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the median is what matters

Sure, but you need to be careful about what the median represents. It doesn't represent the median of all humans, just the humans that have taken the test, and it only reflects performance on the test. This can be useful, but it gets used for a lot of stuff it really shouldn't (e.g. comparing results from one region w/ another, when those regions have very different education systems and thus exposure to different sorts of problem solving).

The person with the 100 IQ

They could also be a professor or other highly educated person. It all depends on how familiar they are with the concepts covered by the test, how well they were feeling that day, how well the questions were worded, how much time they took, etc. There are a ton of variables, and your score on a test could vary quite wildly between takes.

It's just not a good general measure of much of anything. It can be helpful in a clinical setting, though, to diagnose things like neurological divergence and whatnot, but it isn't a particularly good test of "intelligence," whatever that's supposed to mean.