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An intelligence quotient, more commonly known as an IQ, was a measurement of an individual's mental abilities and intellectual development derived from a series of tests. The higher an IQ, the more "intelligent" a person was considered.

The Beta 5 computer considered Roberta Lincoln to have a high IQ despite her "erratic behavior". (TOS: "Assignment: Earth")

After a Lactran child, of a mere 6 years of age, was accidentally transported up to the USS Enterprise, the child picked Montgomery Scott's brain, all the knowledge in the Enterprise computers, before sending the ship flying out of orbit of Lactra VII. After Scott was able to convince the child that they were not pets, Scott discovered that the child had "an IQ in the thousands." (TAS: "The Eye of the Beholder")

The master computer of the Shore Leave Planet believed that the Enterprise, which it referred to as the "sky machine", and the Humans aboard it as the machine's slaves. When told this, Uhura did not understand what was meant, and she requested clarity to the computer's statement, it replied, "your intelligence quotient must be lower than I had assessed…" (TAS: "Once Upon a Planet")

After being genetically enhanced as a child, Doctor Julian Bashir's IQ jumped five points a day over a period of two weeks. (DS9: "Doctor Bashir, I Presume")

In 2366, after being temporarily rendered Human by the Q Continuum, Q claimed he had an IQ of 2,005. (TNG: "Deja Q")

After exposure to a Cytherian probe, Reginald Barclay's IQ temporarily jumped up to somewhere between 1,200 and 1,450. (TNG: "The Nth Degree")

In the script to "Coming of Age", the Academy hopefuls took a Carlundrum IQ Test. This was a timed test where the student had to "predict the variable patterns of platonic solids."

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