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.