Answer to Question #97004 in Statistics and Probability for mani

Question

(b) The runs scored by 3 batsmen are 50, 48 and 12. Arithmetic mean’s respectively. The SD of their runs is 15, 12 and 2 respectively. Who is the most consistent of the three batsmen? If the one of these three is to be selected who is to be selected?

Answer 1

Find the coefficient of variation

$$C.V={SD \over mean}\times100$$

$$C.V\ \text{of\ I}={15 \over 50}\times100=30$$

$$C.V\ \text{of\ II}={12 \over 48}\times100=25$$

$$C.V\ \text{of\ III}={2 \over 12}\times100\approx16.67$$

C.V for III is the least. Hence the batsman III is more consistent.

Evaluation criteria

Less C.V indicates more constant player (player III).

Player I has the highest runs score 50.

Arithmetic mean of batsman I is greater than that of batsman II.

But batsman II is a more consistent than batsman I (C.V of II =25%<30% = C.V of I).

I think that batsman I is to be selected.