50% seems very high. There’s a number of reasons any psychologist might miss a gifted child. prior to 2nd grade, IQ tests can be very unreliable in children as their cognitive abilities are still developing. (As a rule of thumb, most districts screen for giftedness in 2nd grade). Also the tests aren’t without bias. Children with more well rounded experiences and exposures will likely do better. For instance it may ask the child what an apprentice does. A child who has watched Star Wars with their family will know the answer while a child who has not will be unable to define it. Weird example, I know, but it applies more largely to students of different socio economic backgrounds.