We are taught that geometric mean (GM) should only be applied to a dataset of positive numbers, and some insist that it should be strictly positive numbers.
However, I have seen people discussing the calculation of the GM of a dataset which contains $0$s. And there seem to be at least two ways to deal with such situation:
If there exists a $0$ in the dataset, then the GM is also $0$
Substitute the $0$s with some other number (e.g. $1$), then work out the GM as usual
Can someone please share their opinion on when we should apply method 1) instead of method 2) and why (i.e. the justifications), and vice versa? In addition, intuitively, why we want to do 1) as it essentially throws away all the other non-zero values in the dataset? Thanks.