When would you report the median instead of the mean?
When the distribution is skewed or has outliers a mean can't survive — income, latency, time-to-purchase. One executive salary or one 30-second outlier request drags the mean somewhere no typical data point actually sits, while the median stays where the bulk of the data is. In practice you report both plus a percentile like p95, because the gap between mean and median is itself informative about skew.