I compared the join of (chr, location), to determine the end of a run instead of just location by itself.

#!/usr/bin/perl
use strict;
use warnings;
use List::Util qw/ sum /;

chomp(my $line = <DATA>);
my $prev_chr_loc = join "-", (split /\t/, $line)[1,2];

my @lines = $line;

while (my $line = <DATA>) {
    chomp $line;
    my $chr_loc = join "-", (split /\t/, $line)[1,2];
    
    if ($chr_loc eq $prev_chr_loc) {
        push @lines, $line;
    }
    else {
        print "$_\n" for compute_avg( @lines );
        @lines = $line;
    }
    $prev_chr_loc = $chr_loc;
}

print "$_\n" for compute_avg( @lines );

sub compute_avg {
    my @lines = @_;
    
    my $avg_col5 = sprintf "%.9f",
        sum(map {(split /\t/)[5]} @lines) / @lines;
            
    my $avg_col6 = sprintf "%.9f",
        sum(map {(split /\t/)[6]} @lines) / @lines;
        
    for (@lines) {
        my ($c5,$c6) = (split /\t/)[5,6];
        s/$c5\t$c6$/$avg_col5\t$avg_col6/;
    }
    return @lines;
}
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Update: Redid substitution for closer spec.