4 ms·

For the statement to be true, there would have to be zero people with a median IQ, i.e., not a normal distribution but a sharply bimodal distribution. Analogy:

For the statement to be true, there would have to be zero people with a median IQ, i.e., not a normal distribution but a sharply bimodal distribution. Analogy: The median U.S. male height is 5'9". Approximately 15% of the male population is 5'9". How can you have 50% of the population <= 5'8", 50% of the population >= 5'10", and 15% of the population == 5'9"? (This isn't a mathematical constraint on the truth of the statement, but... its truth would also depend on there being zero correlation between being low-IQ and lack of labor force participation, which I find implausible.)

TechBro8615 4y ago
Interesting (I'm really bad at math). It seems dependent on measurement precision, effectively the bucketing resolution of the histogram. If you measure both 69.00 and 69.99 inches as 5'9" then the number of people in the "median height bucket" would be more than if you broke it into 100 buckets from 69.00 to 69.99. Since presumably nobody can be exactly 5'9" (or 5'9.00", or 5'9.000"...), then the number of people in the "median" bucket must represent the inaccuracy of the measurement. So the greater precision you can measure, the less people are "inaccurately" at the exact median score - since buckets of .01 inches will contain fewer people than buckets of 1 inch. (I've noticed a lot of problems end at this boundary of continuity and discreteness. I find it existentially disturbing. As a bewildered non-mathematician, I've gone down quite a few rabbit holes reading about the axiom of choice and intuitionism – My favorite was when I discovered the Hairy Ball Theorem, but I also enjoyed this idea from "Does time really flow?" that describes time as an increase in precision of measurement of uniquely numbered particles [0].) [0] https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu...

TechBro8615 4y ago

Interesting (I'm really bad at math). It seems dependent on measurement precision, effectively the bucketing resolution of the histogram. If you measure both 69.00 and 69.99 inches as 5'9" then the number of people in the "median height bucket" would be more than if you broke it into 100 buckets from 69.00 to 69.99. Since presumably nobody can be exactly 5'9" (or 5'9.00", or 5'9.000"...), then the number of people in the "median" bucket must represent the inaccuracy of the measurement. So the greater precision you can measure, the less people are "inaccurately" at the exact median score - since buckets of .01 inches will contain fewer people than buckets of 1 inch. (I've noticed a lot of problems end at this boundary of continuity and discreteness. I find it existentially disturbing. As a bewildered non-mathematician, I've gone down quite a few rabbit holes reading about the axiom of choice and intuitionism – My favorite was when I discovered the Hairy Ball Theorem, but I also enjoyed this idea from "Does time really flow?" that describes time as an increase in precision of measurement of uniquely numbered particles [0].) [0] https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu...