Just for fun, I will guess too.
I think you probably mean the ISM in the plane of our galaxy
I think you mean to average on a MASS basis.
So if most of the mass is in the form of neutral gas, then for a first approximation of the average, I can neglect dust and ionized stuff.
Eventually someone who has a definite figure will reply. I would guess the average atomic weight is 2.
(because I think the ISM is dominated by molecular hydrogen.
there would also be some neutral atomic hydrogen with weight 1 but that would tend to be balanced out by the heavier molecular species and the dust)
BTW welcome to physicsforums, Mr. Popffabrik.
I like the name, it seems it could be a nickname for the LHC collider. "bang factory"