... # your code thru the definition of sub circ_avg;

print "@times";
print "            => circle vs line";
print "            => @{[angle2time circ_avg time2angle @times]} vs @{[angle2time( sum( time2angle @times ) / @times ) ]}";

for (; @times > 1; shift @times) {
    my @t = @times[0, 1];
    print "@t => @{[angle2time circ_avg time2angle @t]} vs @{[angle2time( sum( time2angle @t ) / @t ) ]}";
}

__END__
__OUTPUT__
17:00 19:00 11:00 13:00 23:00 01:00 10:30 13:00 19:40 01:20 16:00 02:00
            => circle vs line
            => 17:46 vs 12:12
17:00 19:00 => 18:00 vs 18:00
19:00 11:00 => 15:00 vs 15:00
11:00 13:00 => 12:00 vs 12:00
13:00 23:00 => 18:00 vs 18:00
23:00 01:00 => 00:00 vs 12:00
01:00 10:30 => 05:45 vs 05:45
10:30 13:00 => 11:45 vs 11:45
13:00 19:40 => 16:20 vs 16:20
19:40 01:20 => 22:30 vs 10:30
01:20 16:00 => 20:40 vs 08:40
16:00 02:00 => 21:00 vs 09:00