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I agree with puddle. You should only consider going to the program of lower tier (i.e. top10 to top20 constitutes a difference in tier, imho) if it offers you much more financial support (free money, not TA/RA) so that you will have significantly more time for your own research and coursework.
 
When I was an applicant two years ago, I made quite a few friends during campus visits, and in the end most of us chose the highest ranked programs that admitted us, and it turned out that all programs make empty promises during recruitment. I'm not saying "fit" is less important. It's just that at this stage, there is no way you can know how that part of your grad school will work out, so pivot on indicators with less uncertainty.
 
And congrats!

I agree with puddle. You should only consider going to the program of lower tier (i.e. top10 to top20 constitutes a difference in tier, imho) if it offers you much more financial support (free money, not TA/RA) so that you will have significantly more time for your own research and coursework.
 
When I was an applicant two years ago, I made quite a few friends during campus visits, and in the end most of us chose the highest ranked programs that admitted us, and it turned out that all programs make empty promises during recruitment. I'm not saying "fit" is less important. It's just that at this stage, there is no way you can know how that part of your grad school will work out, so pivot on indicators with less uncertainty.
 
And congrats!

Fwiw, I had a good friend get off the waitlist at Harvard on April 14th. He declined their kind, if late, offer to go to Stanford instead. Point of that story is that waitlists do clear and patience is a virtue.
 
Fingers crossed that you get happy news from Michigan. I'm biased, of course, but I can't think of a better place to spend one's graduate years. 
 
Go blue.

Another thing to consider about rankings: with very few exceptions, they are incredibly sticky. I didn't have much of an idea why until I spoke with a senior professor at another university about my possible options. He was concerned about a program due to its recent losses. The main person he brought up left in 2004.
 
A lot of senior faculty—faculty who serve on search committees—simply aren't plugged into what's happening on the personnel side of the discipline. If a school promises X new hires in the next few years you are in their program, it will take a long time before the program is thought of as stronger because of them (well, unless the new hire is Gary King or someone like that).

Two things to bear in mind: 1) Stanford's placements page is missing a bunch of recent placements.  2) Stanford has much smaller grad student cohorts.
 
Some discussion on the first point here:
 
http://www.poliscirumors.com/topic/stanfords-placement-in-2013-2014-was-horrible/page/2

Top programs meaning Harvard, Stanford, UM-Ann Arbor, etc. At what age does your age become a disadvantage, especially if you're coming from a completely different field? For ex. you work in one field then decide to go back to school to get your undergrad and start applying for top PhD programs? 

I'm not feeling up to a long, rambling post right now so I'll just keep it short and sweet.
 
I love being a graduate student and I feel confident in my ability to find employment when I complete my PhD. This employment may not be in academia but I am not entirely sure that I want it to be.
 
I have plenty of additional funding opportunities  and am able to pursue interesting new research and professionalization opportunities that present themselves to me. Research assistant positions, fellowships, and paid work are fairly easily available.
 
The department culture is engaging and supportive -- both academically and inter-personally. No matter how busy my professors are (and they are busy) I always feel like they have time to meet with me to discuss my work or to help me get through other struggles.
 
Generally speaking, graduate school is "the good life". I am paid to study things I find interesting, work with the best and brightest in their respective fields, and explore the possibilities of academic life without committing fully to said life. Also I get a pretty good wage and everything in my town is heavily subsidized by the university so I get to go out for nice dinners (especially when my adviser pays), watch world class theater, and spend quality time with my friends down at our local watering hole.
 
All this said and done - I think that the school I attend has a lot to do with my positive experiences. I didn't really think it out ahead of time so I got lucky... I honestly just went to the highest ranked school that admitted me. But in retrospect I would advise you to chose a school that has the resources to support you and a non-toxic department culture. Do not underestimate the importance of university/department prestige - your life will be made easier if opportunities to meet top academics, attend good conferences, and attain important fellowships are made available to you. Department culture can be hard to gauge but get a few grad students drunk on your visit weekend and see if they start effusively praising their department (apparently this is what I did 2 years ago). Certainly it is possible to get to the top without these things - they just seem to help a whole lot.
 
Happy to answer any questions people may have -- but I'm not going to back my thoughts up with stats. We all know grad school is hard and getting a job is even harder... I'm just here to say that it may well be worth your effort.
 
Darn... that was longer and ramblyer than I intended.

More thread hijacking...
 
Calculus was uses extensively in our first year program, in both our (required) stat methods and (not required) formal theory courses.  Differentiation was used to find maxima of MLE's, derive the information matrix, derive an optimal move in a game etc.  Integration to do expectations of random variables, derive conditional distributions etc.  There was also some very basic linear algebra: adding and multiplying matrices, inverting matrices, checking whether matrix was full rank, etc.
 
Calculus and linear algebra (and other topics) were taught in a math camp, so everyone was more or less brought up to speed, but that treatment definitely wasn't as good as having taken a full course in high school or college.