This is my very first crack at notation and I'm very unsure about the results:
With two sets with values:
QTY: [4, 5, 5, m...], DOSE: [20, 10, 10, n...], and the number 30.
The formula is: ((30 / QTY) * DOSE)
With the above, the example would be:
MEAN = ((((30 / 4) * 20)) + ((30 / 5) * 10)) + ((30 / 5) * 10))) / 3)
Here is what I came up with:
${\overline{x}=}{\frac{1}{n}\sum_{i\in{S}}^n\frac{30}{i}x}$
Not quite, because you use the same $x$ to mean different things in the formula. This would be a bit better ($x_i$ means the dose corresponding to quantity $i$).
$${\overline{x}=}{\frac{1}{n}\sum_{i\in {S}}^n\frac{30}{i}x_i}$$ But this still isn't right because your $S$ is not really a set. A set cannot contain the same number (e.g., $5$) twice; it either contains it or nor. The arrays of quantities and doses are better presented as sequences.
Say, $(Q_i: i=1,2,3,\dots,N)$ is the sequence of quantities and $(D_i: i=1,2,3,\dots,N)$ are the corresponding doses. The number $N$ is how many of these things you have. Then $$\overline{x}=\frac{1}{n}\sum_{i=1}^N \frac{30}{Q_i}D_i$$