From Merriam-Webster:

surmise
noun
sur·mise | \ sər-ˈmīz, ˈsər-ˌmīz \
: a thought or idea based on scanty evidence : conjecture
surmise
verb
sur·mise | \ sər-ˈmīz\
surmised; surmising
transitive verb : to form a notion of from scanty evidence : imagine, infer
First Known Use of surmise
Noun: 1569, in the meaning defined above
Verb: 1647, in the meaning defined above
History and Etymology for surmise
Noun
Middle English, allegation, charge, from Anglo-French, from feminine of surmis, past participle of surmettre to place on, suppose, accuse, from Medieval Latin supermittere, from Late Latin, to place on, from Latin super- + mittere to let go, send
Verb
Middle English, to allege, from surmise, noun
The answer to last week’s question: What relative of Latin mittere begins with “s” and refers to a thought or idea based on scanty evidence?