Date:         Tue, 9 Sep 2003 13:42:58 +0100
Reply-To:     Roland <roland@RASHLEIGH-BERRY.FSNET.CO.UK>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Roland <roland@RASHLEIGH-BERRY.FSNET.CO.UK>
Organization: Universe Monitors
Subject:      stats question on quartiles

If I have a list of 20 values like this:
_val1=19
_val2=104
_val3=147
_val4=167
_val5=186
_val6=224
_val7=226
_val8=299
_val9=299
_val10=302
_val11=306
_val12=332
_val13=337
_val14=340
_val15=357
_val16=361
_val17=365
_val18=392
_val19=395
_val20=443

then when I do a proc univeriate and look at the Q3 and Q1 values it gives
me Q1=205 and Q3=359.

I would have thought it would be Q1=186 (fifth observation) and Q3=357 (15th
observation). Why is it averaging with the next observation along?



This is the code I ran if you want to copy and paste.

data test(keep=val);
  array _val {20} 8 (20*0);

  *- assign a random value to all the cells and display -;
  *- and calculate the sum and mean -;
  sum=0;
  min=9**99;
  max=0;
  ramax=dim(_val);
  do i=1 to 20;
    _val(i)=floor(ranuni(9)*500);
    put _val(i)=;
    sum=sum+_val(i);
    if _val(i)>max then max=_val(i);
    if _val(i)<min then min=_val(i);
  end;
  mean=sum/dim(_val);

  *- bubble sort the values -;
  top=ramax;
  swapdone=1;
  do while(top > 1 and swapdone);
    swapdone=0;
    do i=1 to (top-1);
      if _val(i)>_val(i+1) then do;
        store=_val(i+1);
        _val(i+1)=_val(i);
        _val(i)=store;
        swapdone=1;
      end;
    end;
    top=top-1;
  end;

  *- display the final sorted order and calculate more stats-;
  cssq=0;
  ussq=0;
  do i=1 to 20;
    ussq=ussq+_val(i)**2;
    cssq=cssq+(_val(i)-mean)**2;
    put _val(i)=;
    val=_val(i);
    output;
  end;
  var=cssq/(ramax-1);
  std=var**0.5;
  stdmean=std/ramax**0.5;
  covar=std/mean;
  range=max-min;
  if mod(dim(_val),2) then median=_val(floor(ramax/2));
  else median=(_val(ramax/2)+_val(ramax/2+1))/2;
  put sum= mean= median= min= max= ussq= cssq= var= std= stdmean= covar=
range=;
run;

proc univariate data=test;
  var val;
run;