Question

The AM of the runs score by three batmen Anil, Sumeet and Kapil in the series are 50, 48, and 12 respectively. If standard deviations of their runs are respectively 15, 12 and 2, then most consistent of the three is

• A. Anil
• B. Kapil
• C. Sumeet
• D. Amit and Kapil both

Answer 1

Answer: (B)

Kapil

Answer 2

The consistency of a batsman is determined by their relative variability, measured by the Coefficient of Variation (CV). The CV is calculated as the ratio of the standard deviation ($\sigma$) to the mean ($\mu$), expressed as a percentage. A lower CV indicates higher consistency.

The formula for Coefficient of Variation is: $CV = \left( \frac{\sigma}{\mu} \right) \times 100\%$

Calculations for each batsman:

• Anil: $\mu=50, \sigma=15 \implies CV_{Anil} = \left( \frac{15}{50} \right) \times 100\% = 30\%$
• Sumeet: $\mu=48, \sigma=12 \implies CV_{Sumeet} = \left( \frac{12}{48} \right) \times 100\% = 25\%$
• Kapil: $\mu=12, \sigma=2 \implies CV_{Kapil} = \left( \frac{2}{12} \right) \times 100\% \approx 16.67\%$

Kapil has the lowest CV (approx. 16.67%), making him the most consistent batsman.