Wave are you able to download pdf of receipts?

Turn screw clockwise to tighten friction or turn counterclockwise to loosen friction. If the boat turns more easily to the left, move the trailing edge of trim tab to the left. If the boat turns more easily to the right move the trailing edge of trim tab to the right. Page Pre-Starting Instructions Wash the outboard exterior and flush out the exhaust outlet of the propeller and gearcase with fresh water after each use.

Do not spray on corrosion control anodes as this will reduce the effectiveness of the anodes. For the first hour of operation, run the engine at varied throttle settings up to RPM or at approximately half throttle. Set the lanyard stop switch to "RUN" position. Shift outboard to neutral "N" position.

If the engine fails to start in ten seconds, return the key to the "ON" position, wait 30 seconds and try again. After engine starts, check for a steady stream of water flowing out of the water pump indicator hole. Open fuel tank vent screw in filler cap on manual venting type fuel tanks. Connect the remote fuel line to the outboard. Make sure the connector is snapped into place. Position the fuel line primer bulb so the arrow on the side of the bulb is pointing up. Set the throttle grip to start position.

Check for a steady stream of water flowing out of the water pump indicator hole. No obstruction may indicate a water pump failure or blockage in the cooling system. Push in the engine stop button or turn ignition key to "OFF" position.

Set the engine speed at idle and the gear shift in neutral to prevent the outboard from starting in gear. Pull the starter rope to start the engine. Page Maintenance Record maintenance performed in the Maintenance Log at the back of this book. Save all maintenance work orders and receipts. Make sure thermostat closes completely at room temperature.

See Fuel System. Check more frequently when used in salt water. This will help prevent a buildup of deposits from clogging the internal water passages. Pull out the rear lock lever and remove the top cowl. Lower the top cowl over the engine. Bring the front of the cowl down first and engage the front hook. Turn off the engine before servicing the battery. Add water as necessary to keep the battery full.

Make sure the battery is secure against movement. Read the preceeding fuel system servicing information and warning. Pull out the filter assembly from mount. Hold onto the cover to prevent it from turning and remove the sight bowl. Empty contents into an approved container. This can cause a sudden, unexpected loss of boat control, resulting serious injury or death due to occupants being thrown within or out of the boat.

An anode helps protect the outboard against galvanic corrosion by sacrificing its metal to be slowly corroded instead of the outboard metals.

Each anode requires periodic inspection, especially in salt water which will accelerate the erosion. Page Propeller Replacement - To prevent this type of accidental engine starting and possible serious injury caused from being struck by a rotating propeller, always turn the ignition key or lanyard stop switch to the "OFF" Page 81 5. Pull the propeller straight off the shaft. If the propeller is seized to the shaft and cannot be removed, have the propeller removed by an authorized dealer.

Align the flat sides of the propeller nut with the tabs on the propeller nut retainer. Secure the propeller nut by bending the tabs up and against the flats on the propeller nut. Reinstall the spark plug leads. Remove the spark plug leads to prevent the engine from starting.

Straighten the bent tabs on the propeller nut retainer. Windows users. Windows 8 Select Use this app for all. Windows 10 Select Always use this app to open. Windows Click OK. Mac OS users. Click the PDF file's icon in the Finder to select it. Click Change All. The downside is that most of these are only available on the paid plans of the app. Microsoft OneNote is one of the best note-taking apps you can use. Its generous free plan includes advanced features, such as optical character recognition, ink-to-text conversion, audio and video recording, and sharing right from the get-go.

OneNote is a first-class app that you can use for work, school and personal note-taking and collaboration. The biggest difference between Evernote and Microsoft OneNote is that Evernote really only realizes its full potential on its paid versions, while OneNote offers all of its advanced features on its free version.

It depends on your personal preferences and whether or not you are using the free version of Evernote or one of its paid plans.

Microsoft OneNote definitely outperforms Evernote in some areas, and it has the video capturing and dictation tools that Evernote lacks. However, we still prefer Evernote because of its superior user experience and collaboration features. Evernote is still, in our opinion, the best app for note-taking. While OneNote definitely has its advantages and is totally free, Evernote wins out in the end, thanks to its tools for team management that make it an excellent app for collaborating on work tasks and school projects.

Evernote and OneNote have both been around for a long time. Microsoft OneNote was released in and Evernote launched five years later in To see which one is the best of the best, we have pitted them across four rounds: features, pricing, user experience, and security and privacy. After that, we will take everything into regard, tally up the score and declare the winner. This is because the free version of Evernote is very bare-bones and full of restrictions, something that we will cover in greater detail in the pricing round of the article.

Evernote has a wide array of tools that will make every note-taking activity that much easier. You have rich text formatting options that rival the ones in quality word processors, like Dropbox Paper and Google Docs.

When you want to collaborate with teammates and friends, Evernote lets you share your notes and set permission levels for each person you add. There are many note types that you can create inside Evernote, including meeting notes, to-do lists and project plans.

Coupled with its team administration features that let you manage your team and see their activities, Evernote can perform some basic project management software functionalities. OneNote is no slouch in the features department, either. Conversely, Evernote allows users to only record audio and take screenshots.

While audio and screenshots are very helpful for meetings and lectures, being able to take short video clips allows OneNote users an even greater degree of flexibility.

The dictation tool — available in English, French, German, Italian, Spanish and Chinese — is likewise an excellent time-saver that lets you convert your voice commands directly into text. Evernote and OneNote both have their own web clipper extensions. These are available as add-ons for all major web browsers. With these, you can freely clip out images and text from web pages and add them to your notes. Each web clipper has only basic editing options, so if you want to further edit these photos, we recommend using professional photo editing software.

Plus, its screenshot annotations feature makes it more useful for collaboration and communication purposes. Both of these have optical character recognition, handwriting support, ink-to-text conversion and document scanning tools.

It cannot be overstated how useful these tools are, especially for business needs. For example, instead of typing out the contents of a document, you can take a screenshot of it and then convert this picture to text inside your app. The upside is that OneNote offers these tools for free, while Evernote only offers them in the Premium or Business versions. Through these apps, you will be able to connect Evernote and OneNote to thousands of other apps and automate many tasks and processes inside your favorite note-taking software.

This first round goes to Evernote. It was neck and neck for most of it, but even though OneNote and Evernote share a lot of the same features, Evernote wins out by having more options for its tools and better integrated add-ons. If you plan on using Evernote in any serious professional capacity, get ready to pay for it.

With a 60MB monthly upload limit and a maximum note size of a mere 25MB, you will soon go over the limit if you frequently take and share media files. With this premium version, you will be able to sync across an unlimited number of devices, compared to just the two you get with the free plan. The monthly upload limit jumps to 10GB and the maximum note size increases to MB. The final payment tier is Evernote Business.

For this price, the monthly upload limit goes up to 20GB, with an additional 2GB per user. It also comes with extended team collaboration and management tools. This version even integrates with Salesforce, one of the best CRM tools. OneNote is, on the other hand, a completely free app.

After that, you will receive 5GB of free cloud storage space on your OneDrive account. This space is shared across all apps that use OneDrive. If you want more cloud storage space, there is the option to upgrade your Microsoft Office subscription. This is one of our favorite cloud storage deals. If you are not interested in these apps, this deal loses a lot of its appeal and you are better off using the regular free version of OneNote.

Another similar free note-taking app alternative is Google Keep. When it comes to pricing, OneNote is the better choice. You can also become a paid MS Office user for even more storage and Office apps. Note-taking apps should be easier to use than taking out a notebook to cross off items from a shopping list. Evernote has a lot of options and different things you can do inside the app. To a novice user, this can come off as intimidating at first.

Evernote users can count on other time-saving features as well, such as the inclusion of templates. It has dozens of templates that can be easily used and quickly copied.

Premium and Business plan users can create their own templates for even better productivity and collaboration. It is currently developing a Linux version. You can contact customer support via email or live chat, though this is available only on the paid versions of the app. Free users have to make do with finding the solution to their problems on the community support forum. OneNote shares the same general design principles that all Office apps are built on.

You will have access to all of your system fonts on the desktop version and, once used in a note, these fonts will be available on the web version, too. OneNote has a unique approach when it comes to its notes. These sections can be in different fonts, colors and sizes. They can also be moved around, edited and merged effortlessly with other notes.

Odds are slim that a Linux client will ever happen. Simplenote is one such notes app. Evernote has a superb search tool. With it, you can search by keyword or phrase across text notes, notebooks or files. Search parameters include when a note or notebook has been created or modified, and paid versions allow you to search inside Word docs and PDFs.

These two apps both support customized tagging. Adding your own tags to notes makes organizing them and searching across different notebooks a lot easier and more efficient. Evernote features a classic organization structure: you create notes which are then stored inside notebooks. OneNote notes hierarchy is as follows: notebooks, sections, pages. This extra step of having sections can bother users who are used to quickly accessing their notes.

While OneNote is by no means unpleasant to use, Evernote is more user-oriented. Its search and organization are better handled. Plus, its time-saving features — such as templates and different note types — make using Evernote for taking notes and work a more intuitive and personalized experience in general. It is a typical corporate-style document in which Microsoft explains that it collects your personal data through your use of its products.

This data is used for advertising and can be shared to third-party vendors and law enforcement agencies with a subpoena. Windows 10 users can somewhat customize their privacy settings , but if you are concerned about this, a note-taking app that places greater emphasis on user privacy would be a better choice. It guarantees that your data is yours, your data is protected and that your data is portable.

In effect, this means that Evernote does not claim any copyright on the content of your notes and that it will not sell your info or use it for marketing purposes. Imagine that headline popping up while you are surfing the Web. According to a seemingly impressive study of 36, office workers a huge data set!

Clearly we need to act on this kind of finding—perhaps some kind of national awareness campaign to prevent short breaks on the job. Or maybe we just need to think more clearly about what many workers are doing during that ten- minute break.

My professional experience suggests that many of those workers who report leaving their offices for short breaks are huddled outside the entrance of the building smoking cigarettes creating a haze of smoke through which the rest of us have to walk in order to get in or out. Statistics is like a high-caliber weapon: helpful when used correctly and potentially disastrous in the wrong hands. This is not a textbook, which is liberating in terms of the topics that have to be covered and the ways in which they can be explained.

The book has been designed to introduce the statistical concepts with the most relevance to everyday life. How do scientists conclude that something causes cancer? How does polling work and what can go wrong? How does your credit card company use data on what you are buying to predict if you are likely to miss a payment? Seriously, they can do that. If you want to understand the numbers behind the news and to appreciate the extraordinary and growing power of data, this is the stuff you need to know.

But I have even bolder aspirations than that. I think you might actually enjoy statistics. The underlying ideas are fabulously interesting and relevant. The key is to separate the important ideas from the arcane technical details that can get in the way.

That is Naked Statistics. Students will complain that statistics is confusing and irrelevant. Then the same students will leave the classroom and happily talk over lunch about batting averages during the summer or the windchill factor during the winter or grade point averages always.

The same data completion rate, average yards per pass attempt, percentage of touchdown passes per pass attempt, and interception rate could be combined in a different way, such as giving greater or lesser weight to any of those inputs, to generate a different but equally credible measure of performance. Is the quarterback rating perfect? Does it provide meaningful information in an easily accessible way? I am a Chicago Bears fan. During the playoffs, the Bears played the Packers; the Packers won.

There are a lot of ways I could describe that game, including pages and pages of analysis and raw data. But here is a more succinct analysis. Chicago Bears quarterback Jay Cutler had a passer rating of In contrast, Green Bay quarterback Aaron Rodgers had a passer rating of That tells you a lot of what you need to know in order to understand why the Bears beat the Packers earlier in the season but lost to them in the playoffs.

That is a very helpful synopsis of what happened on the field. Does it simplify things? Yes, that is both the strength and the weakness of any descriptive statistic. The curious thing is that the same people who are perfectly comfortable discussing statistics in the context of sports or the weather or grades will seize up with anxiety when a researcher starts to explain something like the Gini index, which is a standard tool in economics for measuring income inequality.

As such, it has the strengths of most descriptive statistics, namely that it provides an easy way to compare the income distribution in two countries, or in a single country at different points in time.

The statistic can be calculated for wealth or for annual income, and it can be calculated at the individual level or at the household level. All of these statistics will be highly correlated but not identical. A country in which every household had identical wealth would have a Gini index of zero.

As you can probably surmise, the closer a country is to one, the more unequal its distribution of wealth. The United States has a Gini index of. Once that number is put into context, it can tell us a lot. For example, Sweden has a Gini index of. We can also compare different points in time. The Gini index for the United States was. The most recent CIA data are for This tells us in an objective way that while the United States grew richer over that period of time, the distribution of wealth grew more unequal.

Again, we can compare the changes in the Gini index across countries over roughly the same time period. Inequality in Canada was basically unchanged over the same stretch. Sweden has had significant economic growth over the past two decades, but the Gini index in Sweden actually fell from. Is the Gini index the perfect measure of inequality? Absolutely not—just as the passer rating is not a perfect measure of quarterback performance. But it certainly gives us some valuable information on a socially significant phenomenon in a convenient format.

We have also slowly backed our way into answering the question posed in the chapter title: What is the point? The point is that statistics helps us process data, which is really just a fancy name for information. Sometimes the data are trivial in the grand scheme of things, as with sports statistics. Sometimes they offer insight into the nature of human existence, as with the Gini index.

How does Netflix know what kind of movies you like? How can we figure out what substances or behaviors cause cancer, given that we cannot conduct cancer-causing experiments on humans? Does praying for surgical patients improve their outcomes? Is there really an economic benefit to getting a degree from a highly selective college or university? What is causing the rising incidence of autism? Statistics can help answer these questions or, we hope, can soon. The world is producing more and more data, ever faster and faster.

Here is a quick tour of how statistics can bring meaning to raw data. Description and Comparison A bowling score is a descriptive statistic. So is a batting average. Most American sports fans over the age of five are already conversant in the field of descriptive statistics. We use numbers, in sports and everywhere else in life, to summarize information.

How good a baseball player was Mickey Mantle? He was a career. To a baseball fan, that is a meaningful statement, which is remarkable when you think about it, because it encapsulates an eighteen-season career. We evaluate the academic performance of high school and college students by means of a grade point average, or GPA. A letter grade is assigned a point value; typically an A is worth 4 points, a B is worth 3, a C is worth 2, and so on.

By graduation, when high school students are applying to college and college students are looking for jobs, the grade point average is a handy tool for assessing their academic potential. Someone who has a 3. That makes it a nice descriptive statistic.

The GPA does not reflect the difficulty of the courses that different students may have taken. How can we compare a student with a 3. This caused its own problems. Instead, they paid to send me to a private driving school, at nights over the summer. Was that insane? But one theme of this book will be that an overreliance on any descriptive statistic can lead to misleading conclusions, or cause undesirable behavior.

Descriptive statistics exist to simplify, which always implies some loss of nuance or detail. Anyone working with numbers needs to recognize as much. Inference How many homeless people live on the streets of Chicago? How often do married people have sex? These may seem like wildly different kinds of questions; in fact, they both can be answered not perfectly by the use of basic statistical tools.

One key function of statistics is to use the data we have to make informed conjectures about larger questions for which we do not have full information. It is expensive and logistically difficult to count the homeless population in a large metropolitan area.

Yet it is important to have a numerical estimate of this population for purposes of providing social services, earning eligibility for state and federal revenues, and gaining congressional representation. One important statistical practice is sampling, which is the process of gathering data for a small area, say, a handful of census tracts, and then using those data to make an informed judgment, or inference, about the homeless population for the city as a whole.

Sampling requires far less resources than trying to count an entire population; done properly, it can be every bit as accurate. A political poll is one form of sampling. A research organization will attempt to contact a sample of households that are broadly representative of the larger population and ask them their views about a particular issue or candidate. This is obviously much cheaper and faster than trying to contact every household in an entire state or country. The polling and research firm Gallup reckons that a methodologically sound poll of 1, households will produce roughly the same results as a poll that attempted to contact every household in America.

In the mids, the National Opinion Research Center at the University of Chicago carried out a remarkably ambitious study of American sexual behavior. The results were based on detailed surveys conducted in person with a large, representative sample of American adults.

If you read on, Chapter 10 will tell you what they learned. How many other statistics books can promise you that? That does not mean that they are making money at any given moment. When the bells and whistles go off, some high roller has just won thousands of dollars. The whole gambling industry is built on games of chance, meaning that the outcome of any particular roll of the dice or turn of the card is uncertain. At the same time, the underlying probabilities for the relevant events—drawing 21 at blackjack or spinning red in roulette—are known.

This turns out to be a powerful phenomenon in areas of life far beyond casinos. Many businesses must assess the risks associated with assorted adverse outcomes. However, any business facing uncertainty can manage these risks by engineering processes so that the probability of an adverse outcome, anything from an environmental catastrophe to a defective product, becomes acceptably low. Wall Street firms will often evaluate the risks posed to their portfolios under different scenarios, with each of those scenarios weighted based on its probability.

The financial crisis of was precipitated in part by a series of market events that had been deemed extremely unlikely, as if every player in a casino drew blackjack all night. I will argue later in the book that these Wall Street models were flawed and that the data they used to assess the underlying risks were too limited, but the point here is that any model to deal with risk must have probability as its foundation. The entire insurance industry is built upon charging customers to protect them against some adverse outcome, such as a car crash or a house fire.

The insurance industry does not make money by eliminating these events; cars crash and houses burn every day. Sometimes cars even crash into houses, causing them to burn. Instead, the insurance industry makes money by charging premiums that are more than sufficient to pay for the expected payouts from car crashes and house fires.

The insurance company may also try to lower its expected payouts by encouraging safe driving, fences around swimming pools, installation of smoke detectors in every bedroom, and so on. Probability can even be used to catch cheats in some situations.

The mathematical logic stems from the fact that we cannot learn much when a large group of students all answer a question correctly. But when those same test takers get an answer wrong, they should not all consistently have the same wrong answer.

If they do, it suggests that they are copying from one another or sharing answers via text. Of course, you can see the limitations of using probability. A large group of test takers might have the same wrong answers by coincidence; in fact, the more schools we evaluate, the more likely it is that we will observe such patterns just as a matter of chance. A statistical anomaly does not prove wrongdoing. We cannot arrest Mr.

Kinney for fraud on the basis of that calculation alone though we might inquire whether he has any relatives who work for the state lottery. Probability is one weapon in an arsenal that requires good judgment.

We have an answer for that question—but the process of answering it was not nearly as straightforward as one might think. The scientific method dictates that if we are testing a scientific hypothesis, we should conduct a controlled experiment in which the variable of interest e. If we observe a marked difference in some outcome between the two groups e.

We cannot do that kind of experiment on humans. If our working hypothesis is that smoking causes cancer, it would be unethical to assign recent college graduates to two groups, smokers and nonsmokers, and then see who has cancer at the twentieth reunion.

Smokers and nonsmokers are likely to be different in ways other than their smoking behavior. For example, smokers may be more likely to have other habits, such as drinking heavily or eating badly, that cause adverse health outcomes.

If the smokers are particularly unhealthy at the twentieth reunion, we would not know whether to attribute this outcome to smoking or to other unhealthy things that many smokers happen to do. We would also have a serious problem with the data on which we are basing our analysis. Smokers who have become seriously ill with cancer are less likely to attend the twentieth reunion.

As a result, any analysis of the health of the attendees at the twentieth reunion related to smoking or anything else will be seriously flawed by the fact that the healthiest members of the class are the most likely to show up. The further the class gets from graduation, say, a fortieth or a fiftieth reunion, the more serious this bias will be.

We cannot treat humans like laboratory rats. As a result, statistics is a lot like good detective work. The data yield clues and patterns that can ultimately lead to meaningful conclusions. You have probably watched one of those impressive police procedural shows like CSI: New York in which very attractive detectives and forensic experts pore over minute clues—DNA from a cigarette butt, teeth marks on an apple, a single fiber from a car floor mat—and then use the evidence to catch a violent criminal.

The appeal of the show is that these experts do not have the conventional evidence used to find the bad guy, such as an eyewitness or a surveillance videotape.

So they turn to scientific inference instead. Statistics does basically the same thing. The data present unorganized clues—the crime scene.

Statistical analysis is the detective work that crafts the raw data into some meaningful conclusion. After Chapter 11, you will appreciate the television show I hope to pitch: CSI: Regression Analysis, which would be only a small departure from those other action-packed police procedurals.

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.