the quantile function and problems.

Hi 

I am very acquainted with R. I use it occasionally via the org-babel library of GNU emacs.

I wanted to check the first, second and third quartiles of the scientific science index JCR
https://support.clarivate.com/ScientificandAcademicResearch/s/article/Journal-Citation-Reports-Quartile-rankings-and-other-metrics?language=en_U
S 
Its criterion is 
#+begin_src 
| Quartil | range             |                                       |
| ---------+------------------+---------------------------------------|
| Q1      | 0.0 < Z \leq 0.25 | Highest ranked journals in a category |
| Q2      | 0.25 < Z \leq 0.5 |                                       |
| Q3      | 0.5 < Z \leq 0.75 |                                       |
| Q4      | 0.75 < Z          | Lowest ranked journals in a category  |
#+end_src

Z=(X/Y)

Where X is the journal rank in category and Y is the number of journals in the category.

Now I have a list of 267 journals.

What turns me crazy is that the way R, matlab and the JCR calculate the quartiles gives different results.

Here is a table 
#+begin_matlab :exports both :eval never-export :results output latex
#+RESULTS:
| quartil-limit (last member) |    | floor_Rlang | jcr | jcr_check | floor_check |
|-----------------------------+----+-------------+-----+-----------+-------------|
|                        67.5 | Q1 |          67 |  66 |    0.2472 |      0.2509 |
|                         134 | Q2 |         134 | 133 |    0.4981 |      0.5019 |
|                       200.5 | Q3 |         200 | 200 |    0.7491 |      0.7491 |
|                         267 |    |         267 | 267 |         1 |           1 |
#+TBLFM: $5=$4/267::$6=$3/267
#+end_matlab

I calculated using R (I don't provide the vector from 1 to 267)

#+begin_src R :colnames t :var t1=jcr22
  quantile(t1$Data,c(1/4,1/2,3/4,1))
#+end_src
#+begin_src 
#+RESULTS:
|     x |
|-------|
|  67.5 |
|   134 |
| 200.5 |
|   267 |
#+end_src

So you see the problem with Q1 and Q2.

On top of that matlab gives

#+begin_src matlab :exports results :eval never-export :results output latex
format short
x=1:267;
q1 = quantile(x,1/4);
q2 = quantile(x,1/2);
q3 = quantile(x,3/4);
Q=[q1; q2; q3];
sprintf('|%g|   \n', Q)
#+end_src

#+RESULTS:
#+begin_export latex
|67.25|   
|134|   
|200.75|   
#+end_export

Which is also slightly different from R.

Can anybody enlighten me please?
Thanks and regards 

Uwe Brauer