I would like to understand if it is possible to rank graduate schools in the US and/or Canada by the entry/admission standards/requirements (this could be based on GPA/GRE/etc). While it seems that the common university rankings do not provide this type of information for graduate schools, perhaps, there exist some publicly available data sets. I tried looking around and I noticed that some individual universities (or departments) provide this type of information, but this is not very common. I am only interested in the STEM fields and I do not mind if the information is partial (e.g. only Mathematics departments in Canada).
I also put this comment on another question. Such a ranking is not possible.
This is a long comment, not an answer, but I often see this misconception in particular with students from India considering graduate admissions in the US.
Graduate admissions in the US are decided by committees of professors in the department that will admit you. The professors will read your application, and then they will make a collective, subjective, judgement about which students are most likely to succeed in the program, and admit those students. There are no other criteria. Different professors may have different opinions based on their own experiences of what indicators make a student likely to be successful (and different definitions of success!), but these tend to average out in committee discussions.
This seems strange to someone from India, where these kinds of decisions tend to get made based on some formula involving various numerical criteria. You might complain that the US system is subject to bias from the professors and even possible corruption. It is, but in the US we have decided that the benefit of being able to take into account subtle, unmeasurable considerations outweighs (in our context) the disadvantages of bias and the risk of corruption.
It is, of course, possible to make some generalizations about whom committees tend to admit and what they tend to consider in admissions, but these are predictions about human behavior, not rules.