CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
A data set of monthly returns for a small-cap fund contains a few extremely large positive outliers. Compared with the arithmetic mean, the median of this data set is most likely:
The median is most likely lower than the mean. Extreme positive outliers pull the arithmetic mean upward because it uses every value's size, while the median depends only on the middle rank and resists the influence of outliers, as in a positively skewed distribution.
- Ahigher, because outliers pull the median upward
- Blower, because the mean is pulled upward by the outliersCorrect
- Cequal, because both measures use every observation in the same way
Explanation
Large positive outliers raise the arithmetic mean because it uses every value's magnitude. The median depends only on rank position and is resistant to outliers, so it is lower than the mean in a positively skewed set.
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