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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion

In a moderately asymmetrical series, the median is 27 and the mode is 24. Using the empirical relation, the arithmetic mean is approximately:

The mean is about 28.5. From the empirical relation, mode = 3×median − 2×mean, so 24 = 81 − 2×mean, which gives mean = 28.5. Swapping the median and mode values in the formula would wrongly give 22.5.

  1. A28.5Correct
  2. B22.5
  3. C25.5
  4. D30

Explanation

Mode = 3 Median − 2 Mean gives 24 = 81 − 2 Mean, so Mean = 57/2 = 28.5. Check: 3(27) − 2(28.5) = 81 − 57 = 24. The value 22.5 results from putting mode and median in each other's place.

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