mean and median both are nouns.

mean and median both are adjectives.

mean is a verb but median is not a verb.

mean (noun)	median (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n	the number midway between the two middle numbers in a series containing an even or odd number of items

mean (adjective)	median (adjective)
approximating the statistical norm or average or expected value	relating to or constituting the middle value of an ordered set of values (or the average of the middle two in a set with an even number of values)
characterized by malice	dividing an animal into right and left halves
having or showing an ignoble lack of honor or morality	relating to or situated in or extending toward the middle
marked by poverty befitting a beggar
(used of persons or behavior) characterized by or indicative of lack of generosity
(used of sums of money) so small in amount as to deserve contempt
of no value or worth
very good; of the highest quality

mean (verb)	median (verb)
mean or intend to express or convey
have as a logical consequence
denote or connote
have in mind as a purpose
have a specified degree of importance
intend to refer to
destine or designate for a certain purpose