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More specifically, why should the hourly average visit duration graph look like this: google analytics hourly visit duration

It's as if there's some sort of daily artefact in the data or method of calculation. This pattern doesn't appear in any other graphs.

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https://support.google.com/analytics/answer/1006253?hl=en explains how they compute the average visit duration: in short the formula is (The time of the first hit on the last page - the first hit on the first page) / (number of visited pages).

Regarding your second question pertaining to your graph, try http://stackoverflow.com/q/15841370/395857

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