median and mean both are nouns.

median and mean both are adjectives.

median is not a verb while mean is a verb.

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

median (adjective)	mean (adjective)
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)	approximating the statistical norm or average or expected value
dividing an animal into right and left halves	characterized by malice
relating to or situated in or extending toward the middle	having or showing an ignoble lack of honor or morality
	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

median (verb)	mean (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