I'm looking for a book (or other media) which provides an overview of statistics that is both comprehensive (covering all the basic/intermediate concepts) and comprehensible (which, for me, means not being weighed down with unnecessary and especially un-introduced mathematical symbology).
Can anyone offer suggestions?
This question is clearly very subjective. As other commenter's have said, a firm grasp of statistics requires years of academic study.
A few pointers:
First, even assuming that you don't want to go back to school, I always recommend looking at the statistics courses at the top 5 universities and following their syllabi for reading lists (here's one ranking of statistics departments). Particularly where universities have overlap in textbooks, that can be a good indication of a key text. Berkeley offers webcasts of many of their introductory courses (for instance, Stats 2 Introduction to Statistics), also available on iTunes.
If you were just going to get one book that covers computational statistics, I would suggest "Modern Applied Statistics with S" by Venables and Ripley (known as V&R). It is comprehensive and does a commendable job covering both the statistics and the programming (in the S langauge, which is used in both S-Plus and R). That said, it doesn't go into great detail on any subject (given that it covers everything in under 500 pages).
One of my favorite statistics textbooks (while not introductory) is "Data Analysis Using Regression and Multilevel/Hierarchical Models" by Andrew Gelman and Jennifer Hill. Their book also provides plenty of R examples, and fully meets your criteria for comprehension: Gelman is one of the best statistics teachers that I have encountered.
Peter Dalgaard's "Introductory Statistics with R" does a reasonable job of covering basic statistics and R in short order, but IMHO John Chambers' "Software for Data Analysis" is the best book on R itself.
I had a lot of success with "Statistics the Easy Way", one of those Baron's review books that you're supposed to used along side a regular statistics course. The book offers very thorough and clear derivations for algebraic formulas, and walks through concepts with plain English and not just mathematical formulas. When there is any calculus, the explanation section is optional, but even then I found the explanations to be thorough. Unlike regular math textbooks, the authors do not skip steps all that much. This book won't get you up to speed on R, but it will help you wrap your head around Statistics. I don't know if it will be thorough enough for you, however.
I work with quantitative analysts, implementing their ideas and helping them to analyze raw data. The book really helped me to better communicate with them.
Start off with Gonick's Cartoon Guide to Statistics and then move on to more thorough texts from there.
I think "Statistics in a Nutshell" (published by O'Reilly) is quite nice. It unfortunately has a bunch of errors, but if you're paying attention (as you probably should be anyway) then it's pretty easy to catch them.
I don't know if there's a newer edition out yet, but it might not hurt to pick it up.