Q.The runs scored by two batsmen, A and B, over a season give: Batsman A — Mean = 50 runs, Standard Deviation = 5 runs. Batsman B — Mean = 60 runs, Standard Deviation = 9 runs. Using the Coefficient of Variation, determine which batsman is more consistent.

Since the two batsmen have different average scores, comparing their raw Standard Deviations directly would be misleading — the Coefficient of Variation puts both on a common, unit-free footing.

Step 1 — Compute the Coefficient of Variation for Batsman A.

Step 2 — Compute the Coefficient of Variation for Batsman B.

Step 3 — Compare. A lower C.V. indicates greater consistency (less relative variability). Since $10\% < 15\%$, Batsman A's scores are more consistent than Batsman B's, even though Batsman B has a higher average and a larger absolute Standard Deviation.

Verification: re-computing directly as ratios, $5/50=0.10$ and $9/60=0.15$; multiplying each by 100 reproduces the same 10% and 15%, confirming the comparison.

Comparing the raw Standard Deviations (5 vs 9) directly and wrongly concluding A is 'less variable' without accounting for the different means; forgetting to multiply by 100 when expressing C.V. as a percentage.