Listing 3. After Elimination of the Mean Function

sub std_dev_ref_sum {
  my $ar = shift;
  my $elements = scalar @$ar;
  my $sum = 0;
  my $sumsq = 0;
  
  foreach (@$ar) {
    $sum += $_;
    $sumsq += ($_ **2);
  }
  return sqrt( $sumsq/$elements - 
               (($sum/$elements) ** 2));
}
