That "もので" is a a construction that indicates a reason/cause. You could roughly translate it as "because of - for that reason".
The construction is Verb (dict) + もので, and you can think of it as a conjunctive particle that indicates a reason or a cause. You can find more explanations and examples at this link.
This being said, you can translate your sentence as:
The odd numbers are what determines whether (the person) is a "memory type" or not, and (because of
that) people with 4 or more circles are "absent-minded" while people
with more than 6 are "quite absent-minded".
Now some things to be noticed:
- I'm not sure what a good translation of 記憶型 could be here. Looking at your link it seems that it is one between two types of personalities (記憶、注意) described in some research. Here I decided just to leave it as "memory type".
- Without more context, it is indeed difficult to judge what those 丸 refer to. However, it seems logical that since we are talking of some personality test and "odd numbers", this probably refers to circling or anyway selecting certain answers. How many will determine the type of personality, absent-minded or quite absent-minded. Notice also that 丸 is what Japanese people commonly use to select "correct" answers in test or in general making selections depending on the context (but I suppose you know about the まる/ばつ convention already).
- The above is not a literal translation of course but I think it's not what you are asking here. It seems to me the main thing was the もので and the general idea of what's going on.
Since I'm not sure if what follows is actually true, do not consider it as part of the answer but rather as an intellectual speculation. The answer ended two lines above.
Since you try to break down that もので，I wonder if that もの comes simply from 物 and で isn't just です that, since it's connecting two sentences, simply becomes で.
I mean, I wonder if this construction isn't somehow equivalent or anyway related to something like: 何々。。。Vd物であり、何々。。。 which is literally saying that a certain thing is "something that does V", and I guess you would expect the next sentence to explain some consequence of that. Then over time this became the standard construction もので discussed above.