mean and meanness both are nouns.

mean is an adjective but meanness is not an adjective.

mean is a verb but meanness is not a verb.

mean (noun)	meanness (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n	the quality of being deliberately mean
	extreme stinginess

mean (adjective)	meanness (adjective)
approximating the statistical norm or average or expected value
characterized by malice
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

mean (verb)	meanness (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