HUMANIST GALAXY OF SECULAR SCIENCE STARS = DANIEL LEVITIN 7-4-21

ALPHABETICAL BRAIN™ VOCABULARY
HUMANIST GALAXY
OF SECULAR SCIENCE STARS
DANIEL LEVITIN
July 4, 2021

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A FIELD GUIDE TO LIES:
Critical Thinking in the Information Age
by Daniel J. Levitin
Dutton, 2016 (i-xi, 292 pages)
[The updated paperback version was published with the name:
WEAPONIZED LIES:
How to Think Critically in the Post-Truth Era] Dutton, 2017 (i-xxii, 320 pages)]

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Quote =

BOOK OUTLINE
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note = Numbers in parentheses refer to pages

INTRODUCTION — Thinking, critically (ix-xi)

Quote =

Mark Twain

PART 1 — EVALUATING NUMBERS (1-120)

1) PLAUSIBILITY (3-10)

2) FUN WITH AVERAGES (11-25)

3) AXIS SHENANIGANS (26-42)

note = (43-74)

5) HOW NUMBERS ARE COLLECTED (75-96)

6) PROBABILITIES (97-120)

PART 2 — EVALUATING WORDS (121-127)

Quote = "A lie that is half a truth is ever the blackest of lies." by Alfred, Lord Tennyson (121)

7) HOW DO WE KNOW? (123-128)

note = "We are a storytelling species, and a social species easily swayed by the opinions of others... with three ways to acquire information. We can discover it ourselves, we can absorb it implicitly, or we can be told it explicitly. Much of what we know about the world falls in this last category --- somewhere along the line, someone told us a fact or we read about it, and so we know it only secondhand. We rely on people with expertise to tell us." (123)

8) IDENTIFYING EXPERTISE (129-151)

9) OVERLOOKED, UNDERVALUED ALTERNATIVE EXPLANATIONS (152-167)

note = use Cherry-picking (161-166)

note = Will Durant prediction about Catholics that did not come true in 2000 scientific reasoning (154-155)

note = Statistical literacy (166-167)

10) COUNTER-KNOWLEDGE (168-177)

note = Scientifically certain truth vs things that are probably true, including bottom quote “false theory vs true theory” = real knowledge vs counter-knowledge as having social currency (170)

note = Perception of risk (173-175)

note = Use example of dying from cancer risk because we must die of something! (174-175)

note = Persuasion by association (176-177)

PART 3 — EVALUATING THE WORLD (179-197)

Quote = "Nature permits us to calculate only probabilities. Yet science has not collapsed." by Richard P. Feynman (179)

11) HOW SCIENCE WORKS (181-197)

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[1] Deduction and induction explained

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"Scientific progress depends on two kinds of reasoning.

deduction,

induction,

note =

[2] Arguments (193-194)

[3] A deductive argument (194-197)

12) LOGICAL FALLACIES (198-210)

Four pitfalls in reasoning

13) KNOWING WHAT YOU DON'T KNOW (211-215)

note = Use table of knowns and unknowns based on Rumsfeld’s famous knowns and unknowns put in a four-fold table (214)

14) BAYESIAN THINKING IN SCIENCE AND IN COURT (216-221)

note = Use Bayes’ rule to estimate likelihood that god exists (218-221)

15) FOUR CASE STUDIES (222-250)

[] Statistics in the universe (245-250)

note = Higgs boson particle (250)

CONCLUSION — Discovering your own (251-254)

note = Knowledge vs counter knowledge (251)

note = Reference to book 1984 by Orwell (251)

note = Anti-science on web (252)

note = Use bottom paragraph (253)

note = The promise of the Internet is that it is a great democratizing force: if you combine the two — as the Internet and social media do and you have a virtual world of information and misinformation cohabiting side by side. Use last 3 paragraphs (253)

APPENDIX — Application of Bayes's rule (255)

GLOSSARY (257-282)

Abduction = A form of reasoning made popular by

Baysesian reasoning (99-102, 216-221, 222, 223-229)

Confidence intervals --- Visualizing with fourfold
tables (108-111, 118-119)

Critical thinking =

NOTES (263-282)

ACKNOWLEDGMENTS (283-284)

INDEX (285-292)

Abduction
Alternative explanations
Averages
Axes
Baselines for comparison
Baysesian reasoning
Birth rates
Cancer
Car accidents
Conditional probabilities
Confidence intervals
Correlation
Counter knowledge
Critical thinking;

and on going process of;
and the scientific method;
and the scientific revolution
Data collection
Deductive reasoning
Discredited information
Distribution
Emotions
Experts and expertise
Fallacies
Framing
Internet and websites
Known knowns
Known unknowns
Magicians
Mean
Median
Medicine
Misinformation
Mode
Mortality and death
Planned parenthood
Population
Precision
Probabilities
Random sampling
Risk
Sampling
Science and the scientific method
Standard of proof
Subjective probabilities
Syllogisms
Unknown unknowns
Verification of information

AUTHOR NOTES, SUMMARY
AND BOOK DESCRIPTION
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AUTHOR NOTES = Daniel J. Levitin studied electrical engineering at the Massachusetts Institute of Technology and music at the Berkley College of Music before dropping out of college to become a record producer and professional musician. He returned to school in his thirties, where he studied cognitive psychology/cognitive science, receiving a B.A. from Stanford University in 1992 and a M.Science in 1993 and Ph.D. in 1996 from the University of Oregon.

Levitin is a cognitive psychologist, neuroscientist, and author. He runs the Levitin Laboratory for Musical Perception, Cognition, and Expertise at McGill University. And he has published extensively in scientific journals and music trade magazines such as Grammy and Billboard. He is also the author of several other books including This is Your Brain on Music; The World in Six Songs; and The Organized Mind:

SUMMARY = One of our most trusted guides in the information age, internationally acclaimed author Daniel Levitin, shows us how to recognize misleading news stories, statistics, graphs, and websites, revealing the surprising ways lying weasels can make it difficult to separate the wheat from the digital chaff. His charming, humorous, accessible guide can help anyone wake up to a whole lot of things that are not so.

BOOK DESCRIPTION = We are bombarded with more information each day than our brains can process — especially in election season. Therefore, we need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning --- not passively accepting information, repeating it, or making decisions based upon it. The book tackles misinformation in two categories: the numerical (such as mishandled statistics and graphs) and the verbal (including faulty arguments and how to distinguish experts from hacks). It shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them. It is raining bad data, half-truths, and even outright lies. It is a primer to the critical thinking that is more necessary now than ever before.

The book ends with an overview of the scientific method, which is the bedrock of critical thinking. Levitin explains how "infoliteracy" means understanding that there are hierarchies of source, quality, and bias that variously distort our information feeds via every media channel, including Facebook and Twitter. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they often are not. But leaders can learn to avoid the extremes of passive gullibility and cynical rejection.

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EDITORIAL BOOK REVIEWS
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LIBRARY JOURNAL REVIEW = Levitin (James McGill Professor of Psychology, Behavioural Neuroscience, and Music, McGill Univ.; This Is Your Brain on Music) presents a timely, smart analysis of the current trend in American society toward information and mathematical illiteracy. As Levitin reminds listeners, there is now more information available than was present in all preceding history. Also, as Americans text, announce, and declaim at an unprecedented rate, the accompanying democratization of broadcast media systems has been overtaken by a profusion of misinformation, half-truths, and outright lies, all protected by the First Amendment. The author here covers the abuse and lack of mathematical literacy, how to evaluate statements critically, and, most important, the scientific, empirical process of getting to the truth. Dan Piraro's solid, steady reading helps maintain listener focus on what is often complex material.

Levitin's timely work nicely updates Darrell Huff's How To Lie with Statistics and Joel Best's Damned Lies and Statistics; is similar in scope to John Allen Paulos's Innumeracy; and demonstrates the fundamental rationale behind "Lies, Damned Lies, and Statistics," the 21st episode of the first season of The West Wing. The print version includes charts and graphs used to indicate misuse and abuse of factual information. VERDICT Particularly with the disturbing lack of concern for truth in the current U.S. presidential election, Levitin's timely primer on critical thinking should be required listening for all citizens. ["This useful, entertaining, and highly readable guide is ready to arm everyday citizens with the tools to combat the spread of more spurious, and often ridiculous, information"] -- Dale Farris, Groves, TX

PUBLISHERS WEEKLY REVIEW = Levitin (The Organized Mind) equips readers with tools to combat misinformation-bad data, false facts, distortions, and their ilk-in this useful primer on the importance of critical thinking in daily life. Levitin divides information (and misinformation) into two categories: numerical and verbal. He begins with an examination of both deliberate and uninformed misuses of statistics and how to spot them. The concepts explored in this section are perennial favorites of critical-thinking instruction, including plausibility, "Axis Shenanigans," and the different types of probabilities.

The second section, on evaluation words, explores less trodden grounds; particularly the discussion about expertise, which explores the concept in the context of individuals and institutions, and the ways that this expertise can be misapplied or misinterpreted.

In his final third of the book is dedicated to the scientific method and how it actually works, as opposed to pseudoscientific imitations. In all three sections Levitin explores material that has often been written about elsewhere, but the book still serves its purpose as a valuable primer on critical thinking that convincingly illustrates the prevalence of misinformation in everyday life.

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AMAZON READER REVIEWS
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[1] Tough Ideas made Easy and go down Smooth by Daring2doon = For anyone about to start University this is a must have primer. Levitin writes in such an easy going way that you can see him smiling as he provides examples to explain hard ideas in a simple, clear manner. If you find stats and research methods confusing or daunting this is for you. At the same time, as consumer of information everyone of us should be acquainted with the ideas and insights Levitin provides. We would be less likely to fall for the poor analysis and down-right nonsense that characterizes so much of the information we consume today. Who knows... if we up our game, maybe journalists/pundits/bloggers will be forced to up theirs!

[2] Proposition-simplification differs from price-simplification with its focus on making the product by Ian Mannon = The need to simplify your personal life as well as your business, is not new. Every second year I have brought to readers’ attention another book on the subject, so here is my biennial contribution. What makes this book valuable is that it focuses directly on sustainable economic growth. The authors have identified two types of growth that flow from the exercise of simplification: proposition-simplification and price-simplification. These two methods of growing the company are fundamentally different and the decision to pursue one form of simplification over another must be made on reliable grounds. The decision must take cognizance of the culture of the company and its appetite and ability to pursue one type of simplification over the other. Further, the nature of both the company’s offering and the nature of the market will affect the decision-making process. I will describe how the two types of simplification unfold through the descriptions of some of the well-known businesses used in the book as examples.

PRICE SIMPLIFICATION = The sole objective of price-simplification is to slash the costs of the product or service to the consumer. Henry Ford achieved price-simplification by reducing the variety of cars his company initially offered down to one, and in only one colour –black. The very design of the car was aimed at giving people what they needed and nothing more – a way to move faster than on horseback. Ford worked constantly on redesigning his factories so that more cars could be produced ever more cheaply. The company’s success was directly correlated to the constantly dropping selling price.

IKEA, the mass retailer of affordable, attractive furniture, redesigned their products so that they could be flat-packed, saving the company transport and storage costs. This price-simplification model also involved co-opting customers into the sales process to further reduce costs. Not only are there no salespeople for you to discuss your decorating needs with, you select the furniture yourself, but you even take it home yourself in a flat-pack. Then, you assemble the furniture from their remarkably clear instructions.

McDonald’s reduced the price of their burgers by reducing variety, and automating processes wherever possible. They also speeded up the delivery of the food, so allowing for a faster flow-through of customers, and eliminated the cost of waiters. Customers essentially serve themselves. Honda entered the American market by reducing the power of the motor-cycles they offered, and scaling down their offering to the larger segment of small motor-cycle users. Honda also lowered their costs of labor, their most expensive component, through efficiencies of production and management.

PROPOSITION-SIMPLIFICATION = Proposition-simplification differs from price-simplification with its focus on making the product or service a joy to use. The price is not a factor and many who are proposition-simplifiers are more expensive than their competitors. This category benefits from people’s willingness to pay more, if that is what it takes to own something that is easier to use, or more useful or more aesthetically pleasing. Apple Macintosh effectively created the high-end customer segment by manufacturing products that were more intuitive for the user, more user-friendly and more beautiful. Uber has made the experience of using a taxi quicker through the software that hails the drivers closest to you. The newer cars required for use by Uber drivers are expected to be more reliable, comfortable, and the whole experience is often cheaper than conventional taxis. This combination of the speed of getting a ride and the convenience of not having to pay cash, are among many features that have made Uber hugely successful, and an extremely valuable company.

The computer scientists at Xerox PARC invented the modern PC, the mouse and much, much more. However, they failed to capitalize on their inventions partially because they never focused on process simplification. “They snatched defeat from the jaws of victory because they liked complexity more than they liked simplicity,” the authors explain.

PROCESS-SIMPLIFICATION = Process-simplification and the monetization of these technological innovations were left to the late, great Steve Jobs. He brought Apple back to profitability by focusing on just two models of the Mac and producing the easiest-to-use, most fun personal computer on the market. Then came the iPod, another extraordinary example of proposition-simplification. Existing MP3 players were “horrible, absolutely horrible.” They were difficult to use and held about sixteen songs. Jobs and the team devised a far simpler player that had a drive that would hold a thousand songs, with a FireWire connection to sync the thousand songs in under ten minutes, and a battery that would last through a thousand songs. Apple is a prime example of a proposition-simplifier.

What tactics your context requires to use the principle of simplification, will be completely unique. The value of this book is the awareness of the power of simplification, and the guidance it offers to the process: the rest is up to you. Readability Light -+-- Serious; Insights High --+-- Low; and Practical High +---- Low

[*Ian Mann of Gateways consults internationally on leadership and strategy and is the author of the soon to be released ‘Executive Update’.]

[3] Rather Thin Gruel by lecon - This is not a bad book, but is rather superficial = It focuses on two issues: statistics and logic. Both indeed are important, particularly because they are so frequently misused. Unfortunately, the author essentially goes a bit into each, and he then moves on to other topics.

[4] A great read to filter confusion - by Philip Lawsonon = Good introduction to thinking critically about stats and numbers etc. Some good insights and instructions on how to check your facts.

[5] The Author does not introduce anything new - by Dave Son = The author just reminds you not to believe everything you hear and read. Especially graphs, statistics and "expert" studies. One should reread it every few years.

[6] Well Done and Practical by Book FanaticVINE VOICE = This is a good book and I think it does a very good job of helping the intelligent layperson with some basic critical thinking skills. It's pretty broad in scope and doesn't go into deep detail on the topics it covers. However I think it does a good job of giving the reader a basic understanding of those topics. The book is broken into three parts. The first part is evaluating numbers, the second part is evaluating words, and the third part is evaluating the world. So you get some basic probability discussions, basic logic and logical fallacies etc.. Probably the best part of the book is the instruction in how to use fourfold tables as a way to compute conditional probabilities. This is a very valuable and practical technique. All in all this book is well worth reading and has a great deal of practical value.

[7] Outstanding book on critical thinking by Michael Jon = This is an outstanding book on critical thinking and applying statistics to everyday life. I think this should be required reading for high school students. It would be interesting if our culture was more encouraging of critical thinking, rather than believing everything we read or hear in the news or social media.

[8] A great guide to critical thinking by P. Poundson = An outstanding overview of critical thinking. A relatively short read but it does get the brain cells cranked up. You can't just breeze through it; you have to think and that's what makes it great.

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EXCERPT
CHAPTER 1 - PLAUSIBILITY

Statistics, because they are numbers, appear to us to be cold, hard facts. It seems that they represent facts given to us by nature and it's just a matter of finding them. But it's important to remember that people gather statistics. People choose what to count, how to go about counting, which of the resulting numbers they will share with us, and which words they will use to describe and interpret those numbers. Statistics are not facts. They are interpretations. And your interpretation may be just as good as, or better than, that of the person reporting them to you. (pages 3-14)

Sometimes, the numbers are simply wrong, and it's often easiest to start out by conducting some quick plausibility checks. After that, even if the numbers pass plausibility, three kinds of errors can lead you to believe things that aren't so: how the numbers were collected, how they were interpreted, and how they were presented graphically.

In your head or on the back of an envelope you can quickly determine whether a claim is plausible (most of the time). Don't just accept a claim at face value; work through it a bit.

When conducting plausibility checks, we don't care about the exact numbers. That might seem counterintuitive, but precision isn't important here. We can use common sense to reckon a lot of these: If Bert tells you that a crystal wineglass fell off a table and hit a thick carpet without breaking, that seems plausible. If Ernie says it fell off the top of a forty-story building and hit the pavement without breaking, that's not plausible. Your real-world knowledge, observations acquired over a lifetime, tells you so. Similarly, if someone says they are two hundred years old, or that they can consistently beat the roulette wheel in Vegas, or that they can run forty miles an hour, these are not plausible claims.

In the 35 years since marijuana laws stopped being enforced in California, the number of marijuana smokers has doubled every year.

Plausible? Where do we start? Let us assume there was only one marijuana smoker in California thirty-five years ago, a very conservative estimate (there were half a million marijuana arrests nationwide in 1982). Doubling that number every year for thirty-five years would yield more than 17 billion-larger than the population of the entire world. (Try it yourself and you will see that doubling every year for twenty-one years gets you to over a million: 1; 2; 4; 8; 16; 32; 64; 128; 256; 512; 1024; 2048; 4096; 8192; 16,384; 32,768; 65,536; 131,072; 262,144; 524,288; 1,048,576.)

This claim is not just implausible, then, it is impossible. Unfortunately, many people have trouble thinking clearly about numbers because they are intimidated by them. But as you see, nothing here requires more than elementary school arithmetic and some reasonable assumptions.

Here's another. You've just taken on a position as a telemarketer, where agents telephone unsuspecting (and no doubt irritated) prospects. Your boss, trying to motivate you, claims:

OUR BEST SALESPERSON MADE: 1,000 SALES A DAY = Is this plausible? Try dialing a phone number yourself --- the fastest you can probably do it is five seconds. Allow another five seconds for the phone to ring. Now let's assume that every call ends in a sale-clearly this isn't realistic, but let's give every advantage to this claim to see if it works out. Figure a minimum of ten seconds to make a pitch and have it accepted, then forty seconds to get the buyer's credit card number and address. That's one call per minute (5 + 5 + 10 + 40 = 60 seconds), or 60 sales in an hour, or 480 sales in a very hectic eight-hour workday with no breaks. The 1,000 just isn't plausible, allowing even the most optimistic estimates.

Some claims are more difficult to evaluate. Here's a headline from Time magazine in 2013:

MORE PEOPLE HAVE CELL PHONES THAN TOILETS = What to do with this? We can consider the number of people in the developing world who lack plumbing and the observation that many people in prosperous countries have more than one cell phone. The claim seems plausible-that doesn't mean we should accept it, just that we can't reject it out of hand as being ridiculous; we'll have to use other techniques to evaluate the claim, but it passes the plausibility test.

Sometimes you can't easily evaluate a claim without doing a bit of research on your own. Yes, newspapers and websites really ought to be doing this for you, but they don't always, and that's how runaway statistics take hold. A widely reported statistic some years ago was this:

In the U.S., 150,000 girls and young women die of anorexia each year. Okay — let us check its plausibility. We have to do some digging. According to the U.S. Centers for Disease Control, the annual number of deaths from all causes for girls and women between the ages of fifteen and twenty-four is about 8,500. Add in women from twenty-five to forty-four and you still only get 55,000. The anorexia deaths in one year cannot be three times the number of all deaths.

In an article in Science, Louis Pollack and Hans Weiss reported that since the formation of the Communication Satellite Corp, The cost of a telephone call has decreased by 12,000 percent.

If a cost decreases by 100 percent, it drops to zero (no matter what the initial cost was). If a cost decreases by 200 percent, someone is paying you the same amount you used to pay them for you to take the product. A decrease of 100 percent is very rare; one of 12,000 percent seems wildly unlikely. An article in the peer-reviewed Journal of Management Development claimed a 200 percent reduction in customer complaints following a new customer care strategy. Author Dan Keppel even titled his book Get What You Pay For: Save 200% on Stocks, Mutual Funds, Every Financial Need. He has an MBA. He should know better.

Of course, you have to apply percentages to the same baseline in order for them to be equivalent. A 50 percent reduction in salary cannot be restored by increasing your new, lower salary by 50 percent, because the baselines have shifted. If you were getting $1,000/week and took a 50 percent reduction in pay, to $500, a 50 percent increase in that pay only brings you to $750.

Percentages seem so simple and incorruptible, but they are often confusing. If interest rates rise from 3 percent to 4 percent, that is an increase of 1 percentage point, or 33 percent (because the 1 percent rise is taken against the baseline of 3, so 1/3 = .33). If interest rates fall from 4 percent to 3 percent, that is a decrease of 1 percentage point, but not a decrease of 33 percent — it is a decrease of 25 percent (because the 1 percentage point drop is now taken against the baseline of 4). Researchers and journalists are not always scrupulous about making this distinction between percentage point and percentages clear, but you should be.

The New York Times reported on the closing of a Connecticut textile mill and its move to Virginia due to high employment costs. The Times reported that employment costs, "wages, worker's compensation and unemployment insurance — are 20 times higher in Connecticut than in Virginia." Is this plausible? If it were true, you'd think that there would be a mass migration of companies out of Connecticut and into Virginia — not just this one mill — and that you would have heard of it by now. In fact, this was not true and the Times had to issue a correction. How did this happen? The reporter simply misread a company report. One cost, unemployment insurance, was in fact twenty times higher in Connecticut than in Virginia, but when factored in with other costs, total employment costs were really only 1.3 times higher in Connecticut, not 20 times higher. The reporter did not have training in business administration and we shouldn't expect her to. To catch these kinds of errors requires taking a step back and thinking for ourselves-which anyone can do (and she and her editors should have done).

New Jersey adopted legislation that denied additional benefits to mothers who have children while already on welfare. Some legislators believed that women were having babies in New Jersey simply to increase the amount of their monthly welfare checks. Within two months, legislators were declaring the "family cap" law a great success because births had already fallen by 16 percent. According to the New York Times:

After only two months, the state released numbers suggesting that births to welfare mothers had already fallen by 16 percent, and officials began congratulating themselves on their overnight success.

Note that they are not counting pregnancies, but births. What's wrong here? Because it takes nine months for a pregnancy to come to term, any effect in the first two months cannot be attributed to the law itself but is probably due to normal fluctuations in the birth rate (birth rates are known to be seasonal).

Even so, there were other problems with this report that can not be caught with plausibility checks: . . . over time, that 16 percent drop dwindled to about 10 percent as the state belatedly became aware of births that had not been reported earlier. It appeared that many mothers saw no reason to report the new births since their welfare benefits were not being increased.

This is an example of a problem in the way statistics were collected — we are not actually surveying all the people that we think we are. Some errors in reasoning are sometimes harder to see coming than others, but we get better with practice. To start, let's look at a basic, often misused tool.

The pie chart is an easy way to visualize percentages — how the different parts of a whole are allocated. You might want to know what percentage of a school district's budget is spent on things like salaries, instructional materials, and maintenance. Or you might want to know what percentage of the money spent on instructional materials goes toward math, science, language arts, athletics, music, and so on. The cardinal rule of a pie chart is that the percentages have to add up to 100. Think about an actual pie — if there are nine people who each want an equal-sized piece, you can't cut it into eight. After you've reached the end of the pie, that's all there is. Still, this didn't stop Fox News from publishing this pie chart:

First rule of pie charts: the percentages have to add up to 100. (Fox News, 2010). You can imagine how something like this could happen. Voters are given the option to report that they support more than one candidate. But then, the results should not be presented as a pie chart.

FUN WITH AVERAGES = An average can be a helpful summary statistic, even easier to digest than a pie chart, allowing us to characterize a very large amount of information with a single number. We might want to know the average wealth of the people in a room to know whether our fund-raisers or sales managers will benefit from meeting with them. Or we might want to know the average price of gas to estimate how much it will cost to drive from Vancouver to Banff. But averages can be deceptively complex.

There are three ways of calculating an average, and they often yield different numbers, so people with statistical acumen usually avoid the word average in favor of the more precise terms mean, median, and mode. We don't say "mean average" or "median average" or simply just "average" — we say mean, median, or mode. In some cases, these will be identical, but in many they are not. If you see the word average all by itself, it's usually indicating the mean, but you can't be certain.

The mean is the most commonly used of the three and is calculated by adding up all the observations or reports you have and dividing by the number of observations or reports. For example, the average wealth of the people in a room is simply the total wealth divided by the number of people. If the room has ten people whose net worth is $100,000 each, the room has a total net worth of $1 million, and you can figure the mean without having to pull out a calculator: it is $100,000. If a different room has ten people whose net worth varies from $50,000 to $150,000 each, but totals $1 million, the mean is still $100,000 (because we simply take the total $1 million and divide by the ten people, regardless of what any individual makes).

The median is the middle number in a set of numbers (statisticians call this set a "distribution"): half the observations are above it and half are below. Remember, the point of an average is to be able to represent a whole lot of data with a single number. The median does a better job of this when some of your observations are very, very different from the majority of them, what statisticians call outliers.

If we visit a room with nine people, suppose eight of them have a net worth of near $100,000 and one person is on the verge of bankruptcy with a net worth of negative $500,000, owing to his debts. Here's the makeup of the room:

Person 1:    $500,000

Person 2:    $96,000

Person 3:    $97,000

Person 4:    $99,000

Person 5:    $100,000

Person 6:    $101,000

Person 7:    $101,000

Person 8:    $101,000

Person 9:    $104,000

Now we take the sum and obtain a total of $299,000. Divide by the total number of observations, nine, and the mean is $33,222 per person. But the mean doesn't seem to do a very good job of characterizing the room. It suggests that your fund-raiser might not want to visit these people, when it's really only one odd person, one outlier, bringing down the average. This is the problem with the mean: It is sensitive to outliers.

The median here would be $100,000: four people make less than that amount, and four people make more. The mode is $101,000, the number that appears more often than the others. Both the median and the mode are more helpful in this particular example.

There are many ways that averages can be used to manipulate what you want others to see in your data.

Let's suppose that you and two friends founded a small start-up company with five employees. It's the end of the year and you want to report your finances to your employees, so that they can feel good about all the long hours and cold pizzas they've eaten, and so that you can attract investors. Let's say that four employees-programmers-each earned $70,000 per year, and one employee-a receptionist/office manager-earned $50,000 per year. That's an average (mean) employee salary of $66,000 per year (4 $70,000) + (1 $50,000), divided by 5. You and your two friends each took home $100,000 per year in salary. Your payroll costs were therefore (4 $70,000) + (1 $50,000) + (3 $100,000) = $630,000. Now, let's say your company brought in $210,000 in profits and you divided it equally among you and your co-founders as bonuses, giving you $100,000 + $70,000 each. How are you going to report this? (3-14)

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