Not that complicated, really, although it does seem a bit silly to do trigonometry where simple arithmetic would suffice. 

#! /usr/bin/perl -wl

my @times = qw( 17:00 19:00 11:00 13:00 23:00 01:00
                10:30 13:00 19:40 01:20 16:00 02:00 );

# keep angles in range -pi .. pi
sub _PI () { 2 * atan2(1, 0) }
sub _TC () { 24 * 60 / (2 * _PI) }

sub time2angle {
    map {
        my ($h, $m) = split /:/;
        _PI - (60 * $h + $m) / _TC
    } @_
}
sub angle2time {
    map {
        my $m = int _TC * (_PI - $_);
        sprintf "%02d:%02d", $m / 60, $m % 60
    } @_
}

use List::Util qw( sum );
sub circ_avg { atan2 sum(map sin, @_), sum(map cos, @_) }

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

[download]

Thank you for the wikipedia link.

In reply to Re^2: Average start time handling midnight by oiskuu
in thread Average start time handling midnight by chrisjej

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