Which measure is least affected by outliers?

Which measure is least affected by outliers?

• A. The median.
• B. The mean.
• C. The mode.
• D. The range.

Answer: (A)

Outliers distort measures that depend on every data point. The mean takes all values into account, so an extreme value pulls it toward that outlier, changing the central location of the data. The range uses only the smallest and largest values, so an outlier easily makes the range much larger. The mode depends on which value occurs most often; while an outlier could potentially become the mode in rare cases, it doesn’t reliably reflect the data’s typical center. The median, however, is determined by the middle value in the ordered list, so a single extreme value changes only the order slightly and typically leaves the central point unchanged, especially in larger data sets. For example, with data like 1, 2, 3, 4, 1000, the median is 3, while the mean is 210 and the range is 999, illustrating how the outlier heavily distorts the mean and range but barely moves the median.

Outliers distort measures that depend on every data point. The mean takes all values into account, so an extreme value pulls it toward that outlier, changing the central location of the data. The range uses only the smallest and largest values, so an outlier easily makes the range much larger. The mode depends on which value occurs most often; while an outlier could potentially become the mode in rare cases, it doesn’t reliably reflect the data’s typical center. The median, however, is determined by the middle value in the ordered list, so a single extreme value changes only the order slightly and typically leaves the central point unchanged, especially in larger data sets.

For example, with data like 1, 2, 3, 4, 1000, the median is 3, while the mean is 210 and the range is 999, illustrating how the outlier heavily distorts the mean and range but barely moves the median.