If we look at our site's stats on Area51, we find that we're legging in QPD and %Answered. Among them QPD is more considered for beta progress.
According to Graduation, site closure, and a clearer outlook on the health of SE sites,
When a site starts to consistently receive 10 questions/day, we’ll consider it for graduation.
So, QPD (Questions Per Day) is the most affecting factor for site graduation progress.
Earlier I also tried to draw the attention of community towards %Answered stats on Area51, Let's concentrate on "percent answered" stats!
Though it would be better if we achieve 80% for %Answered stats, but if we're looking for the most affecting factor for beta site's graduation, then it is QPD.
In our history of beta phase QPD mostly used to vary from 4 to 6. But recently it started to touch the figure of 10!
In brief, the effect of %Answered stats regarding the graduation progress is less than QPD.
We sometimes discussed in chat room regarding the graduation of the site, one idea for increasing QPD is to encourage users to ask more and more questions but forcing users to ask questions is not a good idea according to some users.
Another point to be noted is our curiosity for graduation. If you say we want to graduate, the reply would be what's the problem with current beta? Actually StackExchange won't close a beta site like this.
Thanks to many devoted users, it’s grown clear that smaller SE sites can do a great job of maintaining themselves and producing high quality Q&A. Not every site is going to be a blockbuster success, but our small sites are serving their own communities well. We’re proud of you, and we want you here.
So, if our site is not getting graduation, it doesn't mean the site will be closed.
If there's enough moderation for a public beta site to consistently remain free of spam, for flags to be cleared, and for our Be Nice policy to be upheld, your site will remain open
So, we don't need to worry much about the graduation.
Also visit couple of answers of Robert Cartaino on Should we rename or remove the "beta" label? and Can we do something about the "graduated" label?
And what are other benefits of graduation? The most notable are 1) Independent Look & Design, 2) Self regulation i.e moderator-election. So, if we're happy with current position, then I don't think we need to bother much about graduation. (Otherwise if we feel a real need or missing feature of graduation, we may think for a quick way towards graduation, btw, note that anything can be feature-requested upon requirement even the phase is beta).
I know that I've somewhat more elaborated with respect to what asked in question but I hope this will help for visitors wandering for such things.
One possible solution for improving %Answered and QPD stats is encouraging users to read scriptures. As one read more and more scriptures, he/she may have more questions and also he/she can provide answers to existing questions. So, reading scriptures can help in improving QPD as well as %Answered stats and also the quality Q/A and ultimately the growth of community and the self.