Which of the following measures is not affected by extreme values in the data?

Question

BlackTom AI · Accepted Answer

Let's evaluate each option in light of how extreme values influence common statistical measures.
Option 1: The mean. The mean is sensitive to extreme values because it takes into account every data point; a very large or very small value can pull the average toward itself, changing the overall mean.
Option 2: The median. The median is the middle value (or the average of the two middle values) when data are ordered. Extreme values at either end do not affect the central position as long as they do not change the order or the central rank significantly; in many distributions, especially with outliers, the median remains stable, showing robustness to outliers.
Option 3: The standard deviation. Standard deviation measures dispersion around the mean and is highly influenced by outliers, since extreme values increase the squared deviations from the mean, inflating the measure of spread.
Option 4: The range. The range is defined as the difference between the maximum and minimum values; extreme values directly expand this gap, so the range is affected by outliers.
Therefore, among these measures, the one that typically remains unaffected by extreme values is the median, while the mean, standard deviation, and range are influenced by outliers or extremes.

Which of the following measures is not affected by extreme values in the data? 单项选择题

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