for (@_) { @differences = (@differences, (($_-$mean)*($_-$mean))); } To my eye,

  foreach ( @_ ) {
      push @differences, $_ - $mean;
  }
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reads better.

In the fragment

   my $standard = 0;
   for (@differences) { $standard = $standard + $_; }
   $standard = sqrt($standard/$sample_size);
   return $standard;
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you use $standard for two semantically different (though related) purposes. Having variables that mean two (or more) different things within a subroutine can get you into trouble later (say, when you pick up the code a couple of months from now). You can eliminate this problem by writing

  my $sum_diff = 0;
  map { $sum_diff += $_ } @differences;
  return sqrt($sum_diff / $sample_size);
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You might also consider using 4 spaces for indentation.

And at some point, somebody is going to pass an empty list...