Standard Deviation

The standard deviation goes something like the variance.

• Statistical simulation of the standard deviation with R-Project
  

  > x <- c(rep(47,1),rep(48,3),rep(49,2),rep(50,8),rep(51,3),rep(52,2)
  ,rep(53,1));
  
  > ni<- table(x);
  
  > n<-sum(ni)
  
  > sqrt((n-1)/n)*sd(x)
  
  [1] 1.465435
  

  
  
  
  

• Statistical simulation of the standard deviation with Mathematica
  

  x := Join[ConstantArray[47, 1], ConstantArray[48, 3], 
     ConstantArray[49, 2], ConstantArray[50, 8], ConstantArray[51, 3], 
     ConstantArray[52, 2], ConstantArray[53, 1]];
     
  ni := Tally [x];
  
  n := Sum[ni[[i, 2]], {i, Length[ni]}];
  
  N[StandardDeviation[x] Sqrt[(n - 1)/n]]
  
  1.4654350889752845`