When a data set contains a single extreme outlier, the median is preferred over the mean because the median:
Correct Answer
B) Is not pulled by the extreme observation
Why this is correct: The median is the middle value when all data points are ranked in order. Because it depends only on rank, not on the actual numerical values, an extreme outlier can only shift the median by moving it one position in the ordered list, if at all. This makes the median a robust measure of central tendency, resistant to distortion from a single extreme value, which is crucial in appraisal when a data set contains one non-typical sale. Why the other choices are wrong: "Uses more of the available information" is wrong because the median, by focusing on the middle rank, actually ignores the specific values of most data points, unlike the mean which uses all values. "Is always larger than the mean" is incorrect; in a positively skewed distribution (with a high outlier), the median is typically smaller than the mean, but the reverse can be true with a low outlier. "Requires a larger sample size" is false; the median can be calculated for any sample size and its resistance to outliers is a property of its calculation, not a sample size requirement. Exam tip: Remember, 'mean' is sensitive to all values; 'median' is resistant to extremes. In appraisal, skewed market data often calls for the median.
Why This Is the Correct Answer
Why this is correct: The median is the middle value when all data points are ranked in order. Because it depends only on rank, not on the actual numerical values, an extreme outlier can only shift the median by moving it one position in the ordered list, if at all. This makes the median a robust measure of central tendency, resistant to distortion from a single extreme value, which is crucial in appraisal when a data set contains one non-typical sale. Why the other choices are wrong: "Uses more of the available information" is wrong because the median, by focusing on the middle rank, actually ignores the specific values of most data points, unlike the mean which uses all values. "Is always larger than the mean" is incorrect; in a positively skewed distribution (with a high outlier), the median is typically smaller than the mean, but the reverse can be true with a low outlier. "Requires a larger sample size" is false; the median can be calculated for any sample size and its resistance to outliers is a property of its calculation, not a sample size requirement. Exam tip: Remember, 'mean' is sensitive to all values; 'median' is resistant to extremes. In appraisal, skewed market data often calls for the median.
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