Which statistic is most affected by outliers?

Which statistic is most affected by outliers?

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

Answer: (C)

Outliers pull on a statistic that uses every value to compute its position. The mean sums all numbers and divides by how many there are, so an extreme value adds a large amount to the total and drags the average toward it. The median, being the central value, resists such a shift because only the ordering matters, and a single outlier doesn't change the middle point much in a reasonably sized data set. The mode depends on how often values occur, so an outlier that doesn’t repeat won’t change it. The range depends only on the smallest and largest values, so it can jump if the outlier becomes the new min or max, but it doesn’t reflect the typical value of the data. Because the mean uses every observation, it is the most affected by outliers.

Outliers pull on a statistic that uses every value to compute its position. The mean sums all numbers and divides by how many there are, so an extreme value adds a large amount to the total and drags the average toward it. The median, being the central value, resists such a shift because only the ordering matters, and a single outlier doesn't change the middle point much in a reasonably sized data set. The mode depends on how often values occur, so an outlier that doesn’t repeat won’t change it. The range depends only on the smallest and largest values, so it can jump if the outlier becomes the new min or max, but it doesn’t reflect the typical value of the data. Because the mean uses every observation, it is the most affected by outliers.