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Attached is a spreadsheet containing the number of people in different queues on NA sampled once every minute. This is possible because when a person joins a queue, the approximate wait time and number of people in queue is returned if you successfully join. So I wrote a script that polls queues for their populations every minute.
The intention was to find out the approximate relative popularity of each of the modes.
NOTE: The number of games currently going on is not reflected in these numbers at all. It's simply the number of people in queue. NOTE2: Times are GMT -7 and there is a large gap when my script stopped working and I didn't notice. NOTE3: JabeBot returns a few queue sizes with the !queue command. It can't return as many because it can't join all the queues.