nose count vs numeration

nose count and numeration both are nouns.

Word	Noun	Adjective	Verb	Adverb
nose count	Yes	No	No	No
numeration	Yes	No	No	No

As nouns, numeration is a hypernym of nose count; that is, numeration is a word with a broader meaning than nose count:

Other hypernyms of nose count include count, counting, enumeration, reckoning, tally.

nose count (noun)	numeration (noun)
a periodic count of the population	the act of counting; reciting numbers in ascending order
	naming numbers