Earlier quoted context omitted.
Another thing to think about is how basically every human trait follows a normal distribution. If mean = 1x (by definition 1x should be the mean) and the std is the maximum possible value (also 1x). Then 10x would be 10 std past the norm. This makes my numbers not arbitrary. 2x or 3x would only be 2 or 3 std past the norm. Which is reasonable (only if the std = 1x which is likely not the case and is most likely lower…
> ...and the std is the maximum possible value (also 1x). Then 10x would be 10 std past the norm. Sorry, but this is a completely arbitrary definition and honestly one I've never seen so far.
So for IQ, or height, no one can have negative or zero height. This limit effectively limits the std. It is not arbitrary. Try it.
For a distribution of integers on a range from 0 to infinite, let's say the mean is 1. The std will also have a maximum value of 1.
If you add extreme data points to change std, you will also change the mean.
This makes sense right? If you add say 9999999 to a distribution of numbers to keep the average the same you have to counterbalance it with a -9999999 or something like that. But however because the domain is limited from 0 to infinite you can't do that. So effectively the maximum value of the std is the mean itself assuming that the system is normally distributed.