The best option in this scenario is "when the data set is U-shaped."
In a U-shaped dataset, the distribution of data points often has two modes, leading to a situation where both the mean and median may not accurately represent the central tendency of the data. The mean could be skewed by the extreme values at either end of the "U," while the median may not capture the prominence of the values near the two peaks. This makes neither the mean nor the median effective descriptors of this kind of dataset.