The problem is in your above_average sub. Perl flattens everything passed into one list. So, your @_ also contains the $average passed in. You should first remove $average using shift. Also, you should explicitly return your @final_list array. Change it to:

sub above_average  {
    my $average_num = shift;
    my @final_list;
    foreach $_ (@_) {
      if ($_ > $average_num) {
         push @final_list, $_
      }
    }
    return @final_list;
 }
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For more details, see perlsub