Generally:
In a distribution X is n-th percentile if at least n% of the numbers in the distribution sample are less than or equal to X.
For example:
(1)
Consider the number sequence
21, 22, 20, 34, 33, 23, 30, 27, 28, 29, 37, 36, 45, 40, 43
We have 15 numbers. We wish to find what is 99th percentile, what is 80th percentile, and what is 60th percentile.
They are in jumbled order; arrange them in decreasing/increasing order
20, 21, 22, 23, 27, 28, 29, 30, 33, 34, 36, 37, 40, 43, 45
99th Percentile: (99/100)*15 = 14.85 --> the 15th number (45) is the 99th percentile [14.85 numbers (99%) are below the 15th number]
80th Percentile: (80/100)*15 = 12 --> 13th number (40) is 80th percentile [12 numbers (80%) are below t he 13th number]
60th Percentile: (60/100)*15 = 9 --> 10th number (34) is 60th percentile [9 numbers (60%) are below the 10th number]
(2)
And now its very clear: Why the 100 percentile does not exist?
Because, generally, in a distribution 100% numbers (all the numbers) cannot be below of equal to a number.
Hope it helps you.
Regards
