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Principles of Statistics (Dover Books on Mathematics) [Paperback]

M.G. Bulmer
4.1 out of 5 stars  See all reviews (26 customer reviews)

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Book Description

March 1, 1979 0486637603 978-0486637600 0002-Revised
There are many textbooks which describe current methods of statistical analysis, while neglecting related theory. There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.
Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)
Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc.
The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

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Principles of Statistics (Dover Books on Mathematics) + Probability Theory: A Concise Course (Dover Books on Mathematics) + An Introduction to Information Theory: Symbols, Signals and Noise (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 252 pages
  • Publisher: Dover Publications; 0002-Revised edition (March 1, 1979)
  • Language: English
  • ISBN-10: 0486637603
  • ISBN-13: 978-0486637600
  • Product Dimensions: 8.2 x 5.6 x 0.5 inches
  • Shipping Weight: 10.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #94,052 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
207 of 211 people found the following review helpful
5.0 out of 5 stars An excellent reference and self-study guide May 5, 2000
I have six books on statistics in my personal library. All of them are bigger than Bulmer's book, but none have been read as many times, and none are as tattered, marked up, and cross-referenced. Simply put, Bulmer's book is the most useful and complete book on basic statistics that I have. It's a nice package in a reasonably sized book with all the most important stuff for dealing with basic statistical problems that many engineers are likely to encounter in a day's work.
Chapter 1 is a short blurb on the concept of probability. This is very useful because it places the rest of the text on a very specific and concise footing. Essentially there are two concepts of probability. One is the relative frequency with which an event occurs in the long run. An example of this is the tossing of a coin many times and counting the number of times it comes up heads. The author describes this as statistical probability.
The second concept of probability is what the author calls inductive probability. Inductive probability is "the degree of belief which it is reasonable to place on a proposition on given evidence." The essential difference between the two concepts of probability is that statistical probability is an empirical concept, while "inductive probability is a logical concept." Bulmer closes chapter 1 by saying, "It has been reluctantly concluded by most statisticians that inductive probability cannot in general be measured and, therefore, cannot be ............" Read chapter 1 to find some interesting arguments in support of this proposition - a proposition that may be surprising to some people. As a result (and as the book's title suggests) Bulmer keeps his book almost exclusively in the domain of statistical probability.
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59 of 61 people found the following review helpful
By A Customer
I've learned probability and statistics from at least four other authors, and have constantly been browsing other textbooks that appear in the bookstore. I chanced upon Bulmer's 1965 book one fortunate day. It is still useful and relevant more than thirty years after its first printing. This clear and elegant book is also concise and straight-to-the-point, offering beautiful and brief developments of material that usually appears hopelessly muddled in many a reputable current statistics textbook (e.g., different notions of probability, the binomial, Poisson, normal distributions, and the Central Limit Theorem). Aside from the solid mathematics and many worked examples, the book includes a few entertaining digressions into the history of the subject.
In short, learn and review statistics from this classic. Thank you, Mr. Bulmer, and Dover Publications (for making this textbook available in a nice format at such a low price).
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34 of 35 people found the following review helpful
5.0 out of 5 stars Rich in Insight September 23, 2002
By A Customer
This modest little book is both a masterpiece and a gem! I can't praise it enough! It is different from any other statistics book I have ever read in that it puts you in the place of famous historical figures in statistics and helps you rediscover their findings. His use of original source material is very well done. The book is self-contained and the author proves almost everything of importance(some of the proofs are more intuitive than rigorous at times, but that's the point). Bulmer has a knack of making the most difficult concepts (hyperspace, degrees of freedom) seem natural. He covers a very broad terrain from distributions, tests of significance, inference, Bayesian methods, etc. Written on many levels, this is useful for a novice or intermediate student but I suspect professional statisticians will find much to keep them thinking about. While reading through this book you will often say "aha, so that's why they do that". For the price it is the best value possible; you won't regret picking up a copy of this book and if you enjoy the inner workings of statistical theory you will refer to it again and again.
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28 of 30 people found the following review helpful
4.0 out of 5 stars Unlocks the mystery behind the equations January 8, 2010
The positive reviews for this book seem to be written by people with a previous background in statistics and/or strong math skills. Furthermore, they want to know the why behind every equation. I mostly fall into this category.

The negative reviews come from people who use this as their introduction to statistics, and who probably don't have a strong grasp of calculus or perhaps higher level math in general.

In my opinion this book offers something that no other statistics book has: clear derivations of all the fundamental and important equations and distributions in statistics; followed by lucid explanations. In other words this book unravels the mystery behind the equations. If you've thought about a statistics equation a lot and wondered, WHY? Then this is the book to read.

Here are 4 questions I had that Bulmer answered:
1) Why is the mean more commonly used than the median (and in which cases is the median better)? p.51-54
2) As a measure of variability why use a root-mean-square procedure (i.e. accepted def. of std deviation ) instead of mean deviation (i.e. take absolute value of deviations)? p.54-59
3) What is the logical error in the gambler's fallacy? p.87-88 (Note: many statistics books treat this, but I've found Bulmer's book to give the most satisfying answer.)
4) Why does the standard deviation of a sample have the n-1 term in the denominator instead of the n term like the stdev of the population? p.129-130

(Note that he answers questions 1, 2, and 4 more than once, but the pages listed are the first time the answer appears.)

Thus, I strongly recommend buying and reading this book if, like me, you have a burning desire to know why the equations are the way they are.
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Most Recent Customer Reviews
5.0 out of 5 stars At this price youd be crazy not to.
Very well done. It was clear the author not only has a deep knowledge of the subject, but also knows how to convey that knowledge. Read more
Published 5 months ago by Amazon Customer
3.0 out of 5 stars Good for the money, but flawed in some ways
While this book did help me get up to speed with the basics of statistics, I found it lacking in terms of examples and in terms of presentation. Read more
Published 9 months ago by Ido Tamir
4.0 out of 5 stars Statistics Review
This is a book to work with. Its style is casual for the most part. It does require some knowledge of math at an undergrad level, and one can learn from this book.
Published 14 months ago by Amazon Customer
2.0 out of 5 stars Meeehhh....
Nice book but too much talking and yapping and it's hard to use it as a reference book. But it's affordable and serves well as a class text. Read more
Published 16 months ago by Yair Daon
4.0 out of 5 stars An excellent primer under the wrong name
The words "statistics" and "math" are often loosely thrown around and used interchangeably. Many social science majors who are required to take a statistics class for their degree... Read more
Published 17 months ago by Kamel
5.0 out of 5 stars Best stats book I ever had
Not being a mathematician, I was looking for a book that could explain stats to me without all the hieroglyphics and "since you're not one of us you will not understand and we... Read more
Published on April 18, 2012 by Amazon Customer
4.0 out of 5 stars Book Review
Great statistics book for a graduate student. You may need some introductory statistics or some undergrad math classes to understand this text. Read more
Published on October 6, 2010 by Nathan A. Maniewski
5.0 out of 5 stars Statistics at a glance
Principles of statistics is not a new book (1967). Therefore, it include a modern approach if compared with that era. Read more
Published on July 19, 2010 by mp
2.0 out of 5 stars Reads like a textbook and is just as vague
I am a very math oriented person. I like formulas to be laid out in front of me and I love looking at the steps that it took to solve a problem. Read more
Published on February 15, 2010 by Matthew Bymaster
3.0 out of 5 stars Way overrated
Having read some great reviews for this book on Amazon, I went to the library to check the book out and was rather disappointed. The book is OK, but nothing to rave about. Read more
Published on January 13, 2010 by pbatchou
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