No need to open a new thread on this related topic, i just want to get this out:
The histogram functions in Mathematica use the right-continuous
$[b1,b2),[b2,b3),[b3,b4),…$ bin specification for determining which bin a number on the border belongs to. My textbook defines them the other way, namely "left-continuous"
$(b1,b2],(b2,b3],(b3,b4],…$ for a good reason: when you have "data" given in form of classes and their counts (absolute frequency) and want to approximate its empirical distribution function by a normal distribution, then the bins can be interpreted as perfect representations of those classes … as long as the right border of the bin is included: A distribution function is always defined for
$X\leq x$ as in
$P(X\leq x)$. From this we can see that the right border is included.
$$P(X\leq x)\approx \phi \left(\frac{x-\mu }{\sigma }\right)$$
I am working on six similar textbook problems and the classes (other word: intervals) are always defined such that the left border is excluded, the right border is included. I found an undocumented way of inputting these classes directly into Mathematica and i am realizing, as i am writing, that the mentioned lamentable bin specification is built-in and could not be altered, not even in future as an option (or maybe global system setting?).
If i am the first ever to complain about this situation, then maybe it isn't of any concern in practice (outside of textbook problems) or practitioners don't care. I just wished that the user had the flexibility to set that bin specification. If i there are more other sources, books, profs, maples, matlabs, youtubes, wikis, several important sources/references etc using the bin specification which i am looking for, then it's maybe motivation enough for Wolfram to offer such an option to the end user, in future.
Of course, it is an arbitrary thing. The same author (of a table, of a book, of article) could define the classes to be right-continuous for problem 3 and to be left-continuous for problem 11, or even mix them. But the mentioned representation/interpretation of (cumulative) classes of an empirical distribution function CDF is a strong argument for my case.