code: public static double standardDeviation(double[] x, double mean) {
          if (x.length == 0) {
              return Double.NaN;
          }
          if (x.length == 1) {
              return 0.0;
          }
          return Math.sqrt(variance(x, mean));
      }
docs: Computes the standard deviation of the vector using the given mean
  
  @param x
  @param mean is the mean value of x
  @return ` \sqrt{\mbox{variance}(x, \bar{x})} `