Averages/Mean time of day

Averages/Mean time of day is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A particular activity of bats occurs at these times of the day:

23:00:17, 23:40:20, 00:12:45, 00:17:19

Using the idea that their are twenty four hours in a day which is analogous to their being 360 degrees in a circle, map times of day to and from angles and using the ideas of Averages/Mean angle compute and show here the average time of the nocturnal activity to an accuracy of a second of time.