For what type of data can I use the empirical rule? What doesn't follow the empricial rule?
Roughly, data with no left and right bound (or where the bounds are far away from the typical final value), and where the value emerges as a sum of individual contributions. E.g. individual growth spurts, or individual cost contributions.
This is because then the central limit theorem kicks in.
It doesn't work if e.g. you only deal with positive values and the standard deviation is comparable in size to the typical value you have. Because then the distribution can't even be approximately symmetric.
If the value is also not a sum of smaller parts in any meaningful way, it's also doubtful if you get a Gaussian.
Often, the way a distribution arises gives a hint for what you deal with in aggregate, and it helps to know some other naturally arising distributions.
This is because then the central limit theorem kicks in.
It doesn't work if e.g. you only deal with positive values and the standard deviation is comparable in size to the typical value you have. Because then the distribution can't even be approximately symmetric.
If the value is also not a sum of smaller parts in any meaningful way, it's also doubtful if you get a Gaussian.
Often, the way a distribution arises gives a hint for what you deal with in aggregate, and it helps to know some other naturally arising distributions.