// sigma_errord.java show error for different methods (double) 

public class sigma_errord
{
  public sigma_errord()
  {
    double sigma1, sigma2;
    double x[] = new double[100];
    int n, i;
    n = 100;
    System.out.println("sigma_errord.java running, n="+n);

    for(i=0; i<n; i++)
      x[i] = (double)(i+1);
    System.out.println("x 1 .. 100 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)^2/n  sigma2 = "+sigma2);

    for(i=0; i<n; i++)
      x[i] = 10.0*(double)(i+1);
    System.out.println("x 10 .. 1000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 = "+sigma2);

    for(i=0; i<n; i++)
      x[i] = 100.0*(double)(i+1);
    System.out.println("x 100 .. 10000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)^2/n  sigma2 = "+sigma2);

    for(i=0; i<n; i++)
      x[i] = 1000.0*(double)(i+1);
    System.out.println("x 1000 .. 100000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)^2/n  sigma2 = "+sigma2);

    for(i=0; i<n; i++)
      x[i] = 10000.0*(double)(i+1);
    System.out.println("x 10000 .. 1000000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)^2/n  sigma2 = "+sigma2);

    for(i=0; i<n; i++)
      x[i] = 10000.0+(double)(i+1);
    System.out.println("x 10001 .. 10100 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)^2/n  sigma2 = "+sigma2);

  } // end sigma_errord

  double stddeva(int n, double x[])
  {
    double sdev, sumx2, sumx, rn;
    int i;

    rn = (double)n;
    sumx2 = 0.0;
    sumx = 0.0;
    for(i=0; i<n; i++)
    {
      sumx = sumx + x[i];
      sumx2 = sumx2 + x[i]*x[i];
    }
    sdev = Math.sqrt((sumx2 - sumx*sumx/rn)/rn);
    return sdev;
  } // end stddeva

  double stddevb(int n, double x[])
  {
    double sdev, mean, sum2, rn;
    int i;

    rn = (double)n;
    mean = 0.0;
    sum2 = 0.0;
    for(i=0; i<n; i++)
      mean = mean + x[i];
    mean = mean/rn;
    for(i=0; i<n; i++)
      sum2 = sum2 +(x[i]-mean)*(x[i]-mean);
    sdev = Math.sqrt(sum2/rn);
    return sdev;
  } // end stddevb

  public static void main (String[] args)
  {
    new sigma_errord();
  }
} // end sigma_errord.java