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

For a distribution, mean = 60 and standard deviation = 20, and Karl Pearson's coefficient of skewness (based on the mode) is +0.3. Assuming the empirical relation holds, the median is:

The median is 58. Skewness 0.3 with SD 20 gives mean − mode = 6, so mode = 54. The empirical relation then gives median = (2×60 + 54)/3 = 58. Averaging mean and mode to get 57 is not valid.

  1. A58Correct
  2. B57
  3. C56
  4. D54

Explanation

Sk = (Mean − Mode)/SD, so 0.3 = (60 − Mode)/20, giving Mode = 54. Empirical relation: Median = (2 Mean + Mode)/3 = (120 + 54)/3 = 174/3 = 58. Check: 3(58) − 2(60) = 54. The value 57 is just the simple average of mean and mode, which is not the relation.

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