A distribution in which the mean exceeds the median is described as:
Correct Answer
C) Positively skewed, with a tail toward higher values
Why this is correct: The correct answer is "Positively skewed, with a tail toward higher values." In a positively skewed (right-skewed) distribution, a long tail extends toward higher values. The mean is sensitive to these extreme high values and is pulled in the direction of the tail, making it greater than the median. This is common in housing price data, where a few very high-priced homes raise the average price above the more typical median price. Why the other choices are wrong: "Perfectly symmetrical around its center" is wrong because in a symmetrical distribution, the mean and median are equal. "Negatively skewed, with a tail toward lower values" is wrong because in a negatively skewed (left-skewed) distribution, the mean is less than the median, pulled down by low outliers. "Bimodal with two distinct peaks" is wrong because bimodality describes the shape's peaks, not the relationship between the mean and median; a bimodal distribution can have its mean either above or below its median. Exam tip: Remember the phrase "mean follows the tail." If the mean > median, the tail (and skew) is positive/right.
Why This Is the Correct Answer
Why this is correct: The correct answer is "Positively skewed, with a tail toward higher values." In a positively skewed (right-skewed) distribution, a long tail extends toward higher values. The mean is sensitive to these extreme high values and is pulled in the direction of the tail, making it greater than the median. This is common in housing price data, where a few very high-priced homes raise the average price above the more typical median price. Why the other choices are wrong: "Perfectly symmetrical around its center" is wrong because in a symmetrical distribution, the mean and median are equal. "Negatively skewed, with a tail toward lower values" is wrong because in a negatively skewed (left-skewed) distribution, the mean is less than the median, pulled down by low outliers. "Bimodal with two distinct peaks" is wrong because bimodality describes the shape's peaks, not the relationship between the mean and median; a bimodal distribution can have its mean either above or below its median. Exam tip: Remember the phrase "mean follows the tail." If the mean > median, the tail (and skew) is positive/right.
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