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Questions  >>  CBSE XI  >>  Math  >>  Statistics
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Q)

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} $

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A)
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.
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