Standard Deviation

• Statistical simulation of the standard deviation 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));
   
   ni<- table(x1);
  n<-sum(ni);
  s1 <-sd(x1)*sqrt((n-1)/n)
  s1
  [1] 12.52664
  

  
  
  
  

• Statistical simulation of the standard deviation 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]}];
  
  s1:=StandardDeviation[x1]  Sqrt[(n - 1)/n];
  
  N[s1]
  
  17.090