Practice question · Sort into groups
You add one extreme outlier to a data set. Sort each statistic by how much that single outlier moves it.
Groups: Strongly affected by the outlier · Barely affected by the outlier
- The mode
- The standard deviation
- The median
- The range
- The mean
Hints
- Ask which statistics use every value's exact size (or the extremes) versus only position or frequency.
- Mean, range, and SD all feed on the actual magnitudes; median and mode depend on position and frequency.
Show the answer
Strongly affected by the outlier: The mean, The range, The standard deviation
Barely affected by the outlier: The median, The mode
Why
The mean, range, and standard deviation all incorporate the outlier's raw magnitude, so they shift strongly; the median (a position) and mode (a frequency) barely move. This robustness split is the whole reason we ever prefer the median.
Practise Descriptive Statistics
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