I've never been great at math, so I apologize if this isn't even the appropriate thread for it. My boyfriend and I have been living together for a few months, and we want to split all our expenses down the middle. At the end of every month I would draft an excel sheet recording all of our expenses, including groceries, electric bills, cable, etc. etc. When I had our totals, I would subtract the numbers from each other to get the difference, to essentially see who had spent more/less money. For example, say I spent a total of $300, and he spent $100, the difference being $200... I would then subtract the $200 from the rent I owed him, since I had spent $200 more than him that month. In my head, I was making up the difference by doing this... But then we sat down to look at our excel sheets, and we asked ourselves if we had been doing it wrong all along.
My boyfriend, said... "Shouldn't we be ADDING our expenses and dividing by two to get the average, since we are splitting everything in half?" So using the example above, we would add 300+100, which is 400 and then half of that... 200. So that means I would have gone over the mean by $100 and he would have been under by $100, which means I would be subtracting the $100 from our rent check.
My brain can't wrap itself around which of these scenarios is actually the correct one. Any insight is greatly appreciated!