CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
The yearly sales of a shop grew by factors of 2, 4 and 8 in three successive years over the previous year. What is the geometric mean of these growth factors?
The geometric mean is 4. The product of the three growth factors is 2 × 4 × 8 = 64, and its cube root is 4. The arithmetic mean 4.67 is unsuitable because growth factors compound by multiplication rather than addition.
- A4Correct
- B4.67
- C3.5
- D5
Explanation
GM = (2 × 4 × 8)^(1/3) = 64^(1/3) = 4. The arithmetic mean (14/3 = 4.67) is wrong because growth factors compound multiplicatively, so it overstates the average growth.
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