David Freedman, Robert Pisani, Roger Purves
Fourth edition: 2007, First edition: 1978
As an undergraduate studying philosophy, I was asked to analyze some data for a small study that I was working on with a physician. Needless to say, I found myself somewhat overwhelmed, but was able to get by by mimicking some old Stata code that a biostatistician friend had given me. The analysis turned out to be good enough to help get the study published, and I had suddenly become interested in this curious field of study called statistics.
The first book on statistics that I read was Statistics, by David Freedman and colleagues. What I liked most about it was its focus on explaining the fundamental concepts of statistical analysis (what do p-values actually mean, why is it important to visualize data, what does it mean for a test to be significant, etc) with concise and accurate language, but without too much mathematics. With that conceptual background, I found it much easier to go on to read more advanced literature with more advanced mathematics.
This book covers all topics covered in a first year statistics course, but does not cover time series or aggregation of large data sets. I feel it does a very good job at teaching a non-statistician how to think like a statistician. From there, adding new methods, like time series, should be relatively easy, and the non-statistician should be well on his way to becoming a life-long student of statistics.