Q76 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics

Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are 6 and 2 respectively and $\sigma_{A^{\prime}} \sigma_B$ are their standard deviations, then

  • Correct answer
    A
    $\sigma_A=3 \sigma_B$
  • B
    $3 \sigma_A=\sigma_B$
  • C
    $\sigma_A=2 \sigma_B$
  • D
    $2 \sigma_A=\sigma_B$

Solution

Let $\bar{x}_A=\bar{x}_B=x$ $$ \begin{aligned} & \frac{\sigma_A}{\bar{x}_A} \times 100=6, \frac{\sigma_B}{\bar{x}_B} \times 100=2 \\ & \frac{\sigma_A}{x} \times 100=6, \frac{\sigma_B}{x} \times 100=2 \\ & \frac{\sigma_A \times 100}{6}=x, \frac{\sigma_B \times 100}{2}=x \\ \Rightarrow \quad & \frac{\sigma_A \times 100}{6}=\frac{\sigma_B \times 100}{2} \Rightarrow \sigma_A=3 \sigma_B \end{aligned} $$

Hence, the correct answer is option: 'A'.

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