Try Time::Duration::Parse, Time::Duration, and List::Util:

use strict;
use warnings;
use Time::Duration::Parse qw(parse_duration);
use Time::Duration qw(duration);
use List::Util qw(sum);

my @times = <DATA>;
my $count = @times;
my $sum   = sum map { parse_duration($_) } @times;
my $avg   = $sum / $count;

print duration($sum, 3), "--Total Time\n";
print duration($avg, 3), "--Avg Time\n";

__DATA__
2:11:20
2:07:44
2:18:41
0:40:17
2:40:53
1:27:21
4:03:43
1:54:42
1:59:40
2:08:49
2:12:21
[download]

prints

23 hours, 45 minutes, and 31 seconds--Total Time
2 hours, 9 minutes, and 35 seconds--Avg Time
[download]

Or just split each string and do the math yourself. And be sure to check for blank or not-valid strings.