Q106 / 180 · KCET 2016 · Mathematics

The coefficient of variation of two distributions are \( 60 \) and \( 70 \). The standard deviation are \( 21 \)
and \( 16 \) respectively, then their mean is

  • A
    35
  • B
    \( 23 \)
  • Correct answer
    C
    \( 28.25 \)
  • D
    \( 22.85 \)

Solution

Given that, $C V_{x}=60 \rightarrow(1)$ We know that, $C V=\frac{\sigma}{\chi} \times 100$ So, $\frac{21}{x} \times 100=60$ $\Rightarrow \bar{\chi}=\frac{2100}{60}=35$ Again, $C V_{y}=70$ $\frac{16}{y} \times 100=70$ $\Rightarrow \bar{y}=\frac{1600}{70}=22.86$ So, mean of two means are $\frac{\bar{x}+\bar{y}}{2}$ $\frac{35+22.86}{2}=28.925$

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

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