Percentile on Fortran

[Ahn210]

Hello-

Can someone teach me how to get percentile value given a sorted array data?

Data
2.56
2.44
1.2
0.99
0.76
0.36
0.35
0.32
0.22
0.11
0.09
0.031

I wish to find 70th and 30th percentile value
(0.921 // 0.25 got from excel)

 

[mikrom]

IMO: You have population of n=12 data values
Then 30 percentile is quantile for p=0.3; n*p = 12*0.3 = 3.6 => rounded up = 4, i.e. 4th element in the population, i.e. 0.99

Similarly, 70 precentile is 0.7 quantile: n*p = 12*0.70 = 8.4 => rounded up = 9, i.e. 9th element in the populatiom, i.e. 0.22

 

[mikrom]

I forgot the link here:

https://en.wikipedia.org/wiki/Quantile

 

[mikrom]

Here is the better link which explains Excel interpolation formula:

http://en.wikipedia.org/wiki/Percentile#Alternative_methods

For example - according to the formula given above:
70th percentile:
N=12, P = 70, n = P *(N-1)/100 + 1 = 70*11/100 + 1 = 8.7 = 8 + 0.7
Then v[sub]70[/sub] = v[sub]8[/sub] + 0.7*(v[sub]9[/sub] - v[sub]8[/sub]) = 0.32 + 0.7*(0.22 - 0.32) = 0.25

30th percentile:
N=12, P = 30, n = P *(N-1)/100 + 1 = 30*11/100 + 1 = 4.3 = 4 + 0.3
Then v[sub]30[/sub] = v[sub]4[/sub] + 0.3*(v[sub]5[/sub] - v[sub]4[/sub]) = 0.99 + 0.3*(0.76 - 0.99) = 0.921

 

[Ahn210]

To mikrom
Thanks for your reply; I always appreciate your posts! explanation on excel percentile was what I needed to apply that on fortran.