A decade ago, computer scientist Douglas Hofstadter coined the term innumeracy, which aptly described the widespread ailment of poor quantitative thinking in American society. So, in What the Numbers Say, Derrick Niederman and David Boyum present clear and comprehensible methods to help us process and calculate our way through the world of "data smog" that we live in. Avoiding abstruse formulations and equations, Niederman and Boyum anchor their presentations in the real world by covering a particular quantitative idea in relation to a context-like probability in the stock market or interest-rate percentages. And while this information is useful toward helping us to be more financially adept, What the Numbers Say is not merely about money. We learn why there were such dramatic polling swings in the 2000 U.S. presidential election and why the system of scoring for women's figure skating was so controversial in the 2002 Winter Olympics, showing us that good quantitative thinking skills are not only practical but fun.
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. -- PUBLISHERS WEEKLY.
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June 07, 2004
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Excerpt from What the Numbers Say by Derrick Niederman
The Quantitative Information Age
Whether we realize it or not, quantitative information pervades our professional and personal lives. Every time a doctor reads a patient's chart, a farmer weighs a hog, a businesswoman reviews a budget, or a driver glances at a speedometer, someone is seeking quantitative information. And thanks to computers and the Internet, numbers are spreading faster than deer populations. A few years back, a car shopper found it hard to get much in the way of guidance--a magazine article here, a friend's opinion there. Now, a little web surfing reveals sticker and invoice prices, dealer holdbacks and incentive packages, depreciation estimates, customer satisfaction ratings, reliability statistics, expected insurance costs, crash test results and various accident, injury, and fatality rates, not to mention a wealth of financing data. We may say we live in the "Information Age," but it might be more accurate to say we live in the "Quantitative Information Age."
As technology builds this crescendo of numbers, our ability to make wise decisions, whether at work or at home, increasingly depends on proficiency with quantitative information. Unfortunately, Americans seem much better at producing numbers than making sense of them. It was to underscore this point that cognitive scientist Douglas Hofstadter coined the term "innumeracy," a word brought into the national spotlight by John Allen Paulos's pathbreaking book of the same name.1 But identifying educational failures is far easier than remedying them, and while countless books, articles, and government reports have diagnosed the widespread ailment of poor quantitative thinking, they have not provided therapy. Or at least not much of it. That's where this book comes in. Our goal is to introduce you to the quantitative concepts, skills, and habits you need for success in work, and success in life.
Sounds dreadful, doesn't it? Yet another remedial math book. Well, if that's what you're expecting, we've got good news. It turns out that formal mathematics is not the best way to teach quantitative thinking, and superior quantitative reasoning is not restricted to those who aced high school math.
Imagine, if you will, the work of an accountant, green eyeshade and all. Few jobs involve greater contact with numbers, and quantitative skills are an obvious prerequisite. If an accountant isn't good with figures, he might not notice a liability that has been excluded from a company's balance sheet, or a depreciation charge that has been miscalculated. Yet how much advanced mathematics is required to assess numbers on financial statements? These numbers get added, subtracted, multiplied, divided, and displayed as fractions, decimals, and percentages. They don't get expressed as Gaussian integers. The last time we looked at a financial statement, we didn't see a --, a , a u, or a $.
Think about other professional occupations--architects, doctors, management consultants, financial planners, marketing executives. Again, large amounts of quantitative information are a feature of many such jobs, and good quantitative thinking is critical to doing the jobs well. But matrix algebra is not required. Nor are high school staples such as quadratic equations, analytic geometry, and imaginary numbers.
This is why high school math teachers fear nothing more than the question, "Why do I need to learn this?" The conventional response, "Because you'll need the skill in your job," is dishonest, because even if the class contains some future engineers, they aren't the ones asking the question. The more honest reply, "Because you'll need it for the SAT," wins points for candor but loses them right back to overt cynicism. Thomas Jefferson's endorsement of mathematics--"The faculties of the mind, like the members of the body, are strengthened and improved by exercise"2--is closer to our idea of why the study of math is so essential, but we admit that such an argument will hardly motivate apathetic teenagers.
But if math isn't the key to good quantitative thinking, what in the world is inside this book? Here's a sneak preview. What distinguishes good quantitative thinkers is not their skill with pure mathematics, but rather their approach to quantitative information. Effective quantitative thinkers possess certain attitudes, skills, and habits that they bring to bear whenever they need to make decisions based on numbers. And with rare exception, these attitudes, skills, and habits are not taught in math classes or textbooks. For example, good quantitative thinkers demand empirical evidence instead of conventional wisdom. At the same time, they assume that figures are often wrong or misleading. Good quantitative thinkers don't examine quantitative information until they have a strategy for doing so. They know that some numbers are far more important than others, and they systematically pare data in an effort to find the most revealing figures. They also make lots of rough estimates, scribble on the backs of envelopes, and use arithmetic shortcuts like the Rule of 72. These are the skills we intend to convey.