Nine sales produce prices whose middle value is $412,000 while the arithmetic mean is $468,000. The gap most likely reflects:
Correct Answer
B) One or more high-priced outliers pulling the mean upward
Why this is correct: The median is the middle value when all are ranked; it is not affected by extreme values. The mean (average) is calculated by summing all values and dividing by the number of observations. A few very high sales will pull the mean upward, creating a gap where the mean exceeds the median, indicating a right-skewed distribution. Why the other choices are wrong: "An arithmetic error in computing the median value" is unlikely; the median is simply the middle-ranked value. "That the sample contains too few observations to analyze" is wrong; nine sales can be analyzed. "A market that has been declining over the period studied" would more likely pull the mean down below the median. Exam tip: Mean is sensitive to outliers; median is robust. A higher mean than median suggests high-value outliers.
Why This Is the Correct Answer
Why this is correct: The median is the middle value when all are ranked; it is not affected by extreme values. The mean (average) is calculated by summing all values and dividing by the number of observations. A few very high sales will pull the mean upward, creating a gap where the mean exceeds the median, indicating a right-skewed distribution. Why the other choices are wrong: "An arithmetic error in computing the median value" is unlikely; the median is simply the middle-ranked value. "That the sample contains too few observations to analyze" is wrong; nine sales can be analyzed. "A market that has been declining over the period studied" would more likely pull the mean down below the median. Exam tip: Mean is sensitive to outliers; median is robust. A higher mean than median suggests high-value outliers.
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