Some Firefox users opted into a study called "Week in the Life of a Browser" that recorded their browser usage; and while the researchers didn't record what users were doing or what sites they were visiting while they were in private mode, they did track when those users turned it on and off. They identified four daily spikes in usage.
The first is around lunchtime, then there's another right after people get home from work around 5:00 PM. Then there's a spike around 10:00 PM and a final, smaller one a couple hours after midnight.
The lunch break would seem to indicate that many office workers don't trust their resident IT guys not to look through their personal information and browsing history when they do non-work browsing. The after-work spike may be less explicable. You can probably formulate some ideas about the late night peaks.
The study determined the average private browsing session lasted 10 minutes, with the 25th percentile at four minutes and the 75th at 22 minutes.
