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CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns

In a box-and-whisker plot of annual returns, the box spans 4% to 12%, the median is 6%, and the upper whisker extends to the largest observation within 1.5 times the interquartile range above the third quartile. A single point at 30% is plotted separately. The 30% observation is most likely:

The 30% observation is an outlier beyond the upper fence of 24%. The IQR is 8, and 12 plus 1.5 times 8 equals 24. Anything above that is plotted separately from the whisker.

  1. Aan outlier beyond the upper fence of 24%Correct
  2. Bwithin the whisker because it is below 36%
  3. Cthe third quartile of the data

Explanation

IQR = 12 - 4 = 8. The upper fence is 12 + 1.5 × 8 = 24%. A value of 30% exceeds 24%, so it is plotted as an outlier. The 36% figure wrongly adds 3 × IQR. The third quartile is 12%. The median of 6% sits below the box midpoint, indicating positive skew.

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