Which measure of central tendency is most affected by extreme values (outliers)?

Question

Accepted Answer

The mean. The mean (arithmetic average) is most affected by extreme values because every data point contributes to its calculation. A single very large or very small value can pull the mean significantly in its direction. For example, in the set {10, 11, 12, 13, 100}, the mean is 29.2, which is much higher than most of the values due to the outlier 100.

The median is resistant to outliers because it depends only on the position of values, not their magnitude. In the same example, the median is 12 regardless of whether the largest value is 14 or 100. The mode depends on which value occurs most frequently and is unaffected by extreme values that occur only once. Claiming all three are equally affected ignores the mathematical properties that make the mean uniquely sensitive to extreme values.

Understanding the properties of mean, median, and mode is essential for the DSST exam. Students should know when each measure is most appropriate: the mean for symmetric distributions without outliers, the median for skewed distributions or data with outliers, and the mode for categorical data or when identifying the most common value.

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