What the Numbers Say: A Field Guide to Mastering Our Numerical World [Hardcover]

Derrick Niederman (Author), David Boyum (Author)

Book Description

Publication Date: June 10, 2003

Our society is churning out more numbers than ever before, whether in the form of spreadsheets, brokerage statements, survey results, or just the numbers on the sports pages. Unfortunately, people’s ability to understand and analyze numbers isn’t keeping pace with today’s whizzing data streams. And the benefits of living in the Information Age are available only to those who can process the information in front of them.

What the Numbers Say offers remedies to this national problem. Through a series of witty and engaging discussions, the authors introduce original quantitative concepts, skills, and habits that reduce even the most daunting numerical challenges to simple, bite-sized pieces. Why do the nutritional values on a Cheerios box appear different in Canada than in the U.S.? How is it that top-performing mutual funds often lose money for the majority of their shareholders? Why was the scoring system for Olympic figure skating doomed even without biased judges?

By anchoring their discussions in real-world scenarios, Derrick Niederman and David Boyum show that skilled quantitative thinking involves old-fashioned logic, not advanced mathematical tools. Useful in an endless number of situations, What the Numbers Say is the practical guide to navigating today’s data-rich world.

Editorial Reviews

From Publishers Weekly

The bad news is that, in an age of science, complex financial planning, and competing deficit forecasts to support competing stimulus packages, the average citizen needs math more than ever. The good news, according to this delightful and eye-opening numeracy primer, is that it's all sixth-grade math. Niederman, a mathematics Ph.D, and author of The Inner Game of Investing, and Boyum, a public policy consultant, assert that quantitative competence is mostly a matter of simple habits of mind, including: trust numerical data over anecdotal observations, but always question what the data are really saying; think in terms of probabilities rather than certainties; and make rough-and-ready estimates so your calculations don't go off track. With such rules of thumb and a little arithmetic, the authors illuminate basic ideas about probability, statistics and measuring and comparing numbers. Their lucid, light-handed, equation-free style is based on a skeptical examination of the dogmas of our modern culture of quantity, in which they take a close look at such numerical sacred cows as the batting average, the body-mass index and the wind-chill factor; clarify the math behind public policy nostrums like Social Security privatization and the flat tax; and reveal what they see as the statistical distortions of The Bible Code and the reasons for taking Zagat scores with a few grains of salt. They conclude with some recommendations on instilling quantitative common sense in students (restricting calculators in the classroom is job one). This engaging book is a great challenge to fuzzy math of all stripes.
Copyright 2003 Reed Business Information, Inc.

From Booklist

Heir to John Allen Paulos (A Mathematician Reads the Newspaper, 1995), this duo continues the noble cause of dispelling math phobia, especially its application in the vital life-skills department. Quantitative information pervades daily affairs, lending an illusion of precision to personal decisions, especially financial ones, that is often just that, illusory. Is lower-priced car A in fact cheaper to own than higher-priced car B? Rather than regard a number as a totem of truth, Niederman and Boyum campaign to instill a healthy skepticism, born of asking, "To what question is this number supposed to be the answer?" Ladling out humor throughout, the authors point out pitfalls in accepting numbers at face value, illustrating how the entity advancing the number often chooses a measurement favorable to itself, a practice notorious in public policy debate. Deception is not inherently intentional, the authors say, and usually stems from lousy quantitative reasoning rather than from dishonesty. Tilting toward an entertaining rather than a didactic presentation, Niederman and Boyum's wry asides and sports examples enliven their message. Gilbert Taylor
Copyright © American Library Association. All rights reserved

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Product Details

• Hardcover: 288 pages
• Publisher: Crown Business; 1st edition (June 10, 2003)
• Language: English
• ISBN-10: 0767909984
• ISBN-13: 978-0767909983
• Product Dimensions: 5.7 x 0.9 x 8.5 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #1,011,995 in Books (See Top 100 in Books)

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28 of 30 people found the following review helpful:

5.0 out of 5 stars and the audience is..., June 8, 2003

By 

Arnold Kling (Silver Spring, Md USA) - See all my reviews
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This review is from: What the Numbers Say: A Field Guide to Mastering Our Numerical World (Hardcover)

This book offers examples of quantitative reasoning, including the topics of compound growth and statistics. Their perspective is that without the ability to work with numbers, people can easily be misled. One of the examples is a statistic used by defense attorney Alan Dershowitz to mislead the jurors in the infamous Simpson trial.

As I was reading the book, I wondered who the audience ought to be. Although the tone is breezy and the examples are presented without the use of algebra or higher mathematics, I am not sure how a math-phobic person would react. My experience with math phobes is that they would feel threatened by the book and be resistant to picking it up.

A better audience for the book might be math educators. As a teacher, I found numerous examples in the book that will be helpful. Moreover, the last chapter, in which they discuss ways to reform math education, is a gem.

What the authors are saying is that people need good basic intuition about numbers in order to understand a world that is increasingly dominated by numerical data. The traditional math curriculum tries to prepare a student to study Newtonian physics. Instead, I think that the authors would argue that the curriculum ought to be aimed at enabling a student to understand stock market ratios and statistical research.

One random note is that the authors attribute the phrase "independence from irrelevant alternatives" to John Nash. I may be wrong, but I believe that it was Kenneth Arrow who brought that concept to the fore.

By filling the book with interesting examples that illustrate the type of quantitative reasoning that they consider important, the authors make a compelling case for the math education reform that they advocate. However, if their primary audience is math educators, that fact is obscured on the book jacket, which makes the intended audience unclear.

19 of 22 people found the following review helpful:

5.0 out of 5 stars Infinitely Interesting! The Russian judge gives it a ...?, November 14, 2003

By 

S. A. Cartwright "Stu Cartwright" (Wayland, MA USA) - See all my reviews
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This review is from: What the Numbers Say: A Field Guide to Mastering Our Numerical World (Hardcover)

Authors Niederman and Boyum articulate that we live today in a new Quantitative Information Age. Strange then, that they did not entitle their book, "Ten Habits of Highly Effective Quantitative Thinkers" (actually the title of Chapter Two) - this book would have sold twice as much.

Ahh! Twice as much as what? As Stephen Covey's books? As much as this book's actual sales? What's the base? Now that I've read this "Field Guide to Mastering Our Numerical World" (actually the subtitle,) I am trained to ask the pertinent questions about numerical comparisons. I have learned to simultaneously "only trust the numbers" and to "never trust the numbers" - habits #1 and #2.

In this entertaining tour of today's quantitative landscape, the authors expose our collective inability to cope with numerical reasoning. From humorous pot shots at "our favorite punching bag, the International Skating Union," whose farcical scoring systems are easily exposed, to a better method of comparing safety between small plane flying and automobile safety, to famous courtroom misuses of statistical data, Niederman and Boyum demonstrate a growing gap between our increasingly data dependent decisions and our nation's declining numerical literacy.

"What The Numbers Say" provides a layman's look at mathematical skills required by everyone. It is a book for non-mathematicians, liberal arts students, teachers of all subjects, political and educational leaders, and above all, parents. To anyone struggling with children struggling to master the multiplication table, and wondering what became of the rote memorization and textbooks from earlier days, the authors make sense of the new teaching techniques. Traditionally, it seems, mathematicians have been Euclideans, "deriving truths, in step-by-step fashion, from first principles or axioms." But, "good quantitative thinkers are Babylonians. They understand that quantities can be measured and expressed in many different ways, and that looking at something from multiple viewpoints enhances perspective and fosters creative thinking." Finally, we understand why our kids can't complete the 9-times Table, but are whizzes at stacking Lego blocks.

Niederman and Boyum embellish their hypotheses deriving wonderful examples of easy-to-comprehend quantitative situations involving baseball, weather forecasting, popular movies, roulette odds, consumer tips, home finance and stock market analysis, timed swimming contests, fair games, and more. Readers cannot fail to understand how simple some of the recipes (Pareto's Law, The Rule of 72, how to interpret Zagat's Restaurant Guides) are for understanding quantitative measurement. Mathematics, long misunderstood as "uncool" for its complicated formulae and notation, in fact, is often a beautiful and handy tool with which to find "the easy way out."

Though the authors uncover highly political ramifications of misunderstood data and twisted statistics (e.g., environmental debates), the book is apolitical save for the last chapter that cries out for educational reforms. Niederman and Boyum sum the book up neatly with suggestions for educators regarding curricula, calculators, and competitiveness. They propose ending the "math wars between Progressives and Traditionalists," and put forth solutions. The authors' main salvo: differentiate between mathematics and quantitative reasoning, and offer training on a separate track for each.

Put this on your 'to-read' list for the coming year. If only to find out how many combinations a 2 X 3 Lego brick can form.

12 of 14 people found the following review helpful:

5.0 out of 5 stars Making Sense of the Numbers We See Every Day., March 16, 2005

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mirasreviews (McLean, VA USA) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (COMMUNITY FORUM 04)    (HALL OF FAME REVIEWER)   

This review is from: What the Numbers Say: A Field Guide to Mastering Our Numerical World (Hardcover)

Premised on the idea that we now live in a "quantitative information age", in which a person can hardly get through a day without reaching some conclusion based on numerical data, but that most people are poor quantitative thinkers who routinely make poor decisions because they are unskilled in analyzing numerical data, authors Derrick Niederman and David Boyum offer us "What the Numbers Say", a guide to spotting the most common kinds of data manipulation and determining what those numbers really mean. I should say that you do not need to know any mathematics beyond a 6th grade level to understand this book or to successfully decipher the numerical data that one encounters in everyday life. "What the Numbers Say" is engaging, clear, and easy to read. There are interesting examples taken from the stock market, business world, and current events for every subject that is discussed. And the examples don't have a pervasive political bias.

"What the Numbers Say" starts off by explaining "The Ten Habits of Highly Effective Quantitative Thinkers" and then dedicates each of six chapters to a different type or facet of quantitative data. "For Good Measure" explains the importance of understanding what unit your numbers are expressing, the problems inherent in distilling an assortment of data into a single number -such as an index, and troubles with rounding numbers. "Playing the Percentages" explores the traps of adding fractions, dealing with negative returns, percentages of percents, and ordinals, i.e. rankings. "Gaining Perspective" talks about very big numbers, very small numbers, and very sensitive numbers -especially denominators. "Throwing a Curve" is about non-linear relationships, including quadratic relationships and exponential relationships (growth and depreciation). "Taking Chances" discusses the three schools of probability: classical, frequentist, subjectivist and various methods of expressing probability. "The Proof is in the Numbers" is a chapter about Statistics that addresses the confusion of correlation and cause, sample sizes, data mining, and surveys. In "A Peace Offering for the Math Wars", the authors offer a critique of the current mathematics curricula and the lack of quantitative thinking instruction in U.S. schools, including their suggestions for remedying some of the problems.

In the book's last chapter, the authors get up on their soapbox about mathematical and quantitative education in American schools, so I trust they won't mind if I get up on mine. I wholeheartedly agree with most of what they say, but I find the authors' reaction to American students' performance in the Trends in International Mathematics and Science Study puzzling. U.S. students are always "smack in the middle of the pack" in those studies, which leads Mr. Niederman and Mr. Boyum to conclude that American students are bad at math and that American schools are bad at teaching it. I don't know why anyone gets bent out of shape about the TIMSS results. Americans do better than average. There are always some anglophone nations that do worse and some that do better. I think the results for American students are rather good considering that we have a significant population of non-native-English speakers in our schools and a very heterogeneous population -culturally, ethnically, and geographically- in general. In any case, the authors acknowledge that "mathematical knowledge and quantitative reasoning are quite different things". So why the fuss?

Speaking on another subject, the authors lament the elementary school mathematics curricula, which is full of useless stuff. That's a hopeless cause, because it doesn't take 6 years to cover basic mathematics. So most of elementary school education is filler and repetition -in all subjects. Junior high school and high school mathematics could be improved though. Not really, but at least in theory. There is nothing in a "pre-algebra" class that anyone needs to do algebra; there's nothing in a "pre-calculus" class that anyone needs to do calculus; and there's nothing in a geometry class that couldn't be memorized in 10 minutes. Ditching those courses would allow school systems to require that all students take a quantitative reasoning course and one year of calculus without placing any more burden on students or budgets. In the meantime, why not design a quantitative reasoning curriculum that could be made available to high school students taking internet or correspondence courses and publishers of homeschooling materials? As for all those students who reach for a calculator when their brain would do just fine... I recommend Isaac Asimov's short story "The Feeling of Power".