arithmetic vs average out

arithmetic is a noun but average out is not a noun.

Word	Noun	Adjective	Verb	Adverb
arithmetic	Yes	Yes	No	No
average out	No	No	Yes	No

arithmetic (noun)	average out (noun)
the branch of pure mathematics dealing with the theory of numerical calculations

arithmetic (adjective)	average out (adjective)
relating to or involving arithmetic

arithmetic (verb)	average out (verb)
	compute the average of
	amount to or come to an average, without loss or gain