Etymology
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inferential (adj.)
1650s, from Medieval Latin inferentia (see inference) + -al (1). Related: Inferentially.
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statistics (n.)
1770, "science dealing with data about the condition of a state or community" [Barnhart], from German Statistik, popularized and perhaps coined by German political scientist Gottfried Aschenwall (1719-1772) in his "Vorbereitung zur Staatswissenschaft" (1748), from Modern Latin statisticum (collegium) "(lecture course on) state affairs," from Italian statista "one skilled in statecraft," from Latin status "a station, position, place; order, arrangement, condition," figuratively "public order, community organization," noun of action from past participle stem of stare "to stand" from PIE root *sta- "to stand, make or be firm."

OED points out that "the context shows that [Aschenwall] did not regard the term as novel," but current use of it seems to trace to him. Sir John Sinclair is credited with introducing it in English use. Meaning "numerical data collected and classified" is from 1829; hence the study of any subject by means of extensive enumeration. Abbreviated form stats first recorded 1961.
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referential (adj.)

"relating to or having reference to," 1650s, from reference (n.) on model of inferential, etc. Related: Referentially.

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statistical (adj.)
1787, from statistics + -al (1). Related: Statistically.
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biometrics (n.)
"application of statistics and mathematics to the study of biology," 1902, from biometry (also see -ics).
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demographics (n.)
1967, the science of divining from demographic statistics; see demography + -ics. Originally in reference to TV audiences and advertisers.
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variate (n.)
in statistics, 1899, from adjective variate (mid-15c.), from Latin variatus, past participle of variare (see vary).
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at-bat (n.)
"baseball player's turn at the plate," 1912, originally a column heading in statistics tables, from the prepositional phrase.
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multivariate (adj.)

in statistics, "involving or having two or more variables," 1928, from multi- "many" + -variate, from Latin variatio "a difference, variation, change," from past-participle stem of variare "to change" (see vary).

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