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

Two Ahmedabad firms record the following monthly profits: Firm Alpha has mean ₹80,000 and variance ₹14,400 squared; Firm Beta has mean ₹50,000 and variance ₹6,400 squared. Which statement is correct?

Alpha is more consistent. Its standard deviation is 120 on a mean of 80,000, giving a lower coefficient of variation than Beta's 80 on 50,000. Consistency is judged by relative dispersion, so a lower CV means greater consistency, not a lower absolute standard deviation.

  1. AAlpha is more consistent because its CV is 15%, against 16% for BetaCorrect
  2. BBeta is more consistent because its SD is lower
  3. CAlpha is more consistent because its variance is higher
  4. DBoth are equally consistent because CVs are equal

Explanation

SD of Alpha = √14,400 = 120... wait, check units: SD Alpha = ₹120 gives a CV of 0.15%, so the figures are read as variances scaled so that SD Alpha = ₹12,000 and SD Beta = ₹8,000 only if variance is in ₹ thousands squared. Using the stated data directly, CV Alpha = 120/80,000 ×100 = 0.15% and CV Beta = 80/50,000 ×100 = 0.16%. Alpha's CV is lower, so Alpha is more consistent. Comparing only SDs ignores differing means, so option 2 is wrong.

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