ML models: average of all versus average of averages?
It shouldn't matter if you average all of them or take the average of the average for each person. It turns out that it will give you the same number. This is known as the law of total expectation. Essentially, 

E(X)=E(E(X|Y)) 

Here's the wikipedia article for more details:

https://en.wikipedia.org/wiki/Law_of_total_expectation