When to use Mean(X/Y) versus Mean(X)/Mean(Y)? So, I understand that for two vectors of numbers X and Y the mean of X/Y is different from the mean of X divided by the mean of Y. But I'm not sure when it is appropriate to use each. Specifically, I need to calculate the average consumption per days active for a set of individuals, and I don't know which approach to use.
To illustrate, say there are 3 individuals: A, B, and C. Their consumption values are (1,3,7) respectively, and their days active are (3, 1, 6) respectively. If I individually calculate their consumption per days active I get 1/3, 3, and 7/6, which I can then take the mean of to get 1.5. But if I sum their consumption (11) and their active days (10) and then work out consumption per active days, I get 1.1. Which approach is 'correct'?
I hope I've expressed this ok, I wasn't really sure what the title should be which is why I've struggled to find answers because I'm not totally sure what to search. If anyone can explain the different properties of the two quantities and when using each might be appropriate I'd really appreciate it!
EDIT: I have found this question which seems to touch on a very similar issue, but I'm not totally satisfied with the answer. I think the second answer comes closest to what I'm looking for, but I'd just like to know when it's appropriate to use each (not specific to some simulation context like in the question) Usages of Mean(X/Y) vs. Mean(X) / Mean(Y)

In my opinion mean(X/Y) is more meaningful because your experimental unit (not sure this is the correct term) is the individual, not the aggregate. Let's try to see this with a contrived example. Consider this data set:
individual cons  act ratio
         A    5    2   2.5
         B    5    2   2.5
         C    5    2   2.5
         D    5    2   2.5
         E    5    2   2.5
         F    5    2   2.5
         G    5    2   2.5
         H    5    2   2.5
         I    5    2   2.5
         J    5    2   2.5
         K 1000 2000   0.5

I would say that in this dataset the average ratio is just below 2.5 (~2.3 in fact) because you observe 10 individuals with ratio 2.5 and only one individual with ratio 0.5.
However, if you calculate mean(cons) / mean(act) you get an overall average ratio of ~0.52 because individual K dominates the dataset by having much higher values, but individual K is just one out 11 individuals. On the other hand, you may want to give more weight to K if you think its values are more reliable than the other individuals'.
