Finding average power signal and its calculation
I will type out the response I put in a comment (and then deleted again) because I felt like it would benefit from a bit more extended explaining:

As an analogy to the two methods shown here:

We go shopping - We go by store A and store B. At the end of the day, we bought 8 products, and we spent a total of 20 Space Bucks. Our average is thus 2.5 Space Bucks per product.

In the method on the left, we look at the averages of the individual stores, and then use those to calculate the total average.

In store A, we buy 4 (=L) items and we pay 8 Space Bucks. That means that the average cost in store A was $$ \frac{8 \  Space\ Bucks}{4 \ Products} =\ 2\ \frac{Space\ Bucks}{Product}$$

In store B we again buy 4 products (same L!), but we pay 12 Space Bucks. This gives us a average cost in store B of 3 Space Bucks per product.

Now we want to find the average of the total shopping we did today. What you are doing on the left of your page would be just adding the two averages up. That would in our case result in $$ Average\ Cost = 2 + 3 = 5\ Space\ Bucks$$
Which is clearly not the correct answer!
The correct answer would be 
$$ Average\ Cost = \frac{Average\ cost\ in\ A + Average\ cost\ in\ B}{2} = 2.5\ Space\ Bucks$$

While a silly analogy, I hope it sheds light on the confusion you are having.