A distribution of sale prices has a long tail toward the high end. What follows for its mean and median?
Correct Answer
C) The mean will lie above the median value
Why this is correct: In a right-skewed distribution (long tail toward high values), the mean is pulled upward by the extreme high values, while the median remains at the 50th percentile. Therefore, the mean will be greater than the median. Why the other choices are wrong: 'The mean will lie below the median value' describes a left-skewed distribution. 'The two measures will be identical in value' occurs only in perfectly symmetrical distributions. 'The median cannot be computed for such data' is false; the median can always be computed for ordered data. Exam tip: For skew, remember 'mean follows the tail'—right tail pulls mean up, left tail pulls mean down.
Why This Is the Correct Answer
Why this is correct: In a right-skewed distribution (long tail toward high values), the mean is pulled upward by the extreme high values, while the median remains at the 50th percentile. Therefore, the mean will be greater than the median. Why the other choices are wrong: 'The mean will lie below the median value' describes a left-skewed distribution. 'The two measures will be identical in value' occurs only in perfectly symmetrical distributions. 'The median cannot be computed for such data' is false; the median can always be computed for ordered data. Exam tip: For skew, remember 'mean follows the tail'—right tail pulls mean up, left tail pulls mean down.
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