'******************************************************
'*        Computing the statistical functions         *
'*             for one or two variables               *
'*                                                    *
'* -------------------------------------------------- *
'* REFERENCE:  "Mathematiques et statistiques By H.   *
'*              Haut, PSI Editions, France, 1981"     *
'*              [BIBLI 13].                           *
'* -------------------------------------------------- *
'* SAMPLE RUN:                                        *
'*                                                    *
'* TUTORIAL                                           *
'*                                                    *
'* 1. Define type of calculus:"                       *
'*    1: Statistical functions for a set X(i)         *
'*    2: Statistical functions for a set X(i), Y(i)   *
'*                                                    *
'* 2. Input number n of data                          *
'*                                                    *
'* 3. Input successively the n values X(i) [and Y(i)] *
'*                                                    *
'* Type of calculus (1 or 2): 2                       *
'*                                                    *
'* Number of data: 5                                  *
'*                                                    *
'*   1 ?  1 12                                        *
'*   2 ?  2 9                                         *
'*   3 ?  3 7                                         *
'*   4 ?  4 15                                        *
'*   5 ?  5 6                                         *
'*                                                    *    
'*                                                    *
'* Mean of X(i)....................: 3                *
'*                                                    *
'* (n-1) standard deviation of X(i): 1.58113883       *
'*   (n) standard deviation of X(i): 1.41421356       *
'*                                                    *
'* (n-1) standard dev. of X mean...: .707106782       *
'*   (n) standard dev. of X mean...: .632455532       *
'*                                                    *
'* Mean of Y(i)....................: 9.80000000       *
'*                                                    *
'* (n-1) standard deviation of Y(i): 3.70135111       *
'*   (n) standard deviation of Y(i): 3.31058908       *
'*                                                    *
'* (n-1) standard dev. of Y mean...: 1.65529454       *
'*   (n) standard dev. of Y mean...: 1.48054045       *
'*                                                    *
'*                                                    *
'* (n-1) covariance of X,Y.........: -1.5             *
'*   (n) covariance of X,Y.........: -1.2             *
'*                                                    *
'* Correlation coefficient.........: -.256307296      *
'*                                                    *
'******************************************************
'Description: This program computes the usual statistical functions
'             for a set of n variables X(i) or for a set of n pairs
'             X(i), Y(i).
defint i-n
defdbl a-h,o-z

cls
print
print " TUTORIAL"
print
print " 1. Define type of calculus:"
print "    1: Statistical functions for a set X(i)"
print "    2: Statistical functions for a set X(i), Y(i)"
print
print " 2. Input number n of data"
print
print " 3. Input successively the n values X(i) [and Y(i)]"
print
input " Type of calculus (1 or 2): ", nt
print
input " Number of data: ", n
print
dim X(n)
if nt=2 then dim Y(n)
'read n data
for i=1 to n
  print "  "; i;"  ";
  if nt=1 then input X(i)
  if nt=2 then input X(i), Y(i)
next i

'call subroutine 1000
gosub 1000

'print results
print
print " Mean of X(i)....................: "; v1
print
print " (n-1) standard deviation of X(i): "; a3
print "   (n) standard deviation of X(i): "; a5
print
print " (n-1) standard dev. of X mean...: "; v3
print "   (n) standard dev. of X mean...: "; v5
print
if nt=1 then end
print " Mean of Y(i)....................: "; v2
print
print " (n-1) standard deviation of Y(i): "; a4
print "   (n) standard deviation of Y(i): "; a6
print
print " (n-1) standard dev. of Y mean...: "; v4
print "   (n) standard dev. of Y mean...: "; v6
print
print
print " (n-1) covariance of X,Y.........: "; v7
print "   (n) covariance of X,Y.........: "; a7
print
print " Correlation coefficient.........: "; v8
print
end

1000 'Subroutine of statistical functions for 1 or 2 variables
'*****************************************************
'* INPUTS:                                           *
'*         nt: type of calculus =1 for one variable  *
'*                              =2 for two variables *
'*          n: number of data X(i) [and Y(i) ]       *
'* OUTPUTS:                                          *
'*         v1: mean of X(i)                          *
'*         v2: mean of Y(i)                          *
'*         v3: (n-1) standard deviation of v1        *
'*         v4: (n-1) standard deviation of v2        *
'*         v5:   (n) standard deviation of v1        *
'*         v6:   (n) standard deviation of v2        *
'*         v7: (n-1) covariance of X,Y               *
'*         v8: correlation coefficient               *
'*         a3: (n-1) standard deviation of X         *
'*         a4: (n-1) standard deviation of Y         *
'*         a5:   (n) standard deviation of X         *
'*         a6:   (n) standard deviation of Y         *
'*         a7:   (n) covariance of X,Y               *
'*****************************************************
  v1=0# : v2=0# : v3=0# : v4=0# : v5=0#
  n1=n-1 : xnr=SQR(n)
  'choose type of calculus
  if nt=2 then goto 500
  'case of one set X(i)
  for i=1 to n
    v1=v1+X(i)
    v3=v3+X(i)^2
  next i
  v6=v3-v1*v1/n
  v1=v1/n
  a3=SQR(v6/n1) : a5=SQR(v6/n)
  v5=a5/xnr : v3=a3/xnr
  return
500 'case of a set X(i), Y(i)
  for i=1 to n
    v1=v1+X(i)
    v2=v2+Y(i)
    v3=v3+X(i)^2
    v4=v4+Y(i)^2
    v5=v5+X(i)*Y(i)
  next i
  v6=v3-v1*v1/n
  v7=v4-v2*v2/n
  v8=v5-v1*v2/n
  v1=v1/n : v2=v2/n
  a3=SQR(v6/n1) : a4=SQR(v7/n1)
  a5=SQR(v6/n) : a6=SQR(v7/n)
  v7=v8/n1 : a7=v8/n
  v3=a3/xnr : v4=a4/xnr
  v5=a5/xnr : v6=a6/xnr

  if (a3=0) or (a4=0) then return 'correlation coefficient not defined
  v8=v8/(n*a5*a6)
return

'end of file fstat.bas