Browse Questions

Coefficient of variance of two distributions are 50 and 60 , and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is:

$\begin{array}{1 1}(A)\; 0 \\(B)\;1 \\(C)\;1.5 \\(D)\;2.5 \end{array}$

Toolbox:
• The formula used to solve this problem are coefficient of variation $=\large\frac{ \sigma}{\bar x} $$\times 100 Given coefficient of variation 1=50 Coefficient of variation 2=60 Arithmetic mean 1=30 Arithmetic mean 2= 25 CV1= \large\frac{\sigma_1}{\bar {x} _1}$$\times 100$
$=> 50 =\large\frac{\sigma 1}{30} $$\times 100 \sigma_1= \large\frac{50 \times 30}{100} \qquad= 15 CV2= \large\frac{\sigma_2}{\bar {x} _2}$$\times 100$
$60= \large\frac{\sigma_2}{25}$$\times 2 \sigma _2 =\large\frac{60 \times 25}{100} \qquad= \large\frac{150}{10}$$=15$
The difference b/w $\sigma_1$ and $\sigma_2$ is zero.
Hence A is the correct answer.