# Calculate average time

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?

• What would you like the average of the sample 00:00, 06:00, 12:00, 18:00 to be? – Did Jan 3 '12 at 12:08
• @DidierPiau: It would be ok if it would yield anything or undefined. However my data samples are rather huge so that would be rather unlikely. – Nihu Jan 3 '12 at 12:20
• My point is that you will stumble on the same problem with huge data samples, namely, these samples will be roughly evenly distributed on the unit circle. Then it is difficult to summarize the sample by anything else than a point near the center of the circle, which is meaningless because this will not be ON the circle... (Re-reading your post, I realize that even a median, whose existence you take for granted, seems difficult to define.) – Did Jan 3 '12 at 12:26

## 1 Answer

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.), [...]

• Unfortunately there is no such natural cutoff. However I'm interested in directional statistics. Do you know any starting ressources? – Nihu Jan 3 '12 at 12:27
• Maybe the WP page linked to... – Did Jan 3 '12 at 12:28