5 Steps to a 5 on the AP: Statistics Review

Average Reviews:

(More customer reviews)You will likely ace your AP Statistics exam if you use this book (I wouldn't know, since I only used it for individual study). There are enough examples to illustrate the concepts. All exercises have solutions, and they are generally carefully chosen. You have a diagnostic test, and explanations on how the grade is calculated. Compared to similar AP Statistics books this one seems more to the point, so I recommend it.
However, some definitions could be more carefully worded and more consistent. Sometimes, the theoretical presentation gives me the impression that the author would describe things rather than define them properly.
For example, on the bottom of page 50 we read "a Random variable can be thought of as a numerical outcome of a random phenomenon or experiment". This passes as a concept description (although, strictly speaking, a random variable is a numerical function, not a numerical outcome; also, this definition may suggest that random variables make sense only in experiments with numerical outomes). However, on top of page 148 we read that "a random variable, X, is a numerical value assigned to an outome of a random phenomenon". So now the random variable is not a numerical outcome anymore, but rather a numerical value associated to an outcome. And it gets worse when using the notation P(X=x) to express that "the random variable X takes on the particular value of x". How can a random variable, which was defined as a value, take on a particular value? A value is a value, like "3", and it cannot take on another value. I think the statistics books should drop the habit of giving such pseudo-definitions to random variables. Tell a spade a spade: a random variable is a function defined on the sample space.
Page 143 features a messy mix between the concepts of "outcomes" and "events". Let's be clear: events are sets of outcomes. They cannot be mixed together. Thus it is wrong to say that "outcomes are sometimes called simple events". The correct definition is this: a simple event is a set that contains exactly one outcome.
On the same page, we read that "the probability of an event is the relative frequency of the outcome". Which outcome is that, anyway, since an event is a set of possible outcomes? This again mixes sets and elements of sets in the same sentence.
The definition of a probability distribution for a Continuous Random Variable given on pp 151 is cyclic, is not actually a definition and it is rather confusing. The fact that it is cyclic is apparent in these two fragments: "There is a smooth curve, called a density curve (defined by a density function)..." and "In this course, there are several CRVs for which we know the probability density functions (a probability distribution defined in terms of some density curve)..." It appears that each of the two concepts (density function and density curve) is defined using the other one.
Finally, by the time I reached the chapter on confidence intervals, I found myself doing what some teachers call "mindless calculations". Perhaps it is a sign that this book gives more recipes than explanations.
I would like to read a new edition of this book, in which the author spells out the definitions more clearly and beefs up the theory a little.

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