Which statistic is most robust to extreme outliers?

• A. Mean
• B. Median
• C. Mode
• D. Range

Answer: (B)

The concept here is how a statistic withstands extreme values, or its robustness. The middle value in an ordered data set, the median, is determined by position rather than the actual magnitudes of extreme numbers. So when an extreme outlier appears, it hardly moves the middle position, unless enough outliers shift the central arrangement.

For example, with data like 1, 2, 3, 4, 5, 1000, the median is near the center of the bulk (the average of the two middle values), while the mean is pulled up by the single large outlier. The range also inflates because it depends on the smallest and largest values. The mode, being the most frequent value, isn’t driven by an outlier in the same way and isn’t a reliable reflection of center for skewed data.

So the median is the best choice for robustness to extreme outliers.