Both the median and the midrange transform linearly, satisfying $\text{Median}(Y) = a\text{Median}(X) + b$ and $\text{Midrange}(Y) = a\text{Midrange}(X) + b$.

Under a transformation where $a = 0$, both the median and the midrange become equal to the constant $b$.

The midrange is highly sensitive to changes in extreme values (outliers) of the dataset, whereas the median is robust to outliers.

Only the median transforms linearly, while the midrange does not transform linearly if $a < 0$.