MIN/MAX IF To Ignore Blanks

Guys, I have an interesting case again. Basically I've got a formula that looks up a minimum with an if condition, that if being a group. I got 2 groups: 1 and 0, BUT some of the values do NOT have a group assigned to them (meaning there's a blank value in those cells). For group 1 formula works just fine, but for group 0 it also processes those blank values as well (apparently thinking that 0 is the same as blank, which in this case is NOT), showing a wrong minimum as a result. Please have a look at the sample attached.

So basically what I'm looking for is a way to use the same formula BUT ignoring blank values when calculating for group 0. Any ideas, good people?