I'm aware that when a quantile is mentioned, it may mean a point or it may mean a group. But i'm not asking about the quantile points.
In the case where it means a group, then there seem to be two meanings..
I'd like to confirm that there are these two meanings for a quantile group.
One is they overlap, smaller within larger, and another is they don't overlap and they are equal size. (I'll explain what I mean).
Note that I understand that with percentiles, then if talking points, you'd have 99 points(Excluding min/max %), and 101(including min/max %).
I notice that this wikipedia page on percentile https://en.wikipedia.org/wiki/Percentile says "every score is in the 100th percentile"
So that seems to be a definition of a percentile group that goes from 0 all the way to that point. So smaller percentile groups exist within larger ones.
Whereas another definition of a quantile group, is used when one refers to "lower quartile" and "upper quartile". In that instance, you have two quartiles of equal percentage size(25% each). And another two quartile groups, the lower-middle quartile and the upper-middle quartile.
Whereas wikipedia mentions the 100th percentile (group) as being not 1% in size, but 100% in size.
Am I correct here that there are these two different definitions of quantile group?
As a side note, I suppose if you have equal sized groups you'd have 100 groups.. Whereas if you have groups going from 0 up to whatever point, then you'd have 101 groups. So that'd be another difference that occurs depending on which definition of quantile group is in use.