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 p th percentile is a value such that at most (100 p )% 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. 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.

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

Note: One quartile is equivalent to 25 percentile while 1 decile is equal to 10 percentile.