/****************************************************
Write a program that reads in the file numbers.txt
and prints out the standard deviation of the numbers 
there.  The file numbers .txt looks like this:

N = 3
DATA:	
67
61
82

I.e. there's a header that tells you how many numbers
are in the file, and then you get all the numbers.
Recall that the standard deviation is

      ______________________
     / -- n   
    /  \     (xi - ave)^2
   /    |    ------------
  /    /        n - 1
\/     -- i = 1

 ****************************************************/
#include <iostream>
#include <fstream>
#include <string>
using namespace std;

int main()
{
  // Open input file, read header, get N = # of int's
  ifstream IN("numbers.txt");
  char c;
  int N;
  string s;
  IN >> c >> c >> N >> s;

  // Create array A and read N int's from input
  int *A = new int[N];
  for(int i = 0; i < N; i++)
    IN >> A[i];

  // Cycle through array summing all the elements
  int sum = 0;
  for(int j = 0; j < N; j++)
    sum = sum + A[j];
  double average = double(sum)/N;

  // Cycle through the array summing the squares of
  // the elements minus the average
  double sqsum = 0;
  for(int j = 0; j < N; j++)
    sqsum = sqsum + (A[j]-average)*(A[j]-average);
  double stddev = sqrt(sqsum/(N-1));
  
  // Print out standard deviation
  cout << "The standard deviation is " << stddev << endl;

  return 0;
}