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> For instance: "you are more likely to have attended a school with more pupils than most other schools" Isn't this statement still true in your example? (Assu

> For instance: "you are more likely to have attended a school with more pupils than most other schools" Isn't this statement still true in your example? (Assuming some small variance among the small schools just so it's still possible to order them by size.) If one school has 1,000,000 students and a million schools had about 9 to 11 students, the median school would have about 10 students. No matter what (ignoring exact ties), 500,000 schools are going have more students than the median school, even if most of those schools just have 10 or 11 students. Sure, most people in your example come from the ~10 person schools, but more students come from the more populated half of those ~10 person schools. There's at least a 54% chance that you "attended a school with more pupils than most other schools" (6 of 11 million students). (It's fair to ignore exact ties because it's unlikely that many planets have the exact same population.) Your distribution makes it likely that there is one school with a much larger population than your own, but not that most schools have a larger population.

moralestapia 5y ago
Yes, but there is no way you can conclude "the typical student should come from school X" from that, which is the main issue with the author's argumentation.
- nearbuy 5y ago
  I think the author is saying that if there's no variance (e.g. all schools have 10 students), then our school is as big as all the other schools, and as you increase the variance, the odds of you being in a larger than average school increases. But no matter the distribution, we're never most likely to be in a smaller than average school. You cut out the context in some of your quotes that makes this clearer. The article says > imagine that planet populations are distributed in the same pattern as countries on Earth ... in that case, most planets will have a very much smaller population They're saying, for purposes of illustration, imagine planet populations were distributed like countries on Earth. But that's not the distribution they use in their actual calculation. It's just to help explain.
  - fergussimpson 5y ago
    Precisely. I'm glad you took the time to understand. :)

moralestapia 5y ago

Yes, but there is no way you can conclude "the typical student should come from school X" from that, which is the main issue with the author's argumentation.

nearbuy 5y ago
I think the author is saying that if there's no variance (e.g. all schools have 10 students), then our school is as big as all the other schools, and as you increase the variance, the odds of you being in a larger than average school increases. But no matter the distribution, we're never most likely to be in a smaller than average school. You cut out the context in some of your quotes that makes this clearer. The article says > imagine that planet populations are distributed in the same pattern as countries on Earth ... in that case, most planets will have a very much smaller population They're saying, for purposes of illustration, imagine planet populations were distributed like countries on Earth. But that's not the distribution they use in their actual calculation. It's just to help explain.
- fergussimpson 5y ago
  Precisely. I'm glad you took the time to understand. :)