A part of my work at my day job needed calculating quartiles. I quickly coded a routine to find the required numbers. But when i checked the numbers through excel and then with Minitab. I was astonished, as for the same set of numbers, i was getting different quartiles results in these two software’s.

**Which one to trust?**

Excel gave a different Q1 and Q3 , while Minitab showed me another. So i googled and found this excellent paper discussing how different software’s calculate quartiles and why they **can and are** different..

With this clarification, i ended my day and came home. But knowing about this three methods of calculating quartiles, as soon as i reached home, i quickly code this following program to see how this work.

So here is the Fortran program that will calculate quartile in all the 3 methods describe in that document.

program quartile

! Fortran program to test the 3 methods of Quartile Calculation.

! Quartiles are calculated differently in EXCEL, Minitab and SAS method 5

! This program tests the 3 methods.implicit none

interface

subroutine sasm5(x,quart)

real*8 :: x(:),quart

end subroutinesubroutine sasm4(x,quart)

real*8 :: x(:),quart

end subroutinesubroutine excel(x,quart)

real*8 :: x(:),quart

end subroutine

end interfacereal*8 :: a,b,c,x(4),quart

data x/1.0d0,2.0d0,3.0d0,4.0d0/Print *, "Excel Method"

quart=0.25d0

call excel(x,quart)

print *,’ q1=’,quartquart=0.500d0

call excel(x,quart)

print *,’ Median=’,quartquart=0.750d0

call excel(x,quart)

print *,’ q3=’,quart

Print *, "Minitab Method"

quart=0.25d0

call sasm4(x,quart)

print *,’ q1=’,quartquart=0.500d0

call sasm4(x,quart)

print *,’ Median=’,quartquart=0.750d0

call sasm4(x,quart)

print *,’ q3=’,quartPrint *, "SAS Method 5"

quart=0.25d0

call sasm5(x,quart)

print *,’ q1=’,quartquart=0.500d0

call sasm5(x,quart)

print *,’ Median=’,quartquart=0.750d0

call sasm5(x,quart)

print *,’ q3=’,quartend

subroutine excel(x,quart)

implicit none

! Excel’s method to calculate quartiles.

! Based on discussion in this paper http://www.haiweb.org/medicineprices/manual/quartiles_iTSS.pdf

!real*8 :: x(:),quart,a,b,c

integer :: n,ibn=size(x)

a=(n-1)*quart

call getgp(a,b,c)ib=int(c)

!print *,n,a,b,c,ibquart= (1-b)*x(ib+1) +b*x(ib+2)

end

subroutine sasm4(x,quart)

implicit none

! Minitab’s method of calculating is the same as the SAS Method 4.

! Based on discussion in this paper http://www.haiweb.org/medicineprices/manual/quartiles_iTSS.pdf

!real*8 :: x(:),quart,a,b,c

integer :: n,ibn=size(x)

a=(n+1)*quart

call getgp(a,b,c)ib=int(c)

!print *,n,a,b,c,ibif((ib+1)>n) then

quart=(1-b)*x(ib) +b*x(n)

else

quart=(1-b)*x(ib) +b*x(ib+1)

end ifend

subroutine sasm5(x,quart)

! Calculate Quartiles using SAS Method 5

! This method is the default method of SAS and is based on the empirical distribution function.

! Based on discussion in this paper http://www.haiweb.org/medicineprices/manual/quartiles_iTSS.pdf

!

implicit none

real*8 :: x(:),quart,a,b,c,tol,diff

integer :: n,ibtol=1.e-8

n=size(x)a=n*quart

call getgp(a,b,c)ib=int(c)

!print *,n,a,b,c,ibdiff=b-0.0d0

if(diff <=tol) then

quart=(x(ib+1)+x(ib))/2.0d0

else

quart=x(ib+1)

end ifend

subroutine getgp(a,b,c)

! Subroutine to that returns the Right hand and Left hand side digits of a decimal number

real*8 :: a,b,cb=mod(a,1.0d0)

c=a-bend

wondering what is a quartile, visit http://en.wikipedia.org/wiki/Quartile

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