Pearson product-moment correlation coefficient

• Statistical simulation of the Pearson product-moment correlation coefficient with R-Project
  

   x1 <- c(rep(10,5),rep(25,5),rep(35,6),rep(45,10),rep(55,38) 
  ,rep(65,30) ,rep(75,20),rep(85,4),rep(95,2));
   
  cvp <- function(x) {
   ni<- table(x);
  n<-sum(ni);
  m1<- mean(x);
  s1 <-sd(x)*sqrt((n-1)/n);
  cv<- s1/abs(m1);
  cv
    }
  
  cvp(x1)
  
  [1] 12.52664
  
  

  
  
  
  

• Statistical simulation of the Pearson product-moment correlation coefficient with Mathematica
  

  x1 := Join[ConstantArray[10, 5], ConstantArray[25, 5], 
     ConstantArray[35, 6], ConstantArray[45, 10], ConstantArray[55, 38]
  , ConstantArray[65, 30], ConstantArray[75, 20], ConstantArray[85, 4]
  , ConstantArray[95, 2]];
     
  ni := Tally [x1];
  
  n := Sum[ni[[i, 2]], {i, Length[ni]}];
  
  m1:=Mean[x1]
  
  s1:=StandardDeviation[x1]  Sqrt[(n - 1)/n];
  
  cv:= (s1/Abs[m1])
  
  N[cv]
  
  0.297009