CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
For a set of observations the mean is 40 and the coefficient of variation is 15%. If every observation is increased by 10, what is the new coefficient of variation?
The new coefficient of variation is 12%. The original SD is 15% of 40, which is 6. Adding 10 to every item does not change the SD but raises the mean to 50, so CV becomes 6/50 × 100 = 12%.
- A15%
- B12%Correct
- C18.75%
- D10%
Explanation
Original SD = 15% of 40 = 6. Adding a constant leaves SD unchanged at 6, while the mean becomes 50. New CV = 6/50 × 100 = 12%. Keeping 15% wrongly assumes CV is unaffected by a change in origin.
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