use two hashes, one for totals an other for counters, them use two loops, one to populate these hashes and other to calculate the averages as total/counter:

my @sequence = ('actg','actg','cggt','cggt');
my @numbers = ('1234','2345','3244','3455');

my (%total, %count, $i);
for ($i=0; $i<@sequence; $i++) {
   $total{$sequence[$i]}+=$numbers[$i];
   $count{$sequence[$i]}++;
}

for (sort keys %total) {
  my $avg=$total{$_}/$count{$_};
  print "$_ avg: $avg\n";
}
[download]