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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 tests which are:
| X |
25 |
85 |
40 |
80 |
120 |
| Y |
50 |
70 |
65 |
45 |
80 |
Which batsman should be selected if we want,
(i) a higher run-getter, or
(ii) a more reliable batsman in the team?
Solution
Batsman X
| X |
`X - overlineX = x` |
x2 |
| 25 | -45 | 2025 |
| 85 | +15 | 225 |
| 40 | -30 | 900 |
| 80 | 10 | 100 |
| 120 | 50 | 2500 |
| ∑X = 350 | `sumx^2 = 5750` |
`overlineX = (sumX)/N = 350/5 = 70`
`sigma = sqrt((sumx^2)/N) = sqrt(5750/5)`
= 33.91
CV = `sigma/overlineX xx 100`
= `33.91/70 xx 100 = 48.44`
Batsman Y
| Y |
`Y - overlineY = y` |
y2 |
| 50 |
-12 |
144 |
| 70 |
8 |
64 |
| 65 |
3 |
9 |
| 45 |
-17 |
289 |
| 80 |
18 |
324 |
| ∑Y = 310 |
|
`sumy^2 = 830` |
`overlineY = (sumY)/N = 310/5 = 62`
`sigma = sqrt((sumy^2)/N) = sqrt(830/5)`
= 12.88
CV = `sigma/overlineY xx 100`
= `12.88/62 xx 100`
= 20.78
(i) Average of Batsman X is higher than that of Batsman Y, so he should be selected if we want to score a higher run.
(ii) The Batsman X is more reliable than Batsman Y. This is because the coefficient of variation of Batsman X is higher than that of Batsman Y.
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