One of the longest routes in the Outer Rim, it began amid the Hutt-controlled Rim worlds near Aduba, meandered Coreward around the tip of Hutt Space, before turning north into the edges of the Tion Cluster. From there it skirted the Radama Void , intersected the Hydian Way at Botajef , and emptied in the northern quadrant. The Braxant Run was the northern quadrant's most important route, beginning at Bandomeer on the Hydian and twisting across the New Territories via Muunilinst to Bastion.
The third of the Outer Rim's three most important routes, the Triellus Trade Route spanned more than 75, light-years from Centares to Enarc , forming one side of the " Spice Triangle ". However, travel along the "Hutt Highway" was slow and often dangerous owing to smugglers, slavers and pirates operating out of Hutt Space.
Thriving trade turned Nal Hutta's moon Nar Shaddaa into a boomworld. However, the supernova of the star of the Kyyr system in BBY made the route unnavigable. The Ootmian was eventually restored, but the rise of the Corellian Run finished Nar Shaddaa as a respectable tradeworld, with legitimate business moving elsewhere and the moon becoming one of the galaxy's most notorious shadowports. It was speculated that the Kyyr supernova was thus responsible for the shift of the Hutt kajidics towards criminal enterprises.
There were some routes that were used for more illegal purposes, in particular the illicit trade of smuggling. One of the most infamous examples of illegal routes was the Kessel Run , an The notorious smuggler Han Solo claimed to have navigated the Kessel Run in under 12 parsecs with his ship, the Millennium Falcon , by skirting close to the black holes that made up part of the Kessel Run. The Ison Corridor was a fairly small route within the Corellian Trade Spine, which had five system stops before reconnecting with the Spine, and was connected from the coreward region to the rimward region.
The Sisar Run was a hyperspace trade route originating in the Tharin sector , where it passed through the heart of the Periphery, passing through Hutt Space and Srillur and bypassing the Si'Klatta Cluster before it splits at Sispe.
Myto's Arrow , named after its discoverer, the Galactic Republic scout Keos Myto , was a route located in the Outer Rim that was used for travel between the Raioballo sector via Dantooine and the Obtrexta sector. The Daragon Trail , well known for being the longest blind jump to have been made successfully in the history of the galaxy, travelled between Korriban in the Outer Rim and Empress Teta which at the time of the route's discovery was named Koros Major in the Deep Core.
Portions of it were merged with the smuggling route Carbonite Run. Under the Galactic Republic, the peoples of the galaxy were represented in the legislative body known as the Galactic Senate. Originally, any sufficiently-populated star system would return a senator , but this was soon rejected as a recipe for gridlock as the Republic expanded massively and thousands of delegates attended Senate meetings.
The Planetary Senate gave way to sectorial representation: the Republic was divided into sectors containing no more than fifty inhabited systems - it was feared that larger sectors would form the seeds of breakaway empires - which were each represented by a single sectorial senator. However, the price of passing this amendment was additional legislation that allowed many of the Republic's Core Founders to retain their planetary seats, giving extra votes to the most powerful Core and Colonies sectors.
To strict Galactic Constitutionalists , this was the Republic's "founding tyranny", a cynical scheme to preserve the power of the Core systems. Indeed, the awarding of single-system votes caused such an outcry that a compromise was reached: anyone recognized as a representative of a single system had the right to petition the full Senate, a right still occasionally invoked under the New Republic Senate.
Sectors grew to include thousands of star systems, but even with the "rule of fifty" widely ignored, the Republic expanded to include millions of sectors by 17, BBY , once again rendering the galaxy ungovernable. In the aftermath of the First Alsakan Conflict , the Challat Compromise was adopted, which split the legislature into a seated Senate, whose members had full rights of address, and an unseated Senate, whose members had to petition for such rights.
Predictably, the seated senators became power-brokers, and corruption thrived, with unseated senators having to trade the vast majority of their votes for the chance to be heard in the Senate. The Ruusan Reformations of BBY saw a remarkable dismantling of central authority and reorganized the Republic into 1, regional sectors, each represented by a single senator, though once again a series of exceptions favored planets in the Core and Colonies.
Additionally, the right of representation was extended to so-called functional constituencies representing discreet cultural and species enclaves.
While the galaxy was once again governable, the Reformations inevitably placed power into the hands of a very few, especially when the definition of functional constituencies was extended in BBY to the galaxy's mightiest guilds and corporations, chief among them the Trade Federation. The Trade Federation bought up vast blocs of votes from poor sectors and gained control of key appointments in the bureaucracy, and by the time of the Separatist Crisis was the Senate's greatest power and paralyzed the Senate in the face of the Confederacy of Independent Systems.
The New Republic restored the body, but it inevitably again became mired in gridlock, archaic tradition, and corruption. When the New Republic was reorganized into the Galactic Federation of Free Alliances during the Yuuzhan Vong War , the very name of the new state seemed to be an acceptance of the need for decentralization of power. However, efforts to rehabilitate the galaxy after the Yuuzhan Vong War depended heavily on centralized power, leading to the rebellion of independent-minded systems in a Confederation led by Corellia , and so the ancient problem of galactic democracy begun a Second Galactic Civil War.
Hutt Space was a large stretch of the Outer and Mid Rims, dominated by the Hutts , that eluded central control for millennia. The Allied Regions were independent states that freely joined the Galactic Republic as it expanded early in its history, with their rulers receiving the honorary title of Moff.
By the time of the Clone Wars, most Allied Regions had been divided into sectors, but a handful endured as regions with a discreet cultural identity, such as the Trailing Sectors or the New Territories ; or a sector dominated by a single species, such as Trianii Space. Several of these governments survived as client states under the Galactic Empire and maintained a degree of independence, and were recognized by the New Republic afterwards.
Hutt Space referred to the large stretch of the Rimward Slice controlled by the Hutt Ruling Council , the governing body of the Hutt species. Originally powerful warriors, the Hutt Empire overthrew the empire of Xim the Despot , but a disastrous civil war around 15, BBY known as the Hutt Cataclysms forced a cultural reformation, beginning a new philosophy known as kajidic , which stressed economic dominance over outright conquest.
Hutt Space's borders ebbed and flowed over the millennia but the Hutts' power in both the economic and the criminal spheres endured, extending as far Coreward as Gyndine as the Galactic Republic decayed during the Separatist Crisis. Hutt Space was nominally part of the Galactic Empire, but the New Order largely tolerated the Hutts' criminal dealings, as the Hutt Ruling Council was a known quantity as opposed to the possibility of hundreds of feuding Hutt crime lords.
Hutt Space was devastated during the Yuuzhan Vong War , but recovered surprisingly quickly, bringing with it a renewed Hutt militarism that was expressed when the region declared for the Confederation during the Second Galactic Civil War. The Corporate Sector Authority CSA referred to the government of the Corporate Sector , a region of close to thirty thousand star systems on the edge of the Tingel Arm ruled from Etti IV , and was a collective of businesses and corporations granted exclusive rights to all resources in the territory.
The experiment in corporate governance, while protecting the rights of workers, began after lessons were learned from the Outer Expansion Zone scandal.
At the suggestion of Baron Orman Tagge , the Corporate Sector was vastly expanded under the Galactic Empire and it became an officially-sanctioned refuge for Loyalist corporations seeking to avoid nationalization. The CSA became the region's sole owner, employer, government, and military, while corporations that invested in the Authority would receive proportional shares of the profits.
The Centrality was a long strip of territory to the north of Hutt Space, founded as a libertarian independent state in BBY. Human -dominated, the capital of Erilnar often fell under the influence of the Hutt kajidics , which were often the beneficiaries of the profits of the Centrality's main export, the life-crystals of Rafa V.
The Centrality was formally an Imperial territory, but was generally left alone by Imperial Center. Emperor Palpatine's sole act concerning the region occurred several years prior to the Battle of Yavin , when he gave de facto control of the Centrality to Rokur Gepta , Sorcerer of Tund , who was later killed by Lando Calrissian in defense of the region's native Oswaft at the Battle of ThonBoka.
Isolationist and matriarchal, the secretive Hapans became legendary for their reputed wealth, beauty, pride, and aristocratic feuds. Emperor Palpatine's tolerance of the region's independence surprised many, and it was suggested that the Emperor maintained Hapes as a lesson to the galaxy in the dangers of insularity and decadence. The Hapes Cluster was an isolationist grouping of 63 inhabited worlds ruled by the matriarchal Queen Mothers.
The political, diplomatic and military writings of Atrisia , in particular the Sayings of Uueg Tching , had been studied for millennia.
The insular territory declared independence after Emperor Palpatine's death at Endor but later accepted Allied Region status in the New Republic. Similarly, Nouane began as a thriving Inner Rim empire beyond the Slice, and was renowned for its philosophers and thinkers, in particular the controversial Four Sages of Dwartii. Nouanese ministers were common in the young Republic, and the territory sought Allied Region status after being ravaged by the Mandalorian Crusaders in BBY.
The region of planets was a loyal supporter of the Empire and declared independence under the New Republic. Bothan Space included some settled systems in the Mid Rim, dominated by Bothan colonists and ruled by the Bothan Council.
One of the few species close to Hutt Space to preserve their independence, the Bothans were credited with the diplomacy and espionage that preserved the stability of much of the Mid Rim. The ursine Botori controlled two dozen star systems within a nebula while the Human Dawferim controlled just over thirty systems.
The two states had fought no less than forty wars even after they accepted Allied Region status under the Galactic Republic, and both declared independence after the Declaration of a New Republic. Herglic Space referred to the shrunken remnant of the Herglic Trade Empire. It consisted of some forty star systems around the Rimma Trade Route , but hundreds of worlds along the Rimma outside Herglic Space had substantial Herglic populations.
Religiously fundamentalist, the region had evolved a common culture where each species was seen as complementary to the other two and the rest of the galaxy was seen as unholy. Each species ruled sixty-three star systems while another three were open to outlanders under strict conditions. Paqwepori was a small cluster of ninety rich star systems just off the Corellian Run in the Mid Rim. Paqwepor Major 's bazaars were popular destinations for Republic traders expanding the Corellian Run for eons.
The Paqwepori were known for their love of business and ambition while despising any law that could limit individual expression or initiative. The spread of technology and civilization throughout the galaxy led to the development of the galactic economy , the system of production, distribution, trade, and consumption of goods.
Few planets were entirely self-sufficient, with some, such as the factory worlds of Telti and Mechis III , devoting their economies solely to the production of high-tech goods but relying on agriworlds for food. In turn, these agriworlds relied on on manufacturing worlds to supply heavy equipment to harvest and process foodstuffs , and chemical industries to produce fertilizers and pesticides. The importance of the galactic economy meant that a number of megacorporations were able to acquire immense economic and political power.
In the years prior to the Clone Wars , the Trade Federation , a conglomerate of shipping and merchant cartels, controlled the votes of hundreds of star systems in the Galactic Senate by making their commerce dependent on its Merchant Fleet and enforcing deals with the Trade Defense Force. TaggeCo controlled hundreds of star systems and dozens of subsidiaries, making it one of the galaxy's most influential organizations. Even relatively small businesses, such as the Figg conglomerate in the Greater Javin , commanded substantial influence on their homeworlds and sectors.
The main currency of the Galactic Republic was the Galactic Credit Standard , divided into ten decicreds. Of the galaxy's one billion settled systems, the majority of these were lightly-settled colonies of little note that were often not even marked on sector maps. During the days of the Galactic Empire more than 69 million systems met the requirements for Imperial representation, and 1. Because only around a quarter of the galaxy's four hundred billion stars had been thoroughly surveyed, scientists were uncertain as to the true number of intelligent species.
The Galactic Empire recognized five million intelligent species, though it was mathematically accepted that galactic civilization had yet to discover a large number of species and the total could be as high as twenty million.
An Ithorian playing holochess against a Human opponent, as a Baragwin observes. In classical history, the dominant species were Humans.
Originating from the Core Worlds, Humans were the most populous species in the galaxy and so tended to form the basis of the major governments. Sentients other than Humans were sometimes known as " aliens ", though the term "non-Human" was considered less offensive. Nevertheless, the Humanocentric definition of races was considered unacceptable by some, and simply another expression of unwarranted Human dominance.
Although not considered a race for obvious reasons, droids formed a significant part of society, helping and coexisting with the population. On Naboo , higher level droids were considered equal as fellow sentients. Whether the Asogian expedition to another galaxy succeeded or not is unknown. Extra-galactic travel was difficult due to a hyperspace disturbance beyond the edge of the galaxy that prevented hyperspace routes very far outside the disk, and beyond this, the barren vastness of the Intergalactic Void.
However, by the time of the Clone Wars , contact had been established with the two small galaxies orbiting the galaxy: the Rishi Maze , also known as Companion Aurek, and Firefist , also known as Companion Besh. The InterGalactic Banking Clan had influence as far as these locations. The Extragalactic Society was an organization devoted to the search for life outside the galaxy. Two major expeditions were launched around the period of the Clone Wars in an effort to explore beyond the galaxy: the Outbound Flight Project was intended to settle another galaxy but was destroyed by the Chiss after it accidentally entered their territory in the Unknown Regions.
The Yuuzhan Vong were the most infamous extra-galactic species. Just after the Battle of Endor, the Nagai and the Tofs , races native to the companion galaxy of Firefist, invaded the galaxy, the Nagai hoping to escape the Tofs, who had oppressed them for centuries. Assisted by the Alliance of Free Planets and the Mandalorians , the Nagai defeated the Tofs and returned to liberate their home galaxy, bringing the Nagai—Tof War to a close.
Among the best known extra-galactic aliens were those that had fled from the Yuuzhan Vong galaxy : the droid races of the Abominor and the Silentium , and the Yuuzhan Vong themselves and their slave soldiers, the Chazrach.
The Abominor and the Silentium fought a devastating war before the Yuuzhan Vong rose up against both and drive them from their galaxy. Of those Silentium and Abominor that survived, two, the Great Heep and Vuffi Raa , established themselves in the galaxy proper around the time of the Galactic Civil War. The former was destroyed on Biitu and the latter was recovered by the Silentium after the Battle of ThonBoka. After driving the Silentium and the Abominor from their galaxy, the Yuuzhan Vong turned inward and fought their own civil war, the Cremlevian War , which stripped much of their galaxy of life.
Seeking a new home, the Yuuzhan Vong and the Chazrach crossed the Intergalactic Void for millennia until they arrived in the galaxy, beginning a religious war which almost destroyed galactic civilization while it was just recovering from the Galactic Civil War.
The second most common language was Huttese , expanded through the criminal and financial activity of the Hutts, and so it was adopted throughout the Outer Rim Territories by other species that were in close cooperation with them throughout the ages, such as the Rodians and the Toydarians. The dominant writing system in the galaxy was Aurebesh , derived from the script of the Rakatan Infinite Empire by its former subject species after the Empire collapsed, though the symbols themselves were possibly much older.
Derived from Tionese characters , the High Galactic alphabet was popular among the upper class, and as late as 22 BBY , one-third of Republic citizens who spoke Basic used the High Galactic alphabet. When you read in the newspaper that eating a bran muffin every day will reduce your chances of getting colon cancer, you need not fear that some unfortunate group of human experimental subjects has been force-fed bran muffins in the basement of a federal laboratory somewhere while the control group in the next building gets bacon and eggs.
Instead, researchers will gather detailed information on thousands of people, including how frequently they eat bran muffins, and then use regression analysis to do two crucial things: 1 quantify the association observed between eating bran muffins and contracting colon cancer e. Of course, CSI: Regression Analysis will star actors and actresses who are much better looking than the academics who typically pore over such data. What individuals are most likely to become terrorists?
Olympic beach volleyball team. When she gets the printout from her statistical analysis, she sees exactly what she has been looking for: a large and statistically significant relationship in her data set between some variable that she had hypothesized might be important and the onset of autism. She must share this breakthrough immediately! The researcher takes the printout and runs down the hall, slowed somewhat by the fact that she is wearing high heels and a relatively small, tight black skirt.
She finds her male partner, who is inexplicably fit and tan for a guy who works fourteen hours a day in a basement computer lab, and shows him the results. Together the regression analysis experts walk briskly to see their boss, a grizzled veteran who has overcome failed relationships and a drinking problem.
Just about every social challenge that we care about has been informed by the systematic analysis of large data sets. In many cases, gathering the relevant data, which is expensive and time-consuming, plays a crucial role in this process as will be explained in Chapter 7.
I may have embellished my characters in CSI: Regression Analysis but not the kind of significant questions they could examine. There is an academic literature on terrorists and suicide bombers—a subject that would be difficult to study by means of human subjects or lab rats for that matter.
One such book, What Makes a Terrorist , was written by one of my graduate school statistics professors. The book draws its conclusions from data gathered on terrorist attacks around the world.
A sample finding: Terrorists are not desperately poor, or poorly educated. Well, that exposes one of the limitations of regression analysis. We can isolate a strong association between two variables by using statistical analysis, but we cannot necessarily explain why that relationship exists, and in some cases, we cannot know for certain that the relationship is causal, meaning that a change in one variable is really causing a change in the other.
In the case of terrorism, Professor Krueger hypothesizes that since terrorists are motivated by political goals, those who are most educated and affluent have the strongest incentive to change society. These individuals may also be particularly rankled by suppression of freedom, another factor associated with terrorism.
This discussion leads me back to the question posed by the chapter title: What is the point? The point is not to do math, or to dazzle friends and colleagues with advanced statistical techniques. The point is to learn things that inform our lives. As a result, there are numerous reasons that intellectually honest individuals may disagree about statistical results or their implications. At the most basic level, we may disagree on the question that is being answered.
As the next chapter will point out, more socially significant questions fall prey to the same basic challenge. What is happening to the economic health of the American middle class? Nor can we create two identical nations —except that one is highly repressive and the other is not—and then compare the number of suicide bombers that emerge in each. Even when we can conduct large, controlled experiments on human beings, they are neither easy nor cheap.
Researchers did a large-scale study on whether or not prayer reduces postsurgical complications, which was one of the questions raised earlier in this chapter. We conduct statistical analysis using the best data and methodologies and resources available. Statistical analysis is more like good detective work hence the commercial potential of CSI: Regression Analysis.
Smart and honest people will often disagree about what the data are trying to tell us. But who says that everyone using statistics is smart or honest? As mentioned, this book began as an homage to How to Lie with Statistics, which was first published in and has sold over a million copies. The reality is that you can lie with statistics. Or you can make inadvertent errors. In either case, the mathematical precision attached to statistical analysis can dress up some serious nonsense. This book will walk through many of the most common statistical errors and misrepresentations so that you can recognize them, not put them to use.
So, to return to the title chapter, what is the point of learning statistics? To summarize huge quantities of data. To make better decisions. To answer important social questions. To recognize patterns that can refine how we do everything from selling diapers to catching criminals.
To catch cheaters and prosecute criminals. To evaluate the effectiveness of policies, programs, drugs, medical procedures, and other innovations. And to spot the scoundrels who use these very same powerful tools for nefarious ends. If you can do all of that while looking great in a Hugo Boss suit or a short black skirt, then you might also be the next star of CSI: Regression Analysis. In that case, the United States would have a Gini Index of The first question is profoundly important.
It tends to be at the core of presidential campaigns and other social movements. The second question is trivial in the literal sense of the word , but baseball enthusiasts can argue about it endlessly. What the two questions have in common is that they can be used to illustrate the strengths and limitations of descriptive statistics, which are the numbers and calculations we use to summarize raw data.
That would be raw data, and it would take a while to digest, given that Jeter has played seventeen seasons with the New York Yankees and taken 9, at bats. Or I can just tell you that at the end of the season Derek Jeter had a career batting average of. It is easy to understand, elegant in its simplicity—and limited in what it can tell us.
Baseball experts have a bevy of descriptive statistics that they consider to be more valuable than the batting average. I called Steve Moyer, president of Baseball Info Solutions a firm that provides a lot of the raw data for the Moneyball types , to ask him, 1 What are the most important statistics for evaluating baseball talent?
Ideally we would like to find the economic equivalent of a batting average, or something even better. We would like a simple but accurate measure of how the economic well-being of the typical American worker has been changing in recent years. Are the people we define as middle class getting richer, poorer, or just running in place? Per capita income is a simple average: total income divided by the size of the population. Congratulations to us. There is just one problem. My quick calculation is technically correct and yet totally wrong in terms of the question I set out to answer.
To begin with, the figures above are not adjusted for inflation. Per capita income merely takes all of the income earned in the country and divides by the number of people, which tells us absolutely nothing about who is earning how much of that income—in or in As the Occupy Wall Street folks would point out, explosive growth in the incomes of the top 1 percent can raise per capita income significantly without putting any more money in the pockets of the other 99 percent.
In other words, average income can go up without helping the average American. As with the baseball statistic query, I have sought outside expertise on how we ought to measure the health of the American middle class.
From baseball to income, the most basic task when working with data is to summarize a great deal of information. There are some million residents in the United States. A spreadsheet with the name and income history of every American would contain all the information we could ever want about the economic health of the country—yet it would also be so unwieldy as to tell us nothing at all. The irony is that more data can often present less clarity. So we simplify. We perform calculations that reduce a complex array of data into a handful of numbers that describe those data, just as we might encapsulate a complex, multifaceted Olympic gymnastics performance with one number: 9.
The good news is that these descriptive statistics give us a manageable and meaningful summary of the underlying phenomenon. The bad news is that any simplification invites abuse. Descriptive statistics can be like online dating profiles: technically accurate and yet pretty darn misleading.
You have finished reading about day seven of the marriage when your boss shows up with two enormous files of data. One file has warranty claim information for each of the 57, laser printers that your firm sold last year. For each printer sold, the file documents the number of quality problems that were reported during the warranty period. The other file has the same information for each of the , laser printers that your chief competitor sold during the same stretch.
In this case, we want to know the average number of quality problems per printer sold for your firm and for your competitor. You would simply tally the total number of quality problems reported for all printers during the warranty period and then divide by the total number of printers sold. Remember, the same printer can have multiple problems while under warranty.
You would do that for each firm, creating an important descriptive statistic: the average number of quality problems per printer sold. That was easy. Or maybe not. Bill Gates walks into the bar with a talking parrot perched on his shoulder.
The parrot has nothing to do with the example, but it kind of spices things up. Obviously none of the original ten drinkers is any richer though it might be reasonable to expect Bill Gates to buy a round or two.
The sensitivity of the mean to outliers is why we should not gauge the economic health of the American middle class by looking at per capita income.
Because there has been explosive growth in incomes at the top end of the distribution—CEOs, hedge fund managers, and athletes like Derek Jeter—the average income in the United States could be heavily skewed by the megarich, making it look a lot like the bar stools with Bill Gates at the end. The median is the point that divides a distribution in half, meaning that half of the observations lie above the median and half lie below. If there is an even number of observations, the median is the midpoint between the two middle observations.
If you literally envision lining up the bar patrons on stools in ascending order of their incomes, the income of the guy sitting on the sixth stool represents the median income for the group.
If Warren Buffett comes in and sits down on the twelfth stool next to Bill Gates, the median still does not change. The number of quality problems per printer is arrayed along the bottom; the height of each bar represents the percentages of printers sold with that number of quality problems. Because the distribution includes all possible quality outcomes, including zero defects, the proportions must sum to 1 or percent. The distribution is slightly skewed to the right by the small number of printers with many reported quality defects.
These outliers move the mean slightly rightward but have no impact on the median. With a few keystrokes, you get the result. Because the Kardashian marriage is getting monotonous, and because you are intrigued by this finding, you print a frequency distribution for your own quality problems. These outliers inflate the mean but not the median. More important from a production standpoint, you do not need to retool the whole manufacturing process; you need only figure out where the egregiously low-quality printers are coming from and fix that.
Meanwhile, the median has some useful relatives. The distribution can be further divided into quarters, or quartiles. The first quartile consists of the bottom 25 percent of the observations; the second quartile consists of the next 25 percent of the observations; and so on. Or the distribution can be divided into deciles, each with 10 percent of the observations. If your income is in the top decile of the American income distribution, you would be earning more than 90 percent of your fellow workers.
We can go even further and divide the distribution into hundredths, or percentiles. The benefit of these kinds of descriptive statistics is that they describe where a particular observation lies compared with everyone else. If I tell you that your child scored in the 3rd percentile on a reading comprehension test, you should know immediately that the family should be logging more time at the library.
If the test was easy, then most test takers will have a high number of answers correct, but your child will have fewer correct than most of the others. Here is a good point to introduce some useful terminology. If I shoot 83 for eighteen holes of golf, that is an absolute figure. I may do that on a day that is 58 degrees, which is also an absolute figure. Absolute figures can usually be interpreted without any context or additional information.
The exception might be if the conditions are particularly awful, or if the course is especially difficult or easy. If I place ninth in the golf tournament, that is a relative statistic.
Most standardized tests produce results that have meaning only as a relative statistic. But when I convert it to a percentile—meaning that I put that raw score into a distribution with the math scores for all other Illinois third graders—then it acquires a great deal of meaning. If 43 correct answers falls into the 83rd percentile, then this student is doing better than most of his peers statewide.
In this case, the percentile the relative score is more meaningful than the number of correct answers the absolute score. Another statistic that can help us describe what might otherwise be a jumble of numbers is the standard deviation, which is a measure of how dispersed the data are from their mean. In other words, how spread out are the observations? Suppose I collected data on the weights of people on an airplane headed for Boston, and I also collected the weights of a sample of qualifiers for the Boston Marathon.
Now assume that the mean weight for both groups is roughly the same, say pounds. Anyone who has been squeezed into a row on a crowded flight, fighting for the armrest, knows that many people on a typical commercial flight weigh more than pounds.
But you may recall from those same unpleasant, overcrowded flights that there were lots of crying babies and poorly behaved children, all of whom have enormous lung capacity but not much mass. When it comes to calculating the average weight on the flight, the heft of the pound football players on either side of your middle seat is likely offset by the tiny screaming infant across the row and the six- year-old kicking the back of your seat from the row behind.
On the basis of the descriptive tools introduced so far, the weights of the airline passengers and the marathoners are nearly identical. My eight-year-old son might point out that the marathon runners look like they all weigh the same amount, while the airline passengers have some tiny people and some bizarrely large people. The standard deviation is the descriptive statistic that allows us to assign a single number to this dispersion around the mean.
The formulas for calculating the standard deviation and the variance another common measure of dispersion from which the standard deviation is derived are included in an appendix at the end of the chapter.
Your doctor draws blood, and a few days later her assistant leaves a message on your answering machine to inform you that your HCb2 count a fictitious blood chemical is You rush to the Internet and discover that the mean HCb2 count for a person your age is and the median is about the same.
Holy crap! You might take up skydiving or try to write a novel very fast. None of these things may be necessary and the e-mail to your boss could turn out very badly. But how could that be? What the heck does that mean? There is natural variation in the HCb2 count, as there is with most biological phenomena e. While the mean count for the fake chemical might be , plenty of healthy people have counts that are higher or lower. The danger arises only when the HCb2 count gets excessively high or low.
For many typical distributions of data, a high proportion of the observations lie within one standard deviation of the mean meaning that they are in the range from one standard deviation below the mean to one standard deviation above the mean.
To illustrate with a simple example, the mean height for American adult men is 5 feet 10 inches. The standard deviation is roughly 3 inches. A high proportion of adult men are between 5 feet 7 inches and 6 feet 1 inch. Or, to put it slightly differently, any man in this height range would not be considered abnormally short or tall. Which brings us back to your troubling HCb2 results. Of course, far fewer observations lie two standard deviations from the mean, and fewer still lie three or four standard deviations away.
In the case of height, an American man who is three standard deviations above average in height would be 6 feet 7 inches or taller.
Some distributions are more dispersed than others. Hence, the standard deviation of the weights of the airline passengers will be higher than the standard deviation of the weights of the marathon runners.
Once we know the mean and standard deviation for any collection of data, we have some serious intellectual traction. For example, suppose I tell you that the mean score on the SAT math test is with a standard deviation of As with height, the bulk of students taking the test will be within one standard deviation of the mean, or between and How many students do you think score or higher?
Probably not very many, since that is more than two standard deviations above the mean. Data that are distributed normally are symmetrical around their mean in a bell shape that will look familiar to you. The normal distribution describes many common phenomena. Imagine a frequency distribution describing popcorn popping on a stove top.
Some kernels start to pop early, maybe one or two pops per second; after ten or fifteen seconds, the kernels are exploding frenetically.
Then gradually the number of kernels popping per second fades away at roughly the same rate at which the popping began. The heights of American men are distributed more or less normally, meaning that they are roughly symmetrical around the mean of 5 feet 10 inches. Each SAT test is specifically designed to produce a normal distribution of scores with mean and standard deviation of The beauty of the normal distribution—its Michael Jordan power, finesse, and elegance—comes from the fact that we know by definition exactly what proportion of the observations in a normal distribution lie within one standard deviation of the mean This may sound like trivia.
In fact, it is the foundation on which much of statistics is built. We will come back to this point in much great depth later in the book. Each band represents one standard deviation. Descriptive statistics are often used to compare two figures or quantities. Those comparisons make sense because most of us recognize the scale of the units involved. Conversely, nine degrees is a significant temperature deviation in just about any climate at any time of year, so nine degrees above average makes for a day that is much hotter than usual.
Unless you know an awful lot about sodium and the serving sizes for granola cereal , that statement is not going to be particularly informative. Should we be worried about Al? The easiest way to give meaning to these relative comparisons is by using percentages. Measuring change as a percentage gives us some sense of scale. You probably learned how to calculate percentages in fourth grade and will be tempted to skip the next few paragraphs.
Fair enough. But first do one simple exercise for me. The assistant manager marks down all merchandise by 25 percent. What is the final price of the dress? This is not merely a fun parlor trick that will win you applause and adulation at cocktail parties. Percentages are useful—but also potentially confusing or even deceptive. The numerator the part on the top of the fraction gives us the size of the change in absolute terms; the denominator the bottom of the fraction is what puts this change in context by comparing it with our starting point.
The increase will be. The point is that a percentage change always gives the value of some figure relative to something else. Therefore, we had better understand what that something else is. I once invested some money in a company that my college roommate started. Since it was a private venture, there were no requirements as to what information had to be provided to shareholders. A number of years went by without any information on the fate of my investment; my former roommate was fairly tight-lipped on the subject.
There was no information on the size of those profits in absolute terms, meaning that I still had absolutely no idea how my investment was performing. Suppose that last year the firm earned 27 cents—essentially nothing. To be fair to my roommate, he eventually sold the company for hundreds of millions of dollars, earning me a percent return on my investment. Since you have no idea how much I invested, you also have no idea how much money I made—which reinforces my point here very nicely!
Let me make one additional distinction. Percentage change must not be confused with a change in percentage points. Rates are often expressed in percentages. The sales tax rate in Illinois is 6.
I pay my agent 15 percent of my book royalties. These rates are levied against some quantity, such as income in the case of the income tax rate. Obviously the rates can go up or down; less intuitively, the changes in the rates can be described in vastly dissimilar ways. The best example of this was a recent change in the Illinois personal income tax, which was raised from 3 percent to 5 percent. There are two ways to express this tax change, both of which are technically accurate.
The Democrats, who engineered this tax increase, pointed out correctly that the state income tax rate was increased by 2 percentage points from 3 percent to 5 percent. The Republicans pointed out also correctly that the state income tax had been raised by 67 percent. Many phenomena defy perfect description with a single statistic. Suppose quarterback Aaron Rodgers throws for yards but no touchdowns. Meanwhile, Peyton Manning throws for a meager yards but three touchdowns.
Who played better? The passer rating is an example of an index, which is a descriptive statistic made up of other descriptive statistics.
Once these different measures of performance are consolidated into a single number, that statistic can be used to make comparisons, such as ranking quarterbacks on a particular day, or even over a whole career.
If baseball had a similar index, then the question of the best player ever would be solved. Or would it? The advantage of any index is that it consolidates lots of complex information into a single number. We can then rank things that otherwise defy simple comparison—anything from quarterbacks to colleges to beauty pageant contestants.
In the Miss America pageant, the overall winner is a combination of five separate competitions: personal interview, swimsuit, evening wear, talent, and onstage question. Miss Congeniality is voted on separately by the participants themselves. Alas, the disadvantage of any index is that it consolidates lots of complex information into a single number.
There are countless ways to do that; each has the potential to produce a different outcome. Malcolm Gladwell makes this point brilliantly in a New Yorker piece critiquing our compelling need to rank things. Using a formula that includes twenty-one different variables, Car and Driver ranked the Porsche number one. If styling is given more weight in the overall ranking 25 percent , then the Lotus comes out on top. But wait. Gladwell also points out that the sticker price of the car gets relatively little weight in the Car and Driver formula.
If value is weighted more heavily so that the ranking is based equally on price, exterior styling, and vehicle characteristics , the Chevy Corvette is ranked number one.
Any index is highly sensitive to the descriptive statistics that are cobbled together to build it, and to the weight given to each of those components. As a result, indices range from useful but imperfect tools to complete charades. The HDI was created as a measure of economic well-being that is broader than income alone. The HDI uses income as one of its components but also includes measures of life expectancy and educational attainment.
The United States ranks eleventh in the world in terms of per capita economic output behind several oil-rich nations like Qatar, Brunei, and Kuwait but fourth in the world in human development. The HDI provides a handy and reasonably accurate snapshot of living standards around the globe. Descriptive statistics give us insight into phenomena that we care about.
In that spirit, we can return to the questions posed at the beginning of the chapter. Who is the best baseball player of all time? More important for the purposes of this chapter, what descriptive statistics would be most helpful in answering that question? According to Steve Moyer, president of Baseball Info Solutions, the three most valuable statistics other than age for evaluating any player who is not a pitcher would be the following: 1.
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