average vs median

average and median both are nouns.

Word	Noun	Adjective	Verb	Adverb
average	Yes	Yes	Yes	No
median	Yes	Yes	No	No

As adjectives, average and median are synonyms defined as:

average and median: 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)

As nouns, median is a hyponym of average; that is, median is a word with a more specific, narrower meaning than average:

average: a statistic describing the location of a distribution
median: the number midway between the two middle numbers in a series containing an even or odd number of items

Other hyponyms of average include age norm, modal value, mode, median value, mean, mean value.

average (noun)	median (noun)
a statistic describing the location of a distribution	the number midway between the two middle numbers in a series containing an even or odd number of items
an intermediate scale value regarded as normal or usual
(sports) the ratio of successful performances to opportunities

average (adjective)	median (adjective)
lacking special distinction, rank, or status; commonly encountered	relating to or situated in or extending toward the middle
around the middle of a scale of evaluation	dividing an animal into right and left halves
lacking exceptional quality or ability	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)
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
relating to or constituting the most frequent value in a distribution

average (verb)	median (verb)
compute the average of
achieve or reach on average
amount to or come to an average, without loss or gain