Ziff, Ray, and Kent Larsen had it right — the Book of Mormon has the largest standard deviation in ratings of any book on the site. The stat is called “25 Books People Can’t Agree On” and you can see it at the bottom of this page.
The Book of Mormon may be at the top of the list, but it’s in good company, since books by Nathaniel Hawthorne and Isaac Newton are also on the list. (Of course, the urban vampire fantasy and regency romance do drag down the neighborhood a bit.)
It’s also the most widely-owned of any book on that list, by far. There are around 1,600 LibraryThing members who own a total of around 1,800 copies of the Book of Mormon. The next most widely held book is Hawthorne’s The Marble Faun, at around 400 copies. There have been some other popular books on the list, but they tend to drop off when they get very popular, because enough people give them an intermediate rating (2.5-3.5 stars) that it lowers the standard deviation of all the ratings. The Secret, a book made popular by Oprah Winfrey, used to be on the list, but now the standard deviation of the ratings is down to 1.34, well below the current top-25 cutoff of 1.42.
Due to some quirks of the site, Mormons may be disproportionately raising the average rating of the book. For starters, you have to have a book in “your catalog” in order to give it a rating. (You can’t just go around rating random books that other people own.) For most people, having a book in their LibraryThing catalog means that they physically own it, although some people (myself included) also enter books that they have read but don’t own or books that they want to read. So, people who hate Mormons or the Book of Mormon can’t rate the book unless they own a copy or are otherwise willing to enter the book into their online library, for all to see. (There actually is an option to make an entire catalog “private,” but I don’t know if books rated in a private catalog contribute to the site-wide average rating of the book.)
Another factor is that if you own and rate multiple copies of a book, each of those ratings counts individually. Most Mormons I know own multiple copies of The Book of Mormon, even if you don’t count quads or triple combinations (one in your mission language, one in a language you studied in college, a few extra English copies, etc.).
The multiple-rating policy doesn’t seem to make a lot of sense, site-wide, because you’d think it would artificially inflate ratings for all sorts of books. (After all, you’re more likely to own multiple copies or editions of a book you already like.) However, it does make sense in an individual user’s catalog, since it may be that you like one translation of Pushkin better than another, or that you find one annotated edition of Shakespeare superior to another. And, truth be told, it may not have a huge effect on the ratings for The Book of Mormon, either; I noticed that many of the users who own multiple copies have only rated one or two of them, if any. (See, for example, the libraries of LT members crowderb and fredheid.)
The last factor that might artificially inflate the Book of Mormon’s ratings comes down to psychology, not software. In my own catalog, 4/5 stars is a very high rating. I try to save 5/5 stars for my very favorite books or the ones that have most influenced my life. By this standard, the Book of Mormon would not merit 5/5 stars in my own catalog; I always get confused in the war chapters and I generally like the New Testament much better. However, when I was going through my catalog and adding more book ratings, I really couldn’t bring myself to give the Book of Mormon less than a 5-star rating. To do otherwise would have seemed to invite misinterpretation, I suppose. (And, to be fair, there are a lot of parts of the Book of Mormon that I really like, but it’s still something I read because it’s “good for me,” not because I want a little something to pass the time while I wait for the bus.)
I can’t speak for the other Mormons on the site, but I do notice that, while fully half (118) of the raters gave the Book of Mormon 5/5 stars, no one has yet ranked it 4.5/5. Granted, not everyone has figured out how to assign half-star rankings and even if you do know how, it involves an extra step. Even so, only 6 members have given it a 4-star rating and no one has rated it 3.5 stars (which is, by the way, the rating closest to its mean ratings value of 3.38 stars). At the low end of the spectrum, 37 members gave it 1 star and 23 members went to the trouble to give it the lowest ranking possible — 0.5 stars.
Incidentally, LibraryThing creator Tim Spalding finds this particular statistic fascinating, and highlights it as a piece of unique social data when giving presentations about LibraryThing.