I have a huge list of times and would like to calculate an average or typical time. If I would just use the median (or other "normal" types of calculating an average), for example 23:59 and 00:01 would yield 12:00 when it should 00:00. Is there a better method?
I see two approaches for this. If there's some time of day when nothing happens, e.g. 4 a.m., you can let the wraparound occur at that time; for instance times from 1 a.m. to 4 a.m. would become times from 25:00 to 28:00.
If there's no such natural cutoff, you could use directional statistics; from the Wikipedia article:
Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), [...]