statistician vs mathematician

statistician and mathematician both are nouns.

Word	Noun	Adjective	Verb	Adverb
statistician	Yes	No	No	No
mathematician	Yes	No	No	No

As nouns, mathematician is a hypernym of statistician; that is, mathematician is a word with a broader meaning than statistician:

statistician (noun)	mathematician (noun)
someone versed in the collection and interpretation of numerical data (especially someone who uses statistics to calculate insurance premiums)	a person skilled in mathematics
a mathematician who specializes in statistics