おそらくラテン語のqui es「あなたは誰ですか」が語源で、語源的にはwhoと同じqui, es, isが語源。 もともとは過去のラテン語の文法試験で、受験者に最初に聞かれた質問だった。後に小さな試験、小試験を指すようになった。
A Quiz, in the common acceptation of the word, signifies one who thinks, speaks, or acts differently from the rest of the world in general. But, as manners and opinions are as various as mankind, it will be difficult to say who shall be termed a Quiz, and who shall not: each person indiscriminately applying the name of Quiz to every one who differs from himself .... ["The London Magazine," November, 1783]According to OED, the anecdote that credits this word to a bet by the Dublin theater-manager Daly or Daley that he could coin a word is regarded by authorities as "doubtful" and the first record of it appears to be in 1836 (in Smart's "Walker Remodelled"; the story is omitted in the edition of 1840).
The word Quiz is a sort of a kind of a word
That people apply to some being absurd;
One who seems, as t'were oddly your fancy to strike
In a sort of a fashion you somehow don't like
A mixture of odd, and of queer, and all that
Which one hates, just, you know, as some folks hate a cat;
A comical, whimsical, strange, droll -- that is,
You know what I mean; 'tis -- in short, -- 'tis a quiz!
[from "Etymology of Quiz," Charles Dibdin, 1842]