Percentile

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

Thanks Badri. That definitely helps!!

Please correct my previous answer:

99th Percentile: (99/100)*15 = 14.85 --> the 15th number (45) is the 99th percentile [14.85 numbers (99%) are EQUAL OR below the 15th number]

80th Percentile: (80/100)*15 = 12 --> 12th number (37) is 80th percentile [12 numbers (80%) are EQUAL OR below the 12th number]

60th Percentile: (60/100)*15 = 9 --> 9th number (33) is 60th percentile [9 numbers (60%) are EQUAL OR below the 9th number]


Here is the Wikipedia definition of 'percentile'

In descriptive statistics, using the percentile is a way of providing estimation of proportions of the data that should fall above and below a given value. The pth percentile is a value such that at most (100p)% of the observations are less than this value and that at most 100(1 − p)% are greater. (p is a value between 0 and 1)

Thus:

* The 1st percentile cuts off lowest 1% of data
* The 98th percentile cuts off lowest 98% of data

The 25th percentile is the first quartile; the 50th percentile is the median.

One definition is that the pth percentile of n ordered values is obtained by first calculating the rank k = \frac{p(n+1)}{100}, rounded to the nearest integer and then taking the value that corresponds to that rank.[1] One alternative method, used in many applications, is to use a linear interpolation between the two nearest ranks instead of rounding.

Linked with the percentile function, there is also a weighted percentile, where the percentage in the total weight is counted instead of the total number. In most spreadsheet applications there is no standard function for a weighted percentile.

[edit] Relation between percentile, decile and quartile

1.) P25 = Q1

2.) P50 = D5 = Q2

3.) P75 = Q3

4.) P100 = D10 = Q4

5.) P10 = D1

6.) P20 = D2

7.) P30 = D3

8.) P40 = D4

9.) P60 = D6

10.) P70 = D7

11.) P80 = D8

12.) P90 = D9