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)

If $x_i =$ number of items consumed on active days (for person $i$) and $y=$ number of active days (for person $i$), then...

*

*$\text{Mean}(x/y)$ is the average number of items consumed per person on a day in which that person is active. This gives equal weight to each person's data.

*$\frac{\text{Mean}(x)}{\text{Mean}(y)} = \frac{\text{Sum}(x)}{\text{Sum}(y)}$ is the total number of items consumed, divided by the total number of active person-days (1 person-day = 1 person active for one day), or the average number of items consumed per active person-day. This gives more weight to more active people, since they contribute more active person-days.

Which one you want depends on your goals, but I would imagine you're almost certainly more interested in people than in person-days.
