Über die Autorin bzw. den Autor

Kaiser Fung is a statistician with more than a decade of experience in applying statistical methods to unlocking the relationship between advertising and customer behaviors. His blog, "Junk Charts," pioneered the genre of critically examining data and graphics in the mass media. Since 2005, "Junk Charts" has received rave reviews from Science magazine, the Guardian, Yahoo!, and Stanford University Libraries. He is an adjunct professor at New York University where he teaches practical statistics to professionals, and holds statistics, business, and engineering degrees from Cambridge, Harvard, and Princeton Universities. Fung is also a fellow of the Royal Statistics Society.

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NUMBERS RULE YOUR WORLD

McGraw-Hill

Contents

Chapter One

The Discontent of Being Averaged

Meter mystery If no one likes, why obey? One car per green, please —Haiku about the Minneapolis–St. Paul commute by reader of the Roadguy blog

Heimlich's Chew Chew Train Good film, big buildup, nice queue Twenty-second ride —Haiku about Disney by Anonymous

In early 2008, James Fallows, longtime correspondent at The Atlantic, published an eye-popping piece about America's runaway trade deficit with China. Fallows explained how the Chinese people were propping up Americans' standard of living. The highbrow journal has rarely created buzz on the Internet, but this article beat the odds, thanks to Netizens who scrapped Fallows's original title ("The $1.4 Trillion Question") and renamed the article "Average American Owes Average Chinese $4,000." In three months, Internet readers rewarded the piece with more than 1,600 "diggs," or positive responses, which is the high-tech way of singing praise. Evidently, the new headline caught fire. Our brains cannot comfortably process astronomical numbers such as $1.4 trillion, but we can handle $4,000 per person with ease. Simply put, we like large numbers averaged.

The statistical average is the greatest invention to have eluded popular acclaim. Everything has been averaged by someone, somewhere. We average people ("average Joe") and animals ("the average bear"). Inanimate things are averaged: to wit, after the terrorist attacks of September 11, 2001, a security dispatch demonstrated how to "weaponize the average water cooler." Economic processes are averaged, as when a market observer in early 2008 proclaimed "the new hope: an average recession," presumably predicting a shallow one that would depart with haste. Even actions cannot escape: when Barack Obama's lawyer interjected on a Clinton conference call during the heated Democratic primary elections of 2008, the media labeled the occasion "not your average conference call."

Can rare items be averaged? You bet. Forbes magazine told us, "The average billionaire [in 2007] is 62 years old." Surely no one averages uncountable things, you think. Not so quick; the U.S. Census Bureau has devised a methodology for averaging time: on an "average day" in 2006, U.S. residents slept 8.6 hours, worked 3.8 hours, and spent 5.1 hours doing leisure and sporting activities. It is a near impossibility to find something that has not been averaged. So pervasive is the idea that we assume it to be inborn and not learned, nor in need of inventing.

Now picture a world without averages. Imagine having the average child, the average bear, and the average such-and-so-forth punched out of our lexicon. We are dumbfounded to learn that such a world did exist once, before a Belgian statistician, Adolphe Quetelet, invented the "average man" (l'homme moyen) in 1831. Who would have thought: such a commonplace idea is younger than the U.S. Constitution!

Before Quetelet, no one had entertained the import of statistical thinking to the social sciences. Up until that time, statistics and probability fascinated only the astronomers who decoded celestial phenomena and the mathematicians who analyzed gambling games. Quetelet himself was first a distinguished astronomer, the founding director of the Brussels Observatory. It was in midlife that he set the ambitious agenda to appropriate scientific techniques to examine the social milieu. He placed the average man at the center of the subject he named "social physics." While the actual methods of analysis used by Quetelet would strike modern eyes as hardly impressive, historians have, at long last, recognized his impact on the instruments of social science research as nothing short of revolutionary. In particular, his inquiry into what made an able army conscript earned the admiration of Florence Nightingale (it is little known that the famous nurse was a superb statistician who became an honorary member of the American Statistical Association in 1874). In this body of work also lay the origin of the body mass index (BMI), sometimes called the Quetelet index, still used by doctors today to diagnose overweight and underweight conditions.

Since the concept of the average man has been so firmly ingrained into our consciousness, we sometimes fail to appreciate how revolutionary Quetelet really was. The average man was literally an invention, for the average anything did not, and does not, physically exist. We can describe it, but we cannot place it. We know it but have never met it. Where does one find the "average Joe"? Which "average bear" can Yogi Bear outsmart? Which call is the "average" conference call? Which day is the "average" day?

Yet this monumental invention constantly tempts us to confuse the imaginary with the real. Thus, when Fallows calculated an average of $4,000 debt to China per American, he implicitly placed all Americans on equal footing, spreading $1.4 trillion evenly among the population, replacing 300 million individuals with 300 million clones of the imaginary average Joe. (Incidentally, the Netizens mistakenly fabricated only 300 million Chinese clones, rhetorically wiping out three-quarters of China's 1.3 billion people. The correct math should have found the average Chinese lending $1,000 to America.) Averaging stamps out diversity, reducing anything to its simplest terms. In so doing, we run the risk of oversimplifying, of forgetting the variations around the average.

Hitching one's attention to these variations rather than the average is a sure sign of maturity in statistical thinking. One can, in fact, define statistics as the study of the nature of variability. How much do things change? How large are these variations? What causes them? Quetelet was one of the first to pursue such themes. His average man was not one individual but many; his goal, to contrast different types of average individuals. For him, computing averages was a means of measuring diversity; averaging was never intended to be the end itself. The BMI (Quetelet index), for good measure, serves to identify individuals who are not average, and for that, one must first decide what the average is.

To this day, statisticians have followed Quetelet's lead, and in this chapter, we shall explore how some of them use statistical thinking to battle two great inconveniences in modern living: the hour-long commute to and from work and the hour-long wait to get on a theme park ride. A reasonable person, when trapped in traffic or stuck in a long queue, will suspect that whoever was in charge of planning must have fallen asleep on the job. To see why this reaction misplaces the blame, we need to know a little about the statistics of averages. Working with engineers and psychologists, statisticians are applying this knowledge to save us waiting time.

* * *

To label Dr. Edward Waller and Dr. Yvette Bendeck Disney World die-hards would be an understatement. On October 20, 2007, they toured every last open attraction in the Magic Kingdom in just under thirteen hours. That meant fifty rides, shows, parades, and live performances. Buzz Lightyear's Space Ranger Spin, Barnstormer at Goofy's Wiseacre Farm, Beauty and the Beast—Live on Stage, Splash Mountain, Mad Tea Party, Many Adventures of Winnie the Pooh, you name...