calculate average from range of hash values (optimize)

[revdiablo]

Hello fair Monks. I am calculating the average of a given range of hash values. For example, given a hash like so:

%hash = (
  100 => '1',
  101 => '23',
  102 => '4',
  ...
  200 => '75'
);

I'd want to, say, calculate the average of the values at keys 100 to 125. I have a routine that does what I want, but it seems to be a bit slow. I can't think of any major optimizations (other than switching to an array, which isn't a good idea, since the hash keys are relatively large numbers). Perhaps someone has some ideas?

Here is my existing code:

#!/usr/bin/perl
use strict;
use warnings;
use Benchmark qw(cmpthese);

my $data = {};

$data->{$_} = rand for (10000 .. 30000);

print average($data, 15000, 25000), "\n";

cmpthese(50, { orig => sub { average($data, 15000, 25000) } });

sub average {
    my ($data, $start_point, $end_point) = @_;

    my @keys = sort keys %{ $data };

    my $start_pos;
    my $end_pos;
    for (0 .. $#keys) {
        $start_pos = $_ if $keys[$_] eq $start_point;
        $end_pos   = $_ if $keys[$_] eq $end_point;
    }
    return undef unless defined $start_pos and defined $end_pos;

    my $count = $end_pos - $start_pos + 1;
    my $amount;
    $amount += $data->{$keys[$_]} for ($start_pos .. $end_pos);

    return $amount / $count;
}

Any help or ideas will be greatly appreciated. In case anybody wonders, I am using this routine to determine a moving average. I am running it many times against barely-differing ranges, so it slows down fairly quickly.