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

For a moderately skewed distribution, the arithmetic mean is 42 and the median is 40. Using the empirical relationship among the three averages, the approximate mode is:

The approximate mode is 36. The empirical relation says mode equals three times the median minus two times the mean, so 3×40 − 2×42 = 36. Reversing mean and median gives 46, which is incorrect.

  1. A36Correct
  2. B46
  3. C41
  4. D38

Explanation

Empirical relation: Mode = 3 Median − 2 Mean = 3(40) − 2(42) = 120 − 84 = 36. The value 46 comes from swapping the roles, 3(42) − 2(40), which is a wrong use of the formula.

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