I recognize that there are many types of averages. That said, does "x per y" (e.g. visits per day) always refer specifically to the arithmetic mean?
For some context, I saw this recently where someone claimed the cited figure was actually in reference to a median. While I think it might have been OK to use the median when declaring something as an average, it seems to me that it is clearly wrong to denote anything besides the arithmetic mean with "x per y." This is highlighted by the common usage of "x/y" to indicate "x per y." Am I correct to always assume usage of the arithmetic mean here?
EDIT: Apparently my original post was not entirely clear. I am specifically referring to situations where y is unit of time, so clearly "x per y" is a frequency or a rate. I would always interpret it as the (arithmetic) mean frequency or mean rate. However, I saw somebody else interpret it as the median frequency (the median of the y discrete time intervals).