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

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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!