"The past day" can mean either yesterday or the previous 24 hours. The survey that went out to students was probably something like: How many hours did you spend playing sports yesterday? But the article is talking about the survey after it happened, so if the article used "yesterday" you would think it meant your (the reader's) yesterday. Instead they use "the past day" to indicate it was the survey-taker's yesterday, at the time they completed the survey.
As others have pointed out, there is ambiguity; the term might refer to the 24 hours immediately preceding the time when the survey-taker is answering the question, or it might refer to the most recent complete midnight-to-midnight 24-hour period. From the context of the article (a secondary source) it is not clear which is meant. Personally, if I were designing the survey I would use "yesterday."
The term "the past day" does not refer to any arbitrary day in the past, except in the sense that the day the survey was handed out may have been arbitrary. "A previous day" carries that sense of arbitrariness, which means it would not be good to use in a statistical survey (which is supposed to be a snapshot in time, and all survey-takers should be answering for the same time period).