Variance of the marginal distributions

• Statistical simulation of the Variance of the marginal distributions de x and y with R-Project
  

  x1<- c(rep(15,4),rep(20,3),rep(25,1),rep(15,1),rep(20,4),rep(25,7));
  y1<- c(rep(5,4),rep(5,3),rep(5,1),rep(10,1),rep(10,4),rep(10,7));
  x2<- (x1-15)/5;
  y2<- (y1-5)/5;
  ni<- table(x1);
  n<-sum(ni);
  vx1 <-var(x1)*(n-1)/n
  vx1
  [1] 15.6875
  
  vy1 <-var(y1)*(n-1)/n
  vy1
  [1] 6
  
  vx2 <-var(x2)*(n-1)/n
  vx2
  [1] 0.6275
  
  vy2 <-var(y2)*(n-1)/n
  vy2
  [1] 0.24
  
  vy2*5^2
  [1] 6
  
  vx2*5^2
  [1] 15.6875
  
  

  
  
  
  

• Statistical simulation of the Variance of the marginal distributions of x and y with Mathematica
  

  x1 := Join[ConstantArray[15,4],ConstantArray[20,3], 
     ConstantArray[25,1],ConstantArray[15,1],ConstantArray[20,4], 
     ConstantArray[25,7]];
  
  y1 := Join[ConstantArray[5,4],ConstantArray[5,3], 
     ConstantArray[5,1],ConstantArray[10,1],ConstantArray[10,4], 
     ConstantArray[15,7]];    
  

  x2:=(x1-15)/5;
  y2:=(y1-5)/5; 
     
  ni := Tally [x1];
  
  n := Sum[ni[[i, 2]], {i, Length[ni]}];
  
  vx1:=(Variance[x1] (n - 1))/n;
  vx2:=(Variance[x2] (n - 1))/n;
  vy1:=(Variance[y1] (n - 1))/n;
  vy2:=(Variance[y2] (n - 1))/n;
  
  
  N[vx1]
  N[vx2]
  N[vy1]
  N[vy2]
  N[vx2 5^2]
  N[vy2 5^2]
  
  
  15.6875
  0.6275
  18.6875
  0.7475
  15.6875
  18.6875