### Book review: Essentials of Statistics, 2e, by Mario F. Triola

[I’ve decided to make a habit of reviewing all of the textbooks I use. This one’s cross-posted on amazon.com, which contains many reviews of math texts, very few of which seem to be written by people who know much about math or math texts. I’ve also reviewed the dreadful precalculus book, and a calculus text that I’m appreciating a lot more in retrospect.]

Triola’s book is, for the most part, an excellent choice for an intro stats course. As an instructor, I find it relatively easy to work with, and the included STATDISK gives students many opportunities to analyze large sets of data without having to enter hundreds of values into calculators or computers. It also contains a lot of examples taken from actual data sets; this is the text that will deflect that ubiquitous “what’s this useful for in real life” question from students. A few issues, though, dog the book. In order of importance:

- Chapter 3-6, on counting methods is either underdeveloped or overdeveloped, depending on perspective. The short section gives an everything-but-the-kitchen-sink survey of the topic - permutations and combinations and such are dealt with in one fell swoop and followed up with only a smattering of problems, giving students little oportunity to fully digest the most mathematically-intense part of the course. If you’re teaching this course to math majors, you’ll need additional time and material for this section (I recommend Sullivan and Mizrahi’s
*Finite Mathematics*); if you’re teaching humanities/social science majors, who are more concerned with data collecting and analysis, I’d recommend skipping this chapter entirely. - The book makes such frequent references to the TI-83+ calculator that one is inclined to wonder if Triola is receiving kickbacks from Texas Instruments. Contrary to what the book would have you believe, it’s not necessary to invest in this beast (retail price: >$100) in order to compute standard deviations and correlation coefficients; my students are managing just fine with their $15 calculators with statistical functions.
- In Chapter 4, there’s some mention of the principle that if, under certain assumptions, the probability of an *observed event* is very low, then the assumptions are probably incorrect. There’s some merit to that, to be sure (if all 1000 of my coin flips came up heads, it’s natural to question the original assumption that my coin was fair), but Triola would do well to apply the critical thinking procedures exalted in Chapter 1 to elaborate on this. For instance: it’s highly unlikely that Betty Terwilliger would have won the jackpot in the Lotto 6-49 if the contest wasn’t rigged (probability: 1/14000000 or thereabouts), and yet, she did. (Similar arguments can be - and have been - used to defend intelligent design and astrology.) It’s a subtle concept, one that deserves more attention than the cursory “this is the law, and it’s important” treatment that Triola gives it.

These flaws aside, *Essentials* is a sound survey of the subject, one that’s very nicely designed with its audience of humanities and social science majors in mind. The examples are timely, and the anecdotes are interesting and relevant. The book justifies the subject matter without getting bogged down in formality, which is an ideal balance for its intended audience. In the hands of a knowledgeable and experienced instructor with sufficient prep time, it provides very good support to a statistics course for non-majors, but it’s not self-contained.