4 ms·

> Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions. > Less than 40 of the 3,864 contestants were average size on just

> Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions. > Less than 40 of the 3,864 contestants were average size on just five of the nine dimensions and none of the contestants — not even Martha Skidmore — came close on all nine dimensions. This seems more an issue of the "curse of dimensionality"[0] more than the "flaw of averages". Be very wary when you are trying to draw conclusions from a dataset with many dimensions. 0. https://en.wikipedia.org/wiki/Curse_of_dimensionality https://en.wikipedia.org/wiki/Curse_of_dimensionality

ken 7y ago
I don’t think so. They also said: > Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size ... less than 3.5 per cent of pilots would be average sized on all three dimensions.
- Someone 7y ago
  FTA: ”These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension.“ 0.3³ = 0.0027 = 2.7%, so if those measurements are independent of each other, it isn’t surprising that he found “less than 3.5 percent”.
  - Retric 7y ago
    I think the general assumption is arm length and height for example are strongly correlated.
  - Worker32850 7y ago
    Human dimensions are closer to a normal distribution. (Not quite normal, but let's pretend.) In that distribution then 46% of subjects should be in the middle 30% of 3 dimensions. [0] [0] With 4000 subjects they presumably have all sizes within ~3.5 stddevs represented. The middle ~1.2 stddevs should hold ~77% of the population. 0.77^3 = ~46%
    - dragonwriter 7y ago
      > Human dimensions are closer to a normal distribution Human height is (it's the textbook example of a real, intuitive_that is, using the normal linear scale—physical measure that is a good fit for a normal distribution) plenty of other human dimensions are not.
      - smabie 7y ago
        Human height should be a negative binomial distribution, since human height can't be negative.
        dragonwriter 7y ago
        > Human height should be a negative binomial distribution, since human height can't be negative. That's a sensible analytical speculation, but it empirically fits very well with a normal distribution. The fact that zero is, for adult male height (the typical cited example for fitting a nor Al distribution, though adult female height also works), around 17 standard deviations below the mean helps: I won't bother to calculate how little should be below that, since below 7σ in a normal distribution is 1/780 billion.

ken 7y ago

I don’t think so. They also said: > Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size ... less than 3.5 per cent of pilots would be average sized on all three dimensions.

Someone 7y ago
FTA: ”These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension.“ 0.3³ = 0.0027 = 2.7%, so if those measurements are independent of each other, it isn’t surprising that he found “less than 3.5 percent”.
- Retric 7y ago
  I think the general assumption is arm length and height for example are strongly correlated.
- Worker32850 7y ago
  Human dimensions are closer to a normal distribution. (Not quite normal, but let's pretend.) In that distribution then 46% of subjects should be in the middle 30% of 3 dimensions. [0] [0] With 4000 subjects they presumably have all sizes within ~3.5 stddevs represented. The middle ~1.2 stddevs should hold ~77% of the population. 0.77^3 = ~46%
  - dragonwriter 7y ago
    > Human dimensions are closer to a normal distribution Human height is (it's the textbook example of a real, intuitive_that is, using the normal linear scale—physical measure that is a good fit for a normal distribution) plenty of other human dimensions are not.
    - smabie 7y ago
      Human height should be a negative binomial distribution, since human height can't be negative.
      - dragonwriter 7y ago
        > Human height should be a negative binomial distribution, since human height can't be negative. That's a sensible analytical speculation, but it empirically fits very well with a normal distribution. The fact that zero is, for adult male height (the typical cited example for fitting a nor Al distribution, though adult female height also works), around 17 standard deviations below the mean helps: I won't bother to calculate how little should be below that, since below 7σ in a normal distribution is 1/780 billion.