extrapolation vs figuring

extrapolation and figuring both are nouns.

Word	Noun	Adjective	Verb	Adverb
extrapolation	Yes	No	No	No
figuring	Yes	No	No	No

As nouns, figuring is a hypernym of extrapolation; that is, figuring is a word with a broader meaning than extrapolation:

extrapolation: (mathematics) calculation of the value of a function outside the range of known values
figuring: problem solving that involves numbers or quantities

Other hypernyms of extrapolation include calculation, computation, reckoning.

extrapolation (noun)	figuring (noun)
(mathematics) calculation of the value of a function outside the range of known values	problem solving that involves numbers or quantities
an inference about the future (or about some hypothetical situation) based on known facts and observations