Dear 100 Hour Board,
After concern due to very poor performance in school, my daughter's intelligence was evaluated by a professional psychologist using the Wechsler Intelligence Scale for Children (WISC-IV) and her full-scale IQ was found to be 93 (near the low end of average).
My son got into his school's gifted program and after inquiring about his screening score, I learned that he took the Naglieri Nonverbal Ability Test 3 Level C and his NAI (Naglieri Ability Index) was found to be 147.
How common is it for two siblings' intelligence measurements to differ by over 50 points?
To directly answer your question, it's pretty common.
1) IQ tests do not measure innate ability or intelligence, as much as we want them to. To assume that we can measure something as complex as intelligence with one single quantity is ridiculous and fallacious. Also, it's based on age, and to assume everyone is or should be at exactly the same places with their literal age and mental age is a pretty big assumption too.
2) Your children took 2 different tests. IQ tests are not always valid (they don't always do a great job of measuring what they think they're measuring) and no two tests are the same, so they often give huge variance in measurements of one person (like Anathema has mentioned). So, if your son took the same test as your daughter, the gap between their scores could get bigger or smaller.
3) IQ is not quite as heritable as popular science says it is. There seems to definitely be some biological component to intelligence, but siblings are not going to both have high IQs just because their parents did. There is a lot of biological variability from person to person anyway. It makes sense for your kids to have such different scores, because intelligence isn't magically genetic.
4) Binet - the original creator of the IQ test - said that the tests should never be used to rank or assume things about the intellectual abilities of different people. There are only designed to create a benchmark to identify kids who are really truly struggling. Everything around average and above is harder to parse out exactly what it means and how much of an impact it really has on day-to-day life. IQ measures a very narrow set of skills that have nothing to do with "competence."
5) IQ scores are standardized based on your age (Basically the test calculates your mental age, then divides by your real age, and multiplies by 100. Approximately). If your daughter is younger than your son and is just a "late bloomer" or struggles in school, that doesn't mean she's innately stupid or whatever (I'm sure you don't think so either, I'm just mentioning it).
Anyway. I know this was probably an unnecessary amount of information as response, but there ya go. I just really don't like IQ tests because they reify the idea that intelligence is innate, measurable, and capturable by a single quantity. AS IF human beings could generate a real test to measure such a complex, vague idea as intelligence.
Your daughter is surely lovely. If she doesn't excel academically, that's okay too. I'm sure you love her all the same.
All I can tell you is my own IQ scores on random internet tests have definitely varied by more than 50 points.
Such differences are byproducts of the metrics, not the people.