mean vs symbolize

mean is a noun but symbolize is not a noun.

Word	Noun	Adjective	Verb	Adverb
mean	Yes	Yes	Yes	No
symbolize	No	No	Yes	No

As verbs, symbolize is a hyponym of mean; that is, symbolize is a word with a more specific, narrower meaning than mean:

Other hyponyms of mean include represent, stand for, symbolise, typify, signify, import, spell, aim, aim, drive, get.

mean (noun)	symbolize (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n

mean (adjective)	symbolize (adjective)
of no value or worth
having or showing an ignoble lack of honor or morality
characterized by malice
approximating the statistical norm or average or expected value
marked by poverty befitting a beggar
(used of sums of money) so small in amount as to deserve contempt
(used of persons or behavior) characterized by or indicative of lack of generosity
very good; of the highest quality

mean (verb)	symbolize (verb)
have in mind as a purpose	express indirectly by an image, form, or model; be a symbol
intend to refer to	represent or identify by using a symbol; use symbols
destine or designate for a certain purpose
mean or intend to express or convey
denote or connote
have as a logical consequence
have a specified degree of importance