Understanding Gaussians

> You can see that the data is clustered around the mean value. Another way of saying this is that the distribution has a definite scale. [..] it might theoretically be possible to be 2 meters taller than the mean, but that’s it. People will never be 3 or 4 meters taller than the mean, no matter how many people you see.

The way the author defines definite scale is that there is a max and a minimum, but that is not true for a gaussian distribution. It is also not true that if we keep sampling wealth (an example of a distribution without definite scale used in the article), there is no limit to the maximum.

I think he’s saying that the distribution of human heights has definite scale, not the Gaussian?

Jinlian (1964–1982) of China was 8 feet, 1 inch (2.46 centimeters) when she died, making her the tallest woman ever. According to Guinness World Records, Zeng is the only woman to have passed 8 feet (about 2.44 meters)

Mean from article 163.

So the facts check out.

Author is correct.

Also very interesting the suggestion that human height is not Gaussian.

Snip :

“ Why female soldiers only? If we were to mix male and female soldiers, we would get a distribution with two peaks, which would not be Gaussian.

“

Which begs the question what other human statistics are non Gaussian if sexes are mixed and does this apply to other strong differentiators like historical time, nutrition, neural tribes ?

Statistics is highly non-trivial. “

It's an oversimplification but at some point there is really no difference between impossible and 'incredibly small probability'.

I mean sure it is possible for all air molecules to randomly all go to the same corner of the room at the same time (heck it is inevitable in some sense), you can play it back in reverse to check no laws of physics were broken, but practically that simply does not happen.

Nothing is Gaussian then. What probability distribution allows for Graham's Number to be a possibility?

> at some point there is really no difference between impossible and 'incredibly small probability'.

This is not true.

Using your air molecules example: Every microstate (i.e. location and speed of all the molecules) possible under the given macrostate (temperature, number of molecules, etc) has a probability of happening of 0, but aren't impossible, simply because the microstates are real variables and real numbers are uncountable. Impossible microstates also have 0 probability but are obviously not the same.