Question

why is the median resistant, but the mean is not?

choose the correct answer below.

a. the median is resistant, while the mean is not, because when there are extreme values in the tail, the value of the median changes while the mean does not.

b. the mean is not resistant because when data are skewed, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. the median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.

c. the mean is not resistant because when data are skewed, there are extreme values in the tail, which do not pull the mean in that direction. however, the median is pulled in the direction of the extreme values, making it resistant.

d. the mean is not resistant because it is dependent upon the sample size, n. the larger n is, the smaller the mean becomes. however, the median is resistant because it is not dependent on the sample size, n.

Explanation:

To determine why the median is resistant and the mean is not, we analyze each option:

• Option A: Incorrect. Extreme values affect the mean, not the median. The median does not change much with extreme values, while the mean does.
• Option B: Correct. When data is skewed, extreme values in the tail pull the mean in the direction of the tail (e.g., right - skewed data has a mean pulled to the right by large extreme values). The median is the middle value when data is ordered and is not influenced by extreme values, so it is resistant.
• Option C: Incorrect. Extreme values pull the mean, not the median. The description here is the opposite of what actually happens.
• Option D: Incorrect. The mean is not resistant because of extreme values, not sample size. The median is also not dependent on sample size, but that's not the reason for its resistance.

Answer:

B. The mean is not resistant because when data are skewed, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.