You need to iterate twice. However the following version should be slightly faster and I think is numerically more stable:

sub std_dev {
  my ($sum, $sqr_sum);
  for (@_) {
    $sum += $_;
    $sqr_sum += $_ * $_;
  }
  sqrt(($sqr_sum - $sum * $sum / @_)/@_);
}
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And, of course, if your set of numbers is a sample set from a random distribution, the standard deviation of the numbers is a biased predictor of the true standard deviation, so you may prefer the following:

# Produces an unbiased estimate of a standard deviation
# from a sample
sub std_dev_samp {
  my ($sum, $sqr_sum);
  for (@_) {
    $sum += $_;
    $sqr_sum += $_ * $_;
  }
  sqrt(($sqr_sum - $sum * $sum / @_)/$#_);
}
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