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

Two Chennai investment schemes have the following annual returns. Scheme X: mean 12%, SD 3%. Scheme Y: mean 20%, SD 4%. Which choice correctly identifies the more variable scheme in relative terms and the CVs?

Scheme X is relatively more variable. Its coefficient of variation is 3 divided by 12 times 100, which is 25 percent, while Scheme Y's is 4 divided by 20 times 100, which is 20 percent. A higher CV means greater relative dispersion.

  1. AX is more variable; CV of X = 25%, CV of Y = 20%Correct
  2. BY is more variable; CV of X = 25%, CV of Y = 20%
  3. CX is more variable; CV of X = 4%, CV of Y = 5%
  4. DY is more variable because its SD is larger; CV of Y = 5%

Explanation

CV of X = 3/12 × 100 = 25%. CV of Y = 4/20 × 100 = 20%. X has the higher CV, so it is more variable relatively. Option 2 correctly computes CVs but picks the wrong scheme, and option 4 relies on absolute SD.

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