If a dataset has outliers, which measure is least affected by them?

If a dataset has outliers, which measure is least affected by them?

• A. The median.
• B. The mean.
• C. The mode.
• D. The standard deviation.

Answer: (A)

When there are extreme values, you want a measure that isn’t pulled toward those extremes. The middle value of the data when they’re ordered does just that: it depends on rank, not on how far away the outliers are. So the median stays close to the center of the data even if one or a few observations are wildly large or small. In contrast, the mean uses every value and can be dragged toward an outlier, and the standard deviation depends on how far each value is from the mean, which also amplifies the effect of outliers. The mode is about the most frequent value and can be unstable or uninformative with continuous data, especially if outliers don’t create a true peak in frequency. So the median is the least affected by outliers.

When there are extreme values, you want a measure that isn’t pulled toward those extremes. The middle value of the data when they’re ordered does just that: it depends on rank, not on how far away the outliers are. So the median stays close to the center of the data even if one or a few observations are wildly large or small. In contrast, the mean uses every value and can be dragged toward an outlier, and the standard deviation depends on how far each value is from the mean, which also amplifies the effect of outliers. The mode is about the most frequent value and can be unstable or uninformative with continuous data, especially if outliers don’t create a true peak in frequency. So the median is the least affected by outliers.