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Let me use a simple example:
 - I kept my first home throughout 2017 with and average balance of 0.5m. This part is clear.
- My second home was bought on December, so only have one interest payment with principal balance of 1.5M. 

What is my average balance of the year?

 

I can see two different ways of calculating it:

Approach 1: avg(home1) = 0.5M, avg(home2) = 1.5M / 1 => avg(total) = 2M

Approach 2: avg(both homes) = (0.5*12 + 1.5) / 12 = 0.625M