The standard deviation calculation for test scores is incorrect. See http://hubpages.com/hub/stddev for how to calculate it correctly.

Note that there are 2 formulas which differ by whether to divide the sums by n or n-1. n-1 is preferred here for consistency with Excel and for example cited here: http://davidmlane.com/hyperstat/A16252.html

See also http://en.wikipedia.org/wiki/Standard_deviation (which refers to n rather than n-1).

The code in samigo thus has 2 errors:

- total is using the existing total score value as a starting point (instead of 0)
- the square root calculation is by n-1 rather than n.

/**
   * Calculate standard Deviation
   *
   * @param scores array of scores
   * @param mean the mean
   * @param total the total
   *
   * @return the standard deviation
   */
  private static double calStandDev(double[] scores, double mean, double total)
  {
    for(int i = 0; i < scores.length; i++)
    {
      total = total + ((scores[i] - mean) * (scores[i] - mean));
    }

    return Math.sqrt(total / scores.length);
  }