Why is the $\mathrm{median}$ considered a resistant measure of center in statistics?

• A. Because the $\mathrm{median}$ uses all data values in its calculation
• B. Because the $\mathrm{median}$ is not affected by extreme values or outliers in the data set
• C. Because the $\mathrm{median}$ is calculated by averaging all the data points
• D. Because the $\mathrm{median}$ always equals the $\mathrm{mean}$ in a symmetric distribution

Answer: (B)

Verified step by step guidance

1. Understand what a measure of center is: it is a value that represents a typical or central point in a data set, such as the mean, median, or mode.
2. Recall that the median is the middle value when the data are ordered from smallest to largest, or the average of the two middle values if there is an even number of observations.
3. Recognize that the median is considered resistant because it depends only on the middle position(s) in the ordered data, not on the actual values of the extreme data points.
4. Contrast this with the mean, which is calculated by summing all data values and dividing by the number of values, making it sensitive to very large or very small values (outliers).
5. Therefore, the median remains stable and unaffected by extreme values or outliers, making it a resistant measure of center.