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AP EAMCET · Maths · Statistics

\(\bar{x}\) and \(\bar{y}\) are the arithmetic means of the runs of two batsmen A and B in 10 innings respectively and \(\sigma_{\mathrm{A}}, \sigma_{\mathrm{B}}\) are the standard deviations of their runs in them. If batsman A is more consistent than B , then he is also a higher run scorer only when

  1. A \(0 \lt \frac{\sigma_A}{\sigma_B} \lt \frac{\bar{x}}{\bar{y}} ; \frac{\bar{x}}{\bar{y}}\gt1\)
  2. B \(\frac{\bar{x}}{\bar{y}}\gt\frac{\sigma_A}{\sigma_B}\gt1\)
  3. C \(\frac{\bar{x}}{\bar{y}} \lt \frac{\sigma_A}{\sigma_B}\gt1\)
  4. D \(\frac{\bar{x}}{\bar{y}}\gt1 ; 1 \leq \frac{\bar{x}}{\bar{y}} \lt \frac{\sigma_A}{\sigma_B}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(0 \lt \frac{\sigma_A}{\sigma_B} \lt \frac{\bar{x}}{\bar{y}} ; \frac{\bar{x}}{\bar{y}}\gt1\)

Step-by-step Solution

Detailed explanation

Batsman A is more consistent than B \(\Rightarrow\) Coefficient of variation of \(\mathrm{A} \lt \) coefficient of variation B \(\Rightarrow \frac{\sigma_A}{\bar{x}} \lt \frac{\sigma_B}{\bar{y}} \Rightarrow 0 \lt \frac{\sigma_A}{\sigma_B} \lt \frac{\bar{x}}{\bar{y}}\) A scores…