If a dataset contains an outlier, which measure of central tendency is least affected by that outlier?

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Multiple Choice

If a dataset contains an outlier, which measure of central tendency is least affected by that outlier?

The central idea here is how different measures of center respond to extreme values. The median is the best at staying close to the true center when an outlier appears because it depends on the order of the data, not on how large each value is. When you sort the data, the median is simply the middle value (or the average of the two middle values). An outlier sits at one end and doesn’t pull the middle position far out of line in most cases, so the central value stays near the cluster of typical data. In contrast, the mean uses every value in the set, so an extreme value drags it toward itself. That makes the mean a poor indicator of the dataset’s center when outliers are present. The mode reflects the most frequent value; an outlier usually won’t change which value occurs most often, though it can in unusual cases. The range measures spread, not center, and it swings a lot if an outlier is far from the rest. For example, data set 1, 2, 3, 4, 5 has a median of 3 and a mean of 3. If you add an outlier 100, the median becomes 3.5 (the average of the two middle values in the now-even-sized list), while the mean becomes about 19.2. This illustrates why the median is the least affected by an outlier.

The central idea here is how different measures of center respond to extreme values. The median is the best at staying close to the true center when an outlier appears because it depends on the order of the data, not on how large each value is. When you sort the data, the median is simply the middle value (or the average of the two middle values). An outlier sits at one end and doesn’t pull the middle position far out of line in most cases, so the central value stays near the cluster of typical data.

In contrast, the mean uses every value in the set, so an extreme value drags it toward itself. That makes the mean a poor indicator of the dataset’s center when outliers are present. The mode reflects the most frequent value; an outlier usually won’t change which value occurs most often, though it can in unusual cases. The range measures spread, not center, and it swings a lot if an outlier is far from the rest.

For example, data set 1, 2, 3, 4, 5 has a median of 3 and a mean of 3. If you add an outlier 100, the median becomes 3.5 (the average of the two middle values in the now-even-sized list), while the mean becomes about 19.2. This illustrates why the median is the least affected by an outlier.

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