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CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion

The coefficient of variation of Dataset A is 15% with mean 200, and the coefficient of variation of Dataset B is 12% with mean 150. Which dataset shows greater absolute variability?

Dataset A has greater absolute variability because its standard deviation is 30 kg, compared to 18 for Dataset B. Although CV is lower, SD is the measure of absolute variability, not relative variability.

  1. ADataset A, because its standard deviation is 30 compared to 18 for Dataset BCorrect
  2. BDataset B, because its coefficient of variation is lower
  3. CDataset A, because it has a larger mean
  4. DDataset B, because its standard deviation is 15 compared to 12 for Dataset A

Explanation

Coefficient of variation = (Standard Deviation ÷ Mean) × 100. For A: SD = (15 ÷ 100) × 200 = 30. For B: SD = (12 ÷ 100) × 150 = 18. Absolute variability is measured by standard deviation, not CV. Dataset A has higher SD despite lower CV, showing greater scatter. Option 3 incorrectly assumes mean size determines variability.

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