \frac{σ_{1}}{{\bar{x}}_{1}} \times 100 \\ \Rightarrow 50 = \frac{σ_{1}}{30} \times 100 \\ ∴ σ_{1} = \frac{30 \times 50}{100} = 15 \\ and {CV}_{2} = \frac{σ_{2}}{{\bar{x}}_{2}} \times 100 \\ \Rightarrow 60 = \frac{σ_{2}}{25} \times 100 \\ ∴ σ_{2} = \frac{60 \times 25}{100} = 15 \\ Now, σ_{1} - σ_{2} = 15 - 15 = 0 \end{array}$

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Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is