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Comment by roel_v | Hacker News Reader

For time, what would then be the average of let's say 3 and 9 o'clock? Center of the clock I presume, but what does that mean in terms of time? Or would you then need to define the average of several points in time as a non-point in time?

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You'd have to talk about a time vector, with your case being the zero-length vector, or "no preference". Then a vector with a longer extent would indicate a "strong preference". Something like the standard deviation or something in a linear measure, I guess.

Hand waving: I'm guessing that you could make a new vector from the average x and the average y. The direction would indicate the average time, and the length would indicate the certainty, so a length of zero would mean total uncertainty.

That's pretty much exactly right - the variance of the von mises distribution is essentially the length of the average vector.

http://en.wikipedia.org/wiki/Von_Mises_distribution

For 24-hours clock you should have said 6 and 18 hours.

How embarrassing - I initially had written a paragraph here pointing out how wrong you are and I was just seconds away from posting it before realizing you're right ;)

So yes you're right, to be consistent with the article and my reply elsewhere in this thread it should've been that. Luckily it seems that most posters managed to derive the underlying question from the circumstances ;)

0 o'clock could be interpreted as 12 o'clock too.

The GP explicitly specified a 24-hour clock face, plus even on a 12-hour clock the question would remain.

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