Calculate Average AWK

I want to calculate the average line by line of some files with several lines on them, the files are identical, just want to average the 3rd columns of those files.:wall:
Example file:

File 1

001     0.046   0.667267
001     0.047   0.672028
001     0.048   0.656025
001     0.049   0.660557

002     0.000   0.669553
002     0.001   0.594648
002     0.002   0.586738
002     0.003   0.593728
002     0.004   0.593658

File 2

001     0.046   0.654565
001     0.047   0.665057
001     0.048   0.660074
001     0.049   0.670424

002     0.000   0.669462
002     0.001   0.594793
002     0.002   0.589329
002     0.003   0.593949
002     0.004   0.592371

Desired Output

001     0.046   Average of the nth line from the two files
001     0.047   Average of the nth line from the two files
001     0.048   Average of the nth line from the two files
001     0.049   Average of the nth line from the two files

002     0.000   Average of the nth line from the two files
002     0.001   Average of the nth line from the two files
002     0.002   Average of the nth line from the two files
002     0.003   Average of the nth line from the two files
002     0.004   Average of the nth line from the two files

Hi,

Test next 'perl' script:

$ cat script.pl
use strict;
use warnings;
use autodie;

@ARGV == 2 or die "Usage: perl $0 file-1 file-2\n";
open my $fh1, "<", $ARGV[0];
open my $fh2, "<", $ARGV[1];

my ($f1, $f2, @f1, @f2);

while ( $f1 = <$fh1> ) {
        $f2 = <$fh2>; 
        do { print "\n"; next } if $f1 =~ /^\s*$/ || $f2 =~ /^\s*$/;
        chomp( $f1, $f2 );
        @f1 = split /\s+/, $f1;
        @f2 = split /\s+/, $f2;
        printf "%s\t%s\t%.6f\n", $f1[0], $f1[1], ($f1[2] + $f2[2]) / 2;
}

close $fh1;
close $fh2;
$ perl script.pl infile1 infile2
001     0.046   0.660916
001     0.047   0.668543
001     0.048   0.658049
001     0.049   0.665490

002     0.000   0.669507
002     0.001   0.594720
002     0.002   0.588033
002     0.003   0.593838
002     0.004   0.593014

Regards,
Birei

---------- Post updated at 05:27 PM ---------- Previous update was at 05:17 PM ----------

I'm not familiar with perl, my filenames follow this sequence and are seven, Stat-zz.dat, zz goes from 00 to 07, i need the average of the seven files, can I put the seven files in your script input?