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

A set of 10 observations has mean 50 and standard deviation 10. Every observation is increased by 50. What happens to the coefficient of variation?

The coefficient of variation falls from 20% to 10%. Adding a constant changes the mean to 100 but does not change the standard deviation of 10, so the new CV is 10/100 × 100 = 10%.

  1. AIt remains 20%
  2. BIt falls from 20% to 10%Correct
  3. CIt rises from 10% to 20%
  4. DIt falls from 20% to 15%

Explanation

Original CV = 10/50 × 100 = 20%. Adding a constant of 50 shifts the mean to 100 but leaves SD at 10. New CV = 10/100 × 100 = 10%. Option 1 wrongly assumes CV is unaffected by a change of origin.

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