A late TMTOWTDI , perhaps not rock-solid:

#!/usr/bin/env perl

use strict;
use warnings;
use List::MoreUtils qw(natatime);
use List::Util qw(reduce);
use IO::All;
use autodie;

my $file     = shift;
my $amount   = 2;
my $io       = io $file;
my $iterator = natatime $amount, @$io;

while ( my @items = $iterator->() ) {
    my @values = map { /^.+\|(.+)$/ } @items;
    my $sum = reduce { $a + $b } @values;
    my $average = $sum / $amount;
    print qq($average\n);
}

__END__
[download]

Update: I took the title of your OP ("...take 'n' at a time...") literally. Or i tried it, at least ;-)

Regards, Karl