When analyzing a data set, identify when the median should be reported instead of the mean: (C:1)

Question

BlackTom AI · Accepted Answer

In statistics, the choice between reporting the median or the mean depends on the data distribution and the presence of skew or outliers.
Option a: 'When the median is less than the mean' This describes a potential skew but does not by itself justify reporting the median; the mean being higher than the median often indicates right-skewed data, but the statement alone is not a sufficient criterion for preferring the median.
Option b: 'When the data has mostly lower values, with very few high values' This describes a distribution with a long tail on the high end (positive/right skew). In such cases the mean is pulled upward by the extreme high values, while the median remains a better measure of central tendency. Therefore reporting the median is appropriate here.
Option c: 'When there are no outliers in the data' The absence of outliers does not necessitate using the median over the mean; in normally distributed data without outliers, the mean and median are often similar, and either could be used, though the mean is commonly reported.
Option d: 'When the mean is less than the median' This is another way to describe left-skew, but the standard guideline is to use the median when the distribution is skewed (which would typically accompany high-value outliers pulling the mean up). Simply stating the inequality is not a general decision rule for reporting the median.
Overall, the key reasoning is that the median is preferred in skewed distributions with outliers that distort the mean, which aligns with option b's description of mostly lower values with a few high values.

When analyzing a data set, identify when the median should be reported instead of the mean: (C:1)单项选择题

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