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Answer: When the variable contains a lot of extreme outliers
The mean and median will be meaningfully different when the data distribution is skewed or contains outliers. The mean is sensitive to extreme values (outliers) because it incorporates all data points in its calculation, while the median is robust to outliers as it only depends on the middle value(s) of the ordered dataset. When there are many extreme outliers, the mean gets pulled toward those extreme values, creating a significant difference from the median. This is supported by the community discussion where all respondents selected E, with detailed explanations about how outliers affect the mean but not the median. The other options are incorrect: A (no outliers) would make mean and median similar; B (no missing values) doesn't directly affect the mean-median relationship; C (boolean type) typically has mean and median close together; D (categorical type) doesn't have meaningful mean/median calculations in the first place.
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In which of the following scenarios would the mean and median of a variable be significantly different?
A
When the variable contains no outliers
B
When the variable contains no missing values
C
When the variable is of the boolean type
D
When the variable is of the categorical type
E
When the variable contains a lot of extreme outliers