Have I been calculating our bills incorrectly?

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!

Re: Have I been calculating our bills incorrectly?

If you spent 300 and he spent 100, then combined 400 was spent, so you each owe 200. You paid 300 though, so he owes you $100. You can subtract that $100 from the rent you owed him.

His views seem to be correct. You want to add all expenses and divide by two. When you do this, one of you will most likely have spent more than the other. Whatever you have spent above the average can be subtracted from the rent check

Re: Have I been calculating our bills incorrectly?

**edit: removed as incorrect**

Re: Have I been calculating our bills incorrectly?

Thank you so much! There is one additional little issue now. Since I did this incorrectly for the past 6 months :( I would like to fix the error. The kicker: I lost all the excel files but one. What I do have is the totals from every check I gave him. I spent about two days trying to deduce how I could come up with what we might owe each other by working with the total alone, and using the file that I did have as a control, since I no longer have our individual expense totals for the rest of the months. So here's what I did...

With May, which is the only month I found, I gave him a check for $580.11. I subtracted this number from the rent amount ($630), so it would give me the difference between our expenses (turns out to be $49.89). AND now adopting the correct method, by dividing that number by 2, I get $24.94, which turns out to be the amount we were both away from the mean. In this case, I deduced that I actually owed him, since the check I gave him was under $630, which means I would have subtracted my expenses from it.

I did this with every month, but here's the problem. Over the course of August, September and October, I was paying him back for a plane ticket that he had gotten me. I paid him $350 back in August, $200 in Sept, and $200 in October. When I did our excel sheets, I remember accidentally placing this number under his expenses, which in fact, it should have been added in at the very end. After all, it was not an expense we were splitting. It was solely mine. Of course, now I don't even know if it's even possible to factor this problem into my solution from above, since I don't have the total of our individual expenses. What a mess :(

Should I just learn from this, or could there be a solution?

THanks again for your help!