Is it possible to calculate the total average between two sets of numbers, without just using the sum of each set of numbers?

Question

I'm working with some really frustrating reporting software that doesn't let me calculate the average by dividing two sums.

To get around this, I need to find a way to get the same result by calculating the average of each value that makes up the sum.

Here's an example:

A   B
1   1
2   
1   
2   
2   
1   1
1   
1   
2   
1   
1   1
15  3

In the above, the sum of column A is 15, and the sum of column B is 3. The result I need is 5 (15/3). But I can't use this method to get this result.

So I'm trying to figure out a calculation for each row that will produce the same result if I either sum or average the total of all these calculations.

For example (obviously the below isn't right but this is the theory):

A   B   C
1   1   1
2       0
1       0
2       0
2       0
1   1   1
1       0
1       0
2       0
1       0
1   1   1
15  3   0.27

In the above, I've divided B by A for each row and then done the average of these calculations, which is 0.27. I need to take the same approach, with a different calculation, to somehow get 5.

Hope this makes sense (fingers crossed that it is even possible),

Thanks!