I am slightly confused w.r.t. to the exact definitions of quartile and percentile.
Considering, a dataset consisting integers 1 to 100, each of which is present exactly once.
i.e, the set {1,2,3,4,......100}
As per my current understanding, for quartile -
25.5= 1st quartile, 50.5= 2nd quartile (Median), 75.5= 3rd quartile
Whereas for percentile, (Percentile tells you what percentage of observations are beneath a particular observation)
26= 25th percentile, 51= 50th percentile, 75= 76th percentile
Is this understanding correct? Also, shouldn't quartile values and percentile values match at 25th, 50th and 75th percentile?
Additionally, if the set consisted of 100 observations, each of which was '100' i.e. 100 present 100 times, what would be the percentile of any 1 value of '100'?