How does using the mean value for imputing missing data differ from using the median value?

Using the mean value for imputing missing data is indeed affected by outliers or skewed data distributions. When the mean is calculated, every value in the dataset contributes to this average, which means that if there are extreme values (outliers), they will disproportionately pull the mean value in their direction. This can lead to an imputed value that does not accurately represent the central tendency of the majority of the data.

In contrast, the median is the middle value in a sorted dataset and is more robust to outliers. When the dataset has extreme values, the median remains unaffected because it only considers the middle point, making it a more reliable measure of central tendency in skewed distributions.

The other options do not appropriately reflect the relationship between the mean and median. The suggestion that the median is strictly for categorical data is misleading, as the median can also be used within numerical datasets. The notion that both methods yield identical results overlooks the nuances of how outliers influence the mean, leading to potentially inaccurate imputations when the means are used in datasets with extreme values.