In "Deja Q," the now-human Q talks to Guinan in Ten Forward, when he states that he is "just one of the boys with an IQ of 2005."

Where did Q get this information? Did Beverly give him an IQ test? Was he informed by the Continuum before being sent away that he'd retain his intellect? If so, that means Q's IQ while fully Q would be 2005. It seems strange that the Q would use intelligence quotient, so that seems unlikely.

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    Rule #1 - Never trust anything said by someone whose nickname is "the God of Lies" – Valorum Feb 18 '17 at 17:03
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    I think we can safely assume that someone with an IQ of 2000+ is perfectly capable of accurately assessing their own IQ. – Valorum Feb 18 '17 at 17:04
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    @Valorum not sure I'd trust Holly from Red Dwarf with that...(an IQ of 6,000 you say Holly? Umm.... okay...) – Jon Clements Feb 18 '17 at 17:37
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    Ask me my IQ ;) Seriously though, the line was put there to show that Q is full of himself. – Brian Ortiz Feb 18 '17 at 17:37
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    He clicked a Facebook link and took an online test. – frеdsbend Feb 19 '17 at 8:31

The current convention is that IQ test results are scaled to fit a normal distribution with mean 100 and standard deviation 15. This means that an IQ of 2005 corresponds to a score which is 127 standard deviations above the mean (since (2005-100)/15=127), which would mean that roughly 1 in 10^3505 people are as intelligent as Q is.

The population of the galaxy cannot possibly be anywhere near as large as 10^3505, and contains more than one member of the Q continuum.

So either:

  1. Q is full of it (this sounds the most likely to me)
  2. Q is massively more intelligent even than other Qs (ha ha ha)
  3. IQ has been redefined in the 24th century to be an absolute measure of intelligence rather than a measurement which is relative to the general population (in which case we don't have enough information to answer this question).
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    We know from various episodes that the galaxy is merely one of an infinite number in a multiverse. Have you taken that into account? – Valorum Feb 18 '17 at 18:17
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    I think trying to count populations across multiverses is fraught with difficulty when many of the people in question are effectively duplicates of each other. If you like, I suppose you could imagine that Q knows some way of doing it, is aware of enough different universes to make that determination, and is telling the truth. Personally I'd rather stick with a general rule of "anyone claiming an IQ over 300, in any work of fiction, is either lying or using a very different definition of IQ than ours." – Micah Feb 18 '17 at 18:45
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    @1252748: This answer would not change significantly if you replaced "the galaxy" with "the observable universe", or even "a number of copies of the observable universe which is equal to the number of atoms in the observable universe". – Micah Feb 18 '17 at 19:01
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    Fourth possibility: IQ is still normally scaled, but only to humans (or close), and not to all possible sentients. E.g. if snails had a SpeedQ metric, normalized to the standard top speeds of snails and slugs, a cheetah would be many thousands of standard deviations off the top of it. How exactly that extrapolation would work without good calibration is a little iffy, though. -- That said, I agree Q being full of it (picking an arbitrary large number to point out he's terribly smart) is the most likely answer. – R.M. Feb 18 '17 at 20:51
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    @R.M. That's actually what I was trying to get at with possibility #3. The problem is, IQ scoring is entirely ordinal — that is, it purports to tell you who's more intelligent than who, but has no notion of how much more intelligent they are except by counting the number of people there are of intermediate intelligence. It's not (at the moment) like speed, which we can measure independently and then perhaps notice that it falls into a normal distribution; the normal distribution is part of the notational convention. – Micah Feb 18 '17 at 21:02

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