$\bar{x}$ and $\bar{y}$ are the arithmetic means of the runs of two batsmen A and B in 10 innings…
$\bar{x}$ 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
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 higher runs $\Rightarrow \Sigma x_{i A}\gt\Sigma x_{i B}$
$\Rightarrow \bar{x}\gt\bar{y} \Rightarrow \frac{\bar{x}}{\bar{y}}\gt1$