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My grandson just received results from testing for the gifted program. His results showed an IQ of 130+ with a score on the WISC-IV of 99.7%. What IQ does this percentile denote?

MawMawSue, did they give you individual subtest scores?

A 99.7th percentile would imply a score between 2.7 and 2.8 standard deviations above the mean. IQ scores are standardized to have mean 100 and SD 15. So it would imply an IQ of between 140 and 142.

Technical: I assumed a normal distribution in the above conversion. True distributions of IQ scores are probably non-normal, but the tables I've seen for converting IQs to percentiles (include the one linked to above) always seem to be based on a normal distribution. If they converted an IQ score to a percentile assuming a normal distribution, then deconverting using the same assumption would make sense, even if the true distribution was non-normal.

The test is normed using their sample population. So functionally the scores are forced into the normal distribution. On the other hand, a population sample of 4800 (as used for WISC norm) starts to lose reliability when you get into the tails and the functional population at the SD+3 (IQ 145+) range is only 14 people total across the full testing age range.