Which statistic is most resistant to outliers?

Which statistic is most resistant to outliers?

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

Answer: (D)

When extreme values appear in a data set, we want a statistic that stays close to the center despite those outliers. The median does this best because it is the middle value once the numbers are ordered, so one very large or very small value doesn’t pull it in that direction. For example, with data 1, 2, 3, 4, 1000, the median is 3, while the mean becomes 210 and the range becomes 999, both dramatically affected by the 1000. The mode might remain the same in simple cases, but it isn’t a reliable summary of center for skewed data or when there are many or no repeats. So the median is the most resistant to outliers.

When extreme values appear in a data set, we want a statistic that stays close to the center despite those outliers. The median does this best because it is the middle value once the numbers are ordered, so one very large or very small value doesn’t pull it in that direction. For example, with data 1, 2, 3, 4, 1000, the median is 3, while the mean becomes 210 and the range becomes 999, both dramatically affected by the 1000. The mode might remain the same in simple cases, but it isn’t a reliable summary of center for skewed data or when there are many or no repeats. So the median is the most resistant to outliers.