My friend/coworker and I got into a pretty heated discussion about a label for a graph I had made and the units I was using. We work in internet advertising where there is a type of unit (I consider it a unit anyway) called a "CPM" (Cost Per Million, in dollars usually). To give some visualization to some data we're collecting, I made a line graph to see CPM over Time (seconds). I used CPM because the amount of money per second was too small to do in normal dollars.

My friend then saw the label for the graph, something like "CPM/Second", and the argument ensued. His claim was it could only be used as a rate and nothing else. Where he is getting confused (again, I think), is saying you are paying per million when you are only paying for one unit is sort of weird to think about. While knowing that it is often used as a rate, I also know it has been used as a unit and I don't see why that wouldn't make sense anyway.

My question is do humans interpret rates (Cost Per Milli, X Per Y, etc...) differently from absolute units? Are their any languages where this might be the case?

  • I thought CPM was "clicks per minute". I also didn't know the M stood for "thousand" :p – acattle Apr 11 '13 at 2:39
  • What do you mean by "over time" in "CPM over time"? As in, the longer the ad, the higher the CPM? In either case, I don't think this is really a question for this forum. – dainichi Apr 11 '13 at 2:51
  • Welcome to Linguistics SE. A lot of people have the wrong idea about linguistics is and what it isn't so we're a bit particular about what we do and don't accept. The way the question is right now, I'm a bit worried it could be considered off topic. I've tried to reword it to make it more relevant. I honestly think there's an interesting Cognitive Science question in there but I'm not sure if it's linguistic – acattle Apr 11 '13 at 2:52
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    Incidentally, the SI Unit for acceleration is m/s^2 (pronounced "meters per second squared"). This effectively means "meters per second per second". Velocity is the rate of change of distance (in meters) over time (in seconds), m/s. Acceleration is the rate of change of velocity (in m/s) over time (in seconds), thus m/s/s, or m/s^2. Therefore there is not mathematical reason why CPM/s shouldn't be allowed. However, I feel your problem isn't rates versus units but more to do with making the data clear so that your client can understand easier. – acattle Apr 11 '13 at 2:54

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