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

A series has a coefficient of variation of 25% and a standard deviation of 10. If every observation is increased by 10, what will the new coefficient of variation be?

The new coefficient of variation is 20%. The original mean is 40 (10 ÷ 0.25). Adding 10 to each value raises the mean to 50 but leaves the standard deviation at 10, so CV becomes 10 ÷ 50 × 100 = 20%.

  1. A25%
  2. B20%Correct
  3. C30%
  4. D12.5%

Explanation

Mean = SD/CV × 100 = 10/25 × 100 = 40. Adding 10 gives mean 50, while SD stays 10 since it is unaffected by change of origin. New CV = 10/50 × 100 = 20%. Keeping 25% wrongly assumes CV is unchanged by shifts.

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