I am stuck in a tricky problem. There are 32 companies. They have their own GHG emission factors and their market shares. This is, $ X_1, X_2, ..., X_n $ and $ Y_1, Y_2, ..., Y_n $. I am looking for its weighted mean. $\sum_{i=0}^n \frac{X_i \times Y_i}{Y_i}$
However, I have some problem.
$ X_1, X_2, X_3, X_4 $ are known. (That is, $ X_5,..., X_n $ are unknown.)
$ Y_1, Y_2, ..., Y_n $ are known.
$ X_1, X_2, X_3, X_4 $ make up 80% of market. (It means $\sum_{i=1}^4 Y_i$ is 80%.)
$ n $ is 32.
Can I estimate weighted mean. $\sum_{i=0}^n \frac{X_i \times Y_i}{Y_i}$? Many thanks in advance!
I think you mean
$$ \frac{\sum_{i=0}^n {X_i \times Y_i}}{ \sum_{i=0}^nY_i}. $$
Assuming the $X_i$ are nonnegative, you can set the unknown ones to $0$ to find a lower bound on the average. Since they can be as large as you like, you can't estimate an upper bound.