The median minimizes the L1 norm and the mean minimizes the L2 norm. (Of the error made between the estimator and the data roughly speaking.) In this sense yes

The median minimizes the L1 norm and the mean minimizes the L2 norm. (Of the error made between the estimator and the data roughly speaking.) In this sense yes, median is some kind of average. But then it is insensitive to the outliners, which is the reason it is suggested above.