NPR thinks the average American looks like the average Trump supporter

Planet Money and the New York Times’ Ben Casselman teamed up to try to demonstrate that, “Mode, not average, is a better way to find the typical American.” They are wrong.

Here is how they set up the issue:

MALONE: My issue is with this thing that people talk about, the average American. …Who is average, really? …I think people don’t mean average American. I think what they actually mean is, who is the person – if I walk outside into America, who is the person I’m most likely to run into?

JACOB GOLDSTEIN: Yes, the person who there’s more of that person than any other person.

MALONE: That ain’t the average. It’s not the median… If you actually want to figure out what human beings exist outside your door, you need to run the mode.

Instead of demonstrating how useful the mode is, they actually do a pretty good job of demonstrating why nobody uses it: it sucks for describing most data.

What is the mode? It is simply the most common value in a set of data. For example, suppose you have a room full of people and their annual incomes are:

$1,000; $1,000; $30,0000; $40,000; $50,000; $60,000; and $100 million

The mode is $1,000 because there are two people with that income and only one person at every other income. The median is the most useful statistic for understanding the central tendency of this group’s income because it is the value in the middle, $40,000, which is the most central value. The mean is $14.4 million which is much closer to the one rich outlier than to anyone else, so it is also a poor measure of central tendency for the group.

The median does the best here because it is the least sensitive to outliers. If another person with $100 million walks into the room, then the mean would nearly double, and the mode would be both $100 million and $1,000. Both of those statistics are unrepresentative whereas the median would still be near the center of the numbers and hardly affected at all.

The mode is only the best measure for categorical data like color. For example, if we have seven colors:

red, red, orange, yellow, green, blue, ultraviolet

In this case, it is impossible to take the mean and if we don’t care about the order of the colors, then we cannot take the median either so the mode is the best possible measure simply because the other two options are impossible. The best you can do is say that red is the most common color which is the same thing as saying that it is the modal color.

But for quantitative data we can calculate the mean or median and the mode is rarely as useful as either of them. Planet Money demonstrated how ridiculous the mode is for numerical data when they determined that the modal income is $30,000 to $75,000.” That is such a big range, it is laughable. It ranges from the poverty line for a family of five up to the upper-middle class. Nearly a third of US households (29%) are in this “modal” range.

Why did they get such a huge range? Well, there are probably a very similar number of households that earn between $30,000 and $75,000 so the mode might be multiple measurements just as with the example above with two modes at both $1,000 and $100 million. There is always some uncertainty in data collection because measurements aren’t always perfect. For example, if a household says they earn $30,000, they might be a little off and they might actually earn $31,000 or $29,000, so the real number could be plus or minus a thousand or more. Given modest uncertainty in the data, there is usually a large range in the possible true value of the mode and perhaps in this case the NPR authors could not give any more precision than that the true modal values must be somewhere between $30,000 and $75.000!

The median income is much easier to pin down. In this case we would just find the observation in the middle, which was about $63,000 in 2018, and if there is uncertainty of plus or minus $1,000 then we would know that the true median is between $62,000 and $64,000. That is much more precise and useful.

UPDATE: In their methodology description, Planet Money explains that they just arbitrarily lumped households into four income groups. This is even worse than I had originally thought. With this methodology, it would be possible to say that the modal income is nearly anything. For example, I could say that the modal income is between $1 million and $1 billion simply by splitting up all the lower-income categories into smaller buckets.

Planet Money’s search for the modal American gets even more bizarre after that. They determine that, “The modal American, based on our criteria, is in fact, a child.” But then because they really wanted the modal American to be an adult, they threw away their criteria. Even though their methodology determined that the modal American is a child, they just changed their criteria to get what they had originally wanted all along.

So they threw out their statistical methodology and just looked at adults and then they arbitrarily divided Americans into buckets according to ethnic categories which happened to clump people from Portugal, Ireland, Russia, and many from Latin America into the “white” category so that they could claim that identity as being “central” to “average” America.

Then they arbitrarily decided that Gen X is more “central” to America even though Gen X is far from the mode. There are both more Baby Boomers and more “echo boomers” (millennials) than members of Gen X, but they don’t really care about the mode and wanted someone who is “middle age” which would be the median age (38). They lamented that this is “one of the least common ages” and instead of staying with the modal age (26), they just switched their criteria and picked someone from Gen X anyway, perhaps by arbitrarily arranging their age buckets to get what they wanted.

In the end, they seemed to arbitrarily pick what they had probably had as their preconceived notion of the average American. Someone who is:

  • Gen X (even though the modal American is age 26)
  • “upper-middle-class income. The household income is between $75,000 and $165,000 a year. ” (Even though this is way higher than either the modal income or the median and is closer to mean household income.)
  • married (Even though the modal American is unmarried)
  • male (Although they admit that the modal American is female, they only interview men and talk about the “average guy” and focus on the “homogeneous experience” of, ” white, Gen X men“)
  • employed (Even though there are more Americans without a job than with a job)
  • no college degree
  • lives in the suburbs
  • white
  • wears plaid shirts! (I think this part was their attempt at a joke.)

Although I only have minor quibbles with the last four criteria, if I didn’t know better, I’d think Planet Money started out with a picture of the kind of guy that they consider to be the most essentially American and then picked arbitrary categories and tortured the statistics until they got what they wanted. They completely ignored the modal value for most of their criteria.

This ‘analysis’ is a good demonstration why nobody uses the mode with this kind of data. Even when Planet Money tried to use the mode, they couldn’t stick with it because it didn’t give them the preconceived results that they were looking for and so they just kept changing their rules until they got… demographics that look like something pretty close to the median Trump supporter. You know, “real Americans“.

Posted in Metrology

Big land

Bloomberg investigated the people that own the most land in America and this map of Maine speaks for itself:

The report found that:

 The 100 largest owners of private property in the U.S., newcomers and old-timers together, have 40 million acres, or approximately 2% of the country’s land mass, according to data from the Land Report and reporting by Bloomberg News. Ten years ago, the top 100 had fewer than 30 million acres.

Many of these individuals own more land area than the entire state of Rhode Island and altogether, these 100 landowners control an area about as big as the entire state of Florida. If anything this investigation understates the concentration of land ownership because a lot of properties is held by private corporations whose owners are hard to identify and sometimes the corporations are owned by other corporations as in the case of President Trump’s holdings. Trump owns approximately 500 business entities (although the exact number is unclear) that are collectively known as the Trump Organization and only about half of them use the Trump name. Even though Trump’s holdings have gotten much more scrutiny than other wealthy people, even here we don’t know exactly what he owns, how wealthy he is, nor how many companies he actually controls. And there are hundreds of Americans who are wealthier than Trump and whose holdings are probably even more complicated and secretive.

Here is a zoom in on another part of the USA that is particularly popular with the biggest 100.

Here is where all of it is located. They haven’t bought much in agricultural Midwest.

In contrast, the government still owns a lot more land than the 100 biggest private landowners:

This map shows the distribution of federally owned land.

Because this map only shows federal ownership, it leaves out vast territories owned by the state governments. For example, this map shows that the federal government owns nearly 3/4 of Alaska and then the state government owns another quarter of the state of Alaska leaving less than 1% of Alaskan territory that is owned by private citizens.

There is a lot more land in the east that is owned by state and local governments including roads, parks, schools, and rivers…

The expensive publically-owned road system connects all of the most important places together as you can see in this a map of nothing but the roads in Florida. The most valuable regions pop out visibly because they have more roads. (This map and many other states are available for purchase from Fathom).

Local government ownership is much more valuable than most privately-held real estate because roads are extremely valuable, particularly in urban areas where road density is concentrated. A newly paved road costs anywhere from a minimum of about $2 million per mile in rural areas to more than $10 million in urban areas. Maintenance is also very expensive. Resurfacing a 4-lane road costs about $1.25 million per mile.  Despite this cost, we call our most expensive roads freeways.

Posted in Public Finance

The occupation that tops them all

Claire Cain Miller at the New York Times gets the key issue with the gender pay gap:

Flexible, predictable hours are the key — across occupations — to shrinking gender gaps, according to the body of research by Claudia Goldin, an economist at Harvard.

Although in most respects women have made dramatic progress towards equality over the past half century, there is one trend that has counterbalanced the other wins:

Jobs increasingly require long, inflexible hours, and pay disproportionately more to people who work them. But if one parent is on call at work, someone else has to be on call at home. For most couples, that’s the woman — which is why educated women are being pushed out of work or into lower-paying jobs.

The fact that medical doctors have high scheduling flexibility is why…

Female doctors are likelier than women with law degrees, business degrees or doctorates to have children. They’re also much less likely to stop working when they do.

High pay, growing demand, rewarding work, high respect from the rest of society, and flexible scheduling. Not bad if you can stomach it.

Posted in Health, Labor

Amazon as a nonprofit

For most of Amazon’s history it made zero profit. That changed a couple years ago, but although its gross profit margin on revenues is now positive, it is still pretty negligible today.

Amazon is a huge conglomerate these days, but roughly speaking, its businesses can be divided into a boring retail business that everybody  knows well and a technology business that almost nobody knows unless you are a CFO or CIO because it operates server farms and provides technology services to other businesses. The technology business has been wildly profitable for most of this history in contrast with the retail business that usually loses money. Although most stand-alone retail businesses are different than Amazon’s in that they can’t constantly lose money every year, most retail businesses have very low profit margins, particularly if they are competing with Amazon, so Amazon’s lack of profits isn’t too far from normal.

So if Amazon’s profits have been zero or negative for most of its history and are negligible today, why is it the third most valuable corporation on the US stock exchange, almost three times more valuable than its competitor Walmart?

Cap Rank


Market Cap 

on 8/20/19

1 Microsoft


2 Apple




4 Alphabet


5 Facebook


6 Berkshire Hathaway


7 Alibaba


8 Visa


9 Johnson & Johnson


10 JPMorgan Chase


11 Walmart


The reason is that Amazon is using its high cash flow to invest in itself and grow its businesses. Investors are betting that Amazon’s businesses will become highly profitable someday in the future and that is elevating its stock market capitalization. Below is another way of looking at Amazon’s business with adds another line of data for its free cash flow.

Free cash flow is an alternative measure of profitability and one of the big differences is that it includes spending on equipment and assets and changes in working capital. By this measure, it isn’t hard to see that Amazon has had a lot of business success in recent years.

Posted in Managerial Micro

Another ineffective health care treatment Americans waste money on

Gabrielle Glasier writes in The Atlantic about the problems of alcohol abuse and how it is treated in America.

The United States already spends about $35 billion a year on alcohol- and substance-abuse treatment, yet heavy drinking causes 88,000 deaths a year—including deaths from car accidents and diseases linked to alcohol. It also costs the country hundreds of billions of dollars in expenses related to health care, criminal justice, motor-vehicle crashes, and lost workplace productivity, according to the CDC. 

It is a serious problem, but unfortunately America has prioritized 12- step treatments that are ineffective and more expensive than treatments that work. Glasier goes on to say,

In 2006, the Cochrane Collaboration, a health-care research group, reviewed studies going back to the 1960s and found that “no experimental studies unequivocally demonstrated the effectiveness of AA or [12-step] approaches for reducing alcohol dependence or problems.”

The Big Book includes an assertion first made in the second edition, which was published in 1955: that AA has worked for 75 percent of people who have gone to meetings and “really tried.” It says that 50 percent got sober right away, and another 25 percent struggled for a while but eventually recovered. According to AA, these figures are based on members’ experiences.

In his recent book, The Sober Truth: Debunking the Bad Science Behind 12-Step Programs and the Rehab Industry, Lance Dodes, a retired psychiatry professor from Harvard Medical School, looked at Alcoholics Anonymous’s retention rates along with studies on sobriety and rates of active involvement (attending meetings regularly and working the program) among AA members. Based on these data, he put AA’s actual success rate somewhere between 5 and 8 percent. That is just a rough estimate, but it’s the most precise one I’ve been able to find.

It is always possible for anyone to claim success at treating addiction because, As Bethany King points out, there is a lot more “spontaneous remission” of addiction than most people think if you give people enough years partly because more years also tends to give more random chances for a major shift in life circumstances which can help too.  For example, 95% of Vietnam-war solders who were addicts in Vietnam ended up spontaneously quitting after returning to the States.  That is a much higher rate of spontaneous remission than we would expect to see in most contexts, but it is a sign of what is possible.

AA is part of the incredible amount of bad medical treatment that we are still using such as the “creative diagnosis” of dentists.  Someday people will probably look back at this like we look back at bleeding people with leeches.  Glasier goes on to explain why naltrexone and acamprosate treatments are more effective than AA and the political history of how AA came to dominate.

Unfortunately AA isn’t even the worst part of the addiction “treatment” racket in America.  The flood of new money for dealing with the opioid epidemic has attracted charlatans and German Lopez has begun a new investigative series about it.

Posted in Health, Labor


Fascinating statistics about marriage.

sociologist Andrew Cherlin points out, just two years after the Supreme Court decision to legalize same-sex marriage in 2015, a full 61 percent of cohabiting same-sex couples were married. This is an extraordinarily high rate of participation.…

sociologists Natalia Sarkisian of Boston College and Naomi Gerstel of the University of Massachusetts at Amherst found that marriage actually weakens other social ties. Compared with those who stay single, married folks are less likely to visit or call parents and siblings—and less inclined to offer them emotional support or pragmatic help with things such as chores and transportation. They are also less likely to hang out with friends and neighbors.

Maybe it is better for society if we let marriage rates decline

Posted in Labor

Dismal state of dentistry

Julie Beck wrote that

In America, we treat the mouth separately from the rest of the body, a bizarre situation that Mary Otto explores in her new book, Teeth: The Story of Beauty, Inequality, and the Struggle for Oral Health in America… Specializing in one part of the body isn’t what’s weird—it would be one thing if dentists were like dermatologists or cardiologists. The weird thing is that oral care is divorced from medicine’s education system, physician networks, medical records, and payment systems, so that a dentist is not just a special kind of doctor, but another profession entirely.

Otto says that state of affairs can be traced back to a historical accident in 1840 when some dentists established the first dental college in Baltimore. They approached the physicians at the University of Maryland to suggest that it be incorporated into the medical school, but they were rejected and so they started their own parallel system of education, research, financing, medical records, and licensure.

This doesn’t make much sense because oral health is an integral part of dental health. Otto says that more than a million people each year go to emergency rooms for dental care because they lack other options, but emergency rooms are not good places to get dental care.  As Olga Khazan says:

Despite the fact that dental procedures are some of the most expensive office visits, dental coverage is treated like a garnish—the parsley of the insurance world.

“Medicaid doesn’t acknowledge that you have teeth unless you’re a child,” said Thomas Ritter, a dentist who was volunteering at the event.

One reason for this is that since the beginning of time, dentistry and medicine have been considered inherently distinct practices. The two have never been treated the same way by either the medical system or public insurance programs. But as we learn more about how diseases that start in our mouths can ravage the rest of our bodies, it’s a separation that’s increasingly hard to rationalize.

There have been some attempts to merge the two systems, but dentists have come to value their professional autonomy and prefer to stay independent now. The current system gives dentists more control. For example, when dental hygienists can practice independently from dentists, they can earn more money and charge less for cleanings so everyone wins except dentists who earn 16% less according to one study. Max Ehrenfreund found that

Dentists in some places are so well compensated that they earn more than the average doctor. According to a 2012 report in The Journal of the American Medical Association, the average hourly wage of a dentist in America is $69.60 vs. $67.30 for a physician.

Although I have been fortunate to have found honest, hardworking dentists who care about my family’s oral health, many dentists have been padding their incomes by using what Jeffrey H. Camm called “creative diagnosis” in a commentary published by the American Dental Association (also known as “supplier-induced demand” in the economics literature). Alison Seiffer wrote about this practice:

My household’s level of confidence in dentistry is at an all-time low. About six months ago, my dentist informed me that my “bunny teeth” were likely getting in the way of my professional success, a problem he could correct with a (pricey) cosmetic procedure. If I let him fix my teeth, he told me, he was sure I would start “dressing better.” A few months later, my husband scheduled a basic cleaning with a new dentist. Once they had him in the chair and looked at his teeth, they informed him that the regular cleaning wouldn’t do at all: He would need to reschedule for an $800 deep cleaning. No thanks.

We were convinced we must look like suckers—until I came across an op-ed in ADA News, the official publication of the American Dental Association. The article, by longtime pediatric dentist Jeffrey Camm, described a disturbing trend he called “creative diagnosis”—the peddling of unnecessary treatments. William van Dyk, a Northern California dentist of 41 years, saw Camm’s op-ed and wrote in: “I especially love the patients that come in for second opinions after the previous dentist found multiple thousands of dollars in necessary treatment where nothing had been found six months earlier. And, when we look, there is nothing to diagnose.”

…Poking around, I found plenty of services catering to dentists hoping to increase their incomes. One lecturer at a privately operated seminar called The Profitable Dentist ($389) aimed to help “dentists to reignite their passion for dentistry while increasing their profit and time away from the office.” Even the ADA’s 2014 annual conference offered tips for maximizing revenue… more and more young dentists are taking jobs with chains, many of which set revenue quotas for practitioners. This has created some legal backlash: In 2012, for example, 11 patients sued (PDF) a 450-office chain called Aspen Dental, claiming that its model turns dentists into salespeople. Some corporate dentists appear to have crossed the line into fraud. In 2010, Small Smiles, a venture-capital-owned chain with offices in 20 states, was ordered to refund $24 million to the government after an investigation found that its dentists had been performing unnecessary extractions, fillings, and root canals on children covered by Medicaid. A new lawsuit alleges that some toddlers it treated underwent as many as 14 procedures—often under restraint and without anesthesia. …Several other pediatric dentistry chains have been sued over similar allegations. ….

This isn’t a new problem although it might be getting worse. As America’s teeth have gotten healthier and need less dental treatment due to better brushing and fluoride, dentistry has found other ways to boost revenues at a double-digit growth rate.

One way dental offices have increased revenues is by offering a more spa-like experience with aromatherapy, nicer decor, Netflix, weighted blankets, hoise-cancelling headphones, massage, cake, and other services that make a dental visit a more pleasant experience and allow them to charge a premium.

Unfortunately, another way they have increased revenues is by tricking patients into getting excessive treatments.  Readers Digest did an experiment in 1997 in which award-winning journalist William Ecenbarger visited 50 dentists in 28 states and wrote an article entitled, “How Honest Are Dentists?” For the baseline, he hired a panel of expert dentists from a dental school to tell him what they thought he should get. They all agreed that he should get one crown and he might need a filling although some thought he could wait and see. They estimated that the total cost for his dental care should be between $500 and $1500. Then he went out into the wild dental marketplace, and he got wildly varying opinions. Indeed 79% of dentists exceeded the recommendations of the panel of experts and creatively diagnosed urgent problems that would generate more revenues. At the same time, 30% missed the real molar problem that needed capping and more than 72% failed to do two low-profit preventative screenings that the ADA recommends:

  • 72% neglected periodontal screening
  • 58% neglected oral-cancer screening

Here is a chart showing the six most egregious examples of “creative diagnosis”. Note that two of the dentists wanted to do 28 crowns!! That would mean crowning every single tooth if (as is likely) he had already had his wisdom teeth extracted.


(# most expensive)

# of crowns (C) and fillings (F)

Total estimate

Panel of Experts 1C, 1F (maybe) $500-$1,500
(6) Englewood, OH 11C, 5F $8,347
(5) Seattle, WA 17C $10,735
(4) Memphis, TN 28C $13,440
(3) Albuquerque, NM 22C $14,445
(2) Salt Lake City, UT 28C $19,402
(1) New York, NY 21C $29,850

Oddly, although there are lots of responses to the original article on the internet, Reader’s Digest doesn’t have anything about it, so they seem to have buried one of their most important and popular pieces of investigative journalism.

Although I have found great dentists, I have also had some who overdiagnosed. One dentist wanted to replace all of my teeth and my wife’s teeth with implants (like you frequently see advertised on the internet) and he told my wife that she has ugly “buck teeth” that she deserves to have replaced. Three other dentists completely invented cavities that no later dentist has seen. And even good dentists frequently exceed the ADA recommendations. For example, they like 6-month checkups whereas the ADA thinks most people are of low risk and only need annual checkups. Dentists also overdo X-rays. The ADA recommends waiting 2-3years between X-rays if there are no cavities.

In addition Joseph Stromberg suggests that dental patents should beware of:

1. Dental practices that advertise and offer deals.  As he says,

The reason for this is that advertising-driven offices often use deals as a tool to get patients in the door and then pressure them to accept an expensive treatment plan, whether they need work done or not. Oftentimes, they’re corporate-owned chains, like Aspen Dental. “These big chains are kind of dental mills,” Mindy Weinman said. “They’re the ones that give you the free cleaning, and the free exam, then they tell you that you need $3,000 worth of dental work.”

2.  A new dentist who prescribes more treatments than usual.

3. Replacing old fillings

4. Veneers.  These cash cows are almost always unnecessary and purely for cosmetic purposes, but they can make teeth problems worse in the long run.

5. Fluoride treatment or sealants for adults or special fluoride toothpaste.  Kids may be able to use fluoride treatments or sealants, but there is rarely any benefit for adults and sealants can actually weaken the teeth through the etching process.

6.  Dentists who don’t show you evidence of problems on your x-rays.  Of course, most dentists take way more x-rays than is healthy for their patients, but if they do take them and tell you that you have a problem, they should show you the problem on the x-ray and let you have a copy of the x-ray.  It is legally your property even though some dentists don’t like to let you see them.  As Stromberg wrote:

Virtually all honest dentists will gladly show you X-rays of your teeth that contain evidence of the work you need. “X-rays, legally, are your property. A dentist can charge for them, but they have to share them with you,” Mindy Weinman said.

You won’t necessarily be able to see evidence of every single type of problem in an X-ray, but many of them should be apparent. A dark spot or blemish, in general, corresponds to a cavity. And in general, the dentist should be willing and able to explain why you need certain procedures, both by using X-rays and other means.

But regardless of what the X-rays show, if you’re skeptical of the treatment a dentist is prescribing — especially if it’s your first visit to the practice, and they’re recommending far more work than you’re ever needed before — the best response is to get a second opinion. This was mentioned to me by every dentist I spoke with, along with the American Dental Association.

For more stories about creative diagnosis at dental offices, see Ferris Jabr’s excellent essay in The Atlantic.  At the same time as some Americans are getting excessive, unnecessary dental care, other Americans lack access because they are too poor or because they live in a rural area where dentists are simply not available.  Olga Khazan says that,

About a third of people in the U.S. don’t visit the dentist every year, and more than 800,000 annual ER visits arise from preventable dental problems. A fifth of Maryland residents have not visited a dentist in the past five years…  There are about 4,000 designated dentist shortage areas all over the U.S. In some of the worst-affected states, between a quarter and a third of the population lacks access to dental care entirely.

Posted in Health

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 49 other followers

Blog Archive