For more practical applications, written in a non-technical way, I recommend:
Lewis, H.W. (1997). Why Flip a Coin? John Wiley & Sons.
Lots of illustrations of how thinking in a statistical way can help you make decisions. Applications include voting, gambling, war, and the stock market. A very enjoyable read.
Mlodinow, Leonard. (2008). The Drunkard’s Walk: How Randomness Rules Our Lives. Pantheon.
If you’re like most people, your intuitions about anything having to do with probability are usually wrong. Without using formulas, Mlodinow gets you to think more clearly about probability, with zillions of real-world examples from all areas of everyday life.
Malkiel, Burton G. (2003). A Random Walk down Wall Street. W.W. Norton & Company.
Malkiel has done exhaustive statistical analysis of the stock market, to help you make wise decisions. He doesn’t just tell you what to do, he shows you the statistical evidence and explains what the statistics mean.
You’ll probably find a later edition; Malkiel updates the book every couple of years.
Vickers, Andrew (2010). What Is a p-Value Anyway? 34 Stories to Help You Actually Understand Statistics. Addison-Wesley.
Statistics really is stories, and these stories are short and fun, but each with a point behind it. Stats can seem like a bunch of formulas, but really it’s about learning to think logically, and Vickers does a great job of leading you to that way of thinking.
Dewdney, A.K. (1993). 200% of Nothing. John Wiley & Sons.
An excellent and highly readable tour through probability. Dewdney presents lots of situations, many from advertising, and helps you see how to use statistical thinking (educated common sense, really) to avoid being taken in.
The book runs out of steam toward the end, but the first nine or ten chapters are excellent — I particularly recommend “The Great Pepsi Challenge” (page 24), the lottery discussion (pages 56–59), and the decision whether to buy a store’s extended warranty (page 91).
Gigerenzer, Gerd. (2002). Calculated Risks. Simon & Schuster.
For ordinary people making legal or medical decisions. Some applications include AIDS counseling and DNA evidence. A very enjoyable read.
Latzko, William J., and David M. Saunders. (1995). Four Days with Dr. Deming. Addison-Wesley.
Dr. W. Edwards Deming is famous for teaching first Japanese and then American businesses to apply statistical methods to management, especially to quality. This book is in the form of a CEO’s “thought journal” at one of Dr. Deming’s seminars, as he finds that pretty much everything he knew about managing his company is wrong. It’s kept lively with lots of pictures and conversations, plus of course quotes from Dr. Deming’s lectures. You’ll want to read this book slowly and let the ideas expand in your mind.
“It’s so simple,” says Dr. Deming, and he’s right. You don’t actually need a statistical background to understand this book, but you’ll recognize that the key ideas come from our week 9, sample variability.
If you can’t find these in your library for regular checkout, ask a librarian to get them from another library for you, or get them from a bookseller.
The best textbook I’ve seen is DeVeaux, Velleman, and Bock’s Intro Stats (Pearson Addison Wesley, 2009). It’s written in a breezy, conversational style, perfect for self study. I really like the many sections “What can go wrong?” because you should always have possible pitfalls in mind.
Another excellent textbook is Freedman, Pisani, and Purves, Statistics (Norton, 2007). There’s not as much eye candy — no color at all, for instance — but it says what needs to be said and spends adequate time on the philosophy behind the methods.
If you’d like something a little less formal than a textbook, I recommend Larry Gonick & Woollcott Smith, The Cartoon Guide to Statistics. (HarperPerennial, 1993, ISBN 0-06-273102-5). Despite its lighthearted appearance, this is actually a pretty good statistics book. Its advantages include high readability, brief explanations, and low cost (under $12 new at Amazon in March 2004). On the down side, it presents things in a different order from our course, it doesn’t cover data types or χ², and you need to look elsewhere for practice problems. Still I think it’s great value for the money.