Question

A batsman is to be selected for a cricket team.The choice is between X and Y on the basis of their scores in five previous scores which are

$\begin{array}{cccccc}X& 25& 85& 40& 80& 120\\ Y& 50& 70& 65& 45& 80\end{array}$

Which batsman should be selected if we want,

(i) a higher run getter, or

(ii) a more reliable batsman in the team?

Answer 1

Batsman X

$\begin{array}{ccc}X& X-\overline{X}=x& x^2\\ & X-70& \\ 25& -45& 2025\\ 85& +15& 225\\ 40& -30& 900\\ 80& 10& 100\\ 120& 50& 2500\\ \sum X=350& & \sum X^2=5750\end{array}$

$\overline{X}=\frac{\sum x}{N}=\frac{350}{5}=70$

$\sigma =\sqrt{\frac{\sum x^2}{N}}=\sqrt{\frac{5750}{5}}=33.91$

$CV=\frac{\sigma }{\overline{X}}\times 100=48.44$

Batsman Y

$\begin{array}{ccc}y& Y-\overline{Y}=y& y^2\\ 50& -12& 144\\ 70& 8& 64\\ 65& 3& 9\\ 45& -17& 289\\ 80& 18& 324\\ \sum Y=310& & \sum y^2=830\end{array}$

$\overline{Y}=\frac{\sum y}{N}=\frac{310}{5}=62$

$\sigma =\sqrt{\frac{\sum y^2}{N}}=\sqrt{\frac{830}{5}}=12.88$

$CV=\frac{\sigma }{\overline{X}}\times 100=20.78$

(i) Average of Batsman X is higher than that of Batsman Y, so he should be selected if we want a high scorer.

(ii) The Batsman Y is more reliable than Batsman X. This is because the coefficient of variation of Batsman X is higher than that of Batsman Y.