Lesson 1 of 7 · 14 min
Mean, median, mode and outliers
A measure of central tendency condenses a return series into one number for where it is centred; which measure you trust depends on outliers and on the type of data.
In short
- The arithmetic mean weights every observation equally. It is the standard summary, but one extreme value can pull it far off.
- The median is the middle of the sorted data. It ignores how extreme the extremes are, so outliers do not move it.
- The mode is the most frequent value. It is the only centre measure for categorical data, and for continuous returns you report the modal interval.
- Outliers can be kept, deleted (trimmed mean) or replaced by boundary values (winsorized mean).
- If the trimmed or winsorized mean is above the plain mean, the extreme values were mostly large losses.
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