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Anyone have any idea or does one have to run a single ad at a time to find out?
So, say you have 3 keywords: kw1, kw2 and kw3 in your group and two ads: ad1 and ad2. There will be a QS for each of kw1-ad1, kw1-ad2, kw2-ad1, kw2-ad2, kw3-ad1 and kw3-ad2. Each ad you create will create a new set of QS for each keyword you have. Some people say there's a keyword QS and an ad QS. What I explained is essentially that, I just think Google calculates each combination, not each keyword and ad separately.
Not sure how Google calculates the QS it shows you in your account, probably just an average of all active ads.
Running only one ad may not help you much. It's clear Google uses more than the round number QS they show you. It's not 7, it may be anywhere between 6.50000 and 7.49999 rounded off. The quality score is also a relative value compared to all advertisers of that keyword. Since the QS is calculated for each search on your keyword, it changes and so does every other advertiser's QS. If yours changes from 7 to 6 or from 7 to 8, is it because that ad has better/lesser quality, because your QS was on the edge of the true QS (near the x.5 value) or because you were affected by better/lesser quality of competitors' ads?
The best way to increase your QS, is to increase your click rate. The two are closely related.