A situation in which neither the mean nor the median is a good descriptor for a dataset is when the dataset is U-shaped.
In a U-shaped distribution, the greatest frequencies occur at the extremes, while values in the middle are less common. As a result, both the mean and the median may not accurately represent the central tendency of the data. For instance, the mean could be influenced significantly by the lower and upper tails, and the median could fall in a low-frequency region, leading to misleading interpretations of the dataset's behavior.