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CMA Intermediate · Financial Management and Business Data Analytics · Data Analysis and Modelling

A distribution of loan amounts is strongly right-skewed because a few very large loans exist. Which ordering of the three averages is most likely?

The likely ordering is Mode < Median < Mean. In a right-skewed distribution, a few very large loans drag the mean upward most, the median sits between, and the mode remains at the peak of the distribution on the lower side.

  1. AMean < Median < Mode
  2. BMode < Median < MeanCorrect
  3. CMedian < Mode < Mean
  4. DMean = Median = Mode

Explanation

In a right-skewed distribution, the long tail of large values pulls the mean upward the most, the median lies in between and the mode sits at the peak on the lower side. Hence Mode < Median < Mean. The reverse ordering applies to left skew.

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