When taking an IQ test, if a subject responds to all questions correctly, they will achieve the maximum (raw) score, a finite number. Yet, due to the test's normalisation that takes the median raw score across the population and defines it into a standardised score of 100, IQ scores are expressed not as raw scores but as standardised scores, or equivalently, a number of standard deviations (SDs) away from 100. My question is: what sense does it make to speak of very high IQ scores, such as for instance 170, that correspond to an extreme in the distribution's tail, when, if one were to convert back to raw scores, this would seem to result in a raw score higher than the one corresponding to an all answers correct result.Put more simply, my question is: since there is a hard-limit on raw scores, why is it that the normal distribution used to describe an IQ score can (theoretically) lead, along its tails, to infinitely-large numbers - as well as, conversely, to negative numbers - as raw scores, both extremes being out of the raw-scores range?
IQ scores - fixed raw scores vs infinite tails of the underlying normal distribution of standard scores
statistics;iq