Briefed by Data

Immigration Status by Age and Race

Tue, 03 Nov 2026 20:02:02 GMT

Last week’s post, U.S. Hispanic Population by Age & Generation, included a graph of age and generation for Hispanics, which is reposted in Figure 1. I said this about the graph:

Hispanic household wealth is low, but this group is unique in the U.S. because many members are recent immigrants.

After thinking about the post, I started to wonder if this statement was really true, and I was just curious about what Figure 1 would look like for the Asian, Black, and White populations. Hence today’s post. As a review from last Tuesday, note that 1st generation are immigrants, 2nd generation have at least one parent who is an immigrant, and 3rd generation plus means both parents are citizens.

Figure 1: Data from IPUMS.

Up first is the Asian graph in Figure 2. It turns out that Asians in the U.S. are more likely to be first generation than Hispanics. 51.4% of Asians aged 30 and older are immigrants. Only 7.3% of Asians are third generation or more.

My argument for Hispanics was that, since adults are mostly first generation, this explains some of their lower wealth. Well, Asians are even more likely to be immigrants yet have the highest wealth as a group in the U.S. I’m assuming that there is a real difference in how each group arrives in the U.S. Hispanics enter the U.S. poorer and less formally educated, while Asians are more educated and start in higher-paying jobs. I’d like more data on this topic, but that is my working assumption.

Figure 2: Data from IPUMS.

It is also worth noting how the distribution of ages differs between Figures 1 and 2. Asians are older, with a lower percentage of kids aged 0-19, 21.4% versus 32.1% for Hispanics.

The next two graphs are very different. Figure 3 is the graph for the Black population, with 73.7% of the population in the third generation of higher. Overall, a very small percentage of the Black population are immigrants. I’ll add that their youth percentage, aged 0-19, is 26.8%.

Figure 3: Data from IPUMS.

Moving to Figure 4, the White non-Hispanic population, we see that 85% are third generation or higher, with the smallest percentage of youths at 18.3%. When we consider the four major groups, we see two very distinct immigration profiles. The Black and White populations have very few immigrants in terms of percentages, while the Asian and Hispanic populations are skewed toward immigrants. It seems this is worth knowing as the media discusses voting patterns and general views. Your thoughts on this are welcomed in the comments.

Figure 4: Data from IPUMS.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I’m a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS Oct 29, 2026

Thu, 29 Oct 2026 19:02:00 GMT

As I see it . . .

My experience in higher education has provided me with plenty of examples of terrible administrators: deans, provosts, and presidents. It may be just as bad in other sectors, but I can’t say for sure. In the past, when college had plenty of students and money, poor leadership wasn’t a significant issue, but today, with the challenges higher education is facing, it’s a big issue. The question becomes, why are our administrators so poor?

One explanation I’ve had is it’s a pipeline problem. The faculty most capable of being good administrators are filtered out early. The pipeline begins as a department chair or associate dean or provost. Department chair is a position few people want or are willing to do. You have responsibility but little power to get anything done. Most of the job is tedious. The associate dean and provost positions are largely about paperwork.

As I see it, my own data rule, “Always consider other factors as single-factor explanations are rare,” tells me I need more of an explanation than a pipeline problem. This week, I came across two things that add to the explanation.

The first was a post on LinkedIn by Jeff Selingo (bold mine).

What separates the innovative universities from the rest?

It's a question I was asked twice this past week by a board of an R1 public university and by a president of a small private.

Leadership, and presidents who, in particular, see a lane to success and drive it to win. Three examples:

🔬 ASU: AAU research university doesn't have to be incompatible with an access mission
🏆 Georgia State: lots of small experiments to move the needle on student success
💻 Southern New Hampshire: a sleepy online division scaled by a high-performing division separate from the university

From our most recent Future U. Podcast with the president of Unity Environmental University, I discussed the need for more presidents to recognize where a university can really play, then to have a bias to action to want to win by putting their energy and the resources of the institution behind

In the video clip in the post, he says, “Not enough of them want to win; they just want to wait it out.” This comment is in reference to the demographic cliff and general higher education challenges. The idea is that other colleges will close, so you don’t have to do anything; you can just wait.

My pipeline explanation starts with the Ph.D. In general, getting a Ph.D. is a risk-averse path. Most faculty were well-behaved, good students. They just kept going to school to get that nice faculty job. They aren’t entrepreneurial, and they don’t like to rock the boat. They don’t want to win; they want to be safe.

The second piece is from a 1999 paper that circulated this week, Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments. Here is part of the abstract.

People tend to hold overly favorable views of their abilities in many social and intellectual domains. The authors suggest that this overestimation occurs, in part, because people who are unskilled in these domains suffer a dual burden: Not only do these people reach erroneous conclusions and make unfortunate choices, but their incompetence robs them of the metacognitive ability to realize it. Across 4 studies, the authors found that participants scoring in the bottom quartile on tests of humor, grammar, and logic grossly overestimated their test performance and ability.

Here is one graph from the paper, which says, for example, the bottom quartile had an actual logic test score around the 10th percentile, but their perceived ability put their score at about the 55th percentile.

The problem with those of us with a Ph.D. is that we think we know everything because of it, even though the Ph.D. was achieved by learning something in a very narrow domain of knowledge.

In recap, faculty by nature are risk averse. You hire them, and then which of them will do paper-pushing administrative jobs? They are more risk averse and also have a certain confidence that they will be great administrators someday, most likely vastly overestimating their ability, as shown in the figure above. Those who understand how challenging leadership in higher education can be—those on the right side of the graph—don’t enter the pipeline, even though they may be the best candidates for it. At the same time, people who underestimate their skills are the ones who are more likely to keep learning. If you think you know it all, you don’t need to learn anything.

We are at a time when higher education needs leaders who aren’t risk averse, want to win, and aren’t overconfident. Waiting it out is not a brilliant strategy. I’ll note that there are good higher education leaders, and if you listen to the Future U podcast in the link above, you’ll hear from some.

I’d love to hear how wrong I am for those of you in higher education and if any of this relates to other sectors for those of you not in higher ed.

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Let’s go to some data.

Equal land

Why Do Older People Have Most of the Money? (10/25/2026) is a great post by Adam Nash. The main point is that when younger people see wealth by age graphs, they scream “unfairness.” Nash then creates a simple model:

As a thought experiment, let’s consider a totally equal society called Equal Land.
In Equal Land everyone has the same financial life:
Everyone works from the ages of 25 to 64, retiring at 65
Everyone lives to the age of 85
Everyone makes the same amount, $100,000 per year
Everyone saves 10% of their income, every year while they work
Everyone makes 8% on their savings, every year
Everyone spends 4% of their portfolio, every year in retirement
So what does the distribution of wealth look like in Equal Land?

Ready for the graph? Yup, inequality, lots of it. Why? Because wealth is accumulated over time.

I’ve made this point before in comparing groups. The median age of Asian, Black, Hispanic, and White populations is different. You have to take this difference into consideration when comparing group wealth or income. Similarly, I made this point in Tuesday’s post, U.S. Hispanic Population by Age & Generation. We are at a point in time where it is easy to get simple data and make basic graphs, yet we understand the world less.

More on screen time being bad

From the IFS (10/15/2026)

At age 3, children with very limited screen time were most likely to tell stories, especially if they did not exceed the one-hour recommended limit. However, children who had higher screen time were less likely to be able to use three-word sentences, ask a question, or tell a story.

The U.S. is #1

Well, in oil production anyway. This graph is from Our World in Data (9/29/2026). It is worth noting that the U.S. has increased oil production since about 2008, and it doesn’t matter which party holds the presidency or Congress. There is simply too much money and a standard of living tied to oil.

How hot was Sept 2026?

Here is what NOAA has to say.

The global surface temperature for September 2026 was 1.33°C (2.39°F) above the 20th-century average, ranking as the second-warmest September since global records began in 1850. This value falls behind 2023 by 0.07°C (0.13°F). September 2026 marked the 51st consecutive September with global temperatures above the 20th-century average. Notably, the past four Septembers (2023–2026) represent the four warmest Septembers on record and are the only Septembers to exceed a +1.0°C (+1.8°F) departure. All 10 of the warmest Septembers have occurred since 2015.

The usual two graphs are below. Sept 2026 will officially be an El Niño month once October data is complete. Given that it is no surprise, it is a second-highest anomaly for September. El Niño events tend to increase in intensity as they evolve, so we should expect to see monthly records over the next few months.

When we look at all months, we see September 2026 as one of the higher months. It isn’t higher than the last round of El Niño, but it is higher than the first few red bars of the last El Niño. I would expect we’ll go above the 2.5°F threshold soon, along with a media panic as if the outcome is a surprise. I did say in the last El Niño that the next one would likely be worse because the red bars have been growing quadratically. We aren’t stopping or slowing the trend anytime soon; figuring out how to adapt is imperative. I expect that just as we have done little to slow down or stop the warming, we will be well behind in adapting.

The Globe

Fun images from the LOC post The American Globe: a Landmark Achievement (10/27/2026).

Pictured above is the earliest dated American-made globe. It is housed in the Geography and Map Division. Created in 1811 by James Wilson, the first commercial globemaker in the United States, it is made of paper gores over papier-mâché and plaster. It sits in a wooden stand with four legs supporting a wooden circle with mounted zodiacal paper and a brass meridian ring. The globe is 34 centimeters (about 13.5 inches) in diameter and is commonly referred to as a 13-inch globe.

The spinning CD

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Please let me know if you think I expressed something incorrectly or misinterpreted the data. I would rather know the truth and understand the world than simply be correct. I welcome comments and disagreement. I encourage you to share article ideas, feedback, or any other thoughts at briefedbydata@substack.com.

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Bio

I am a tenured mathematics professor at Ithaca College, holding a PhD in math (stochastic processes), an MS in applied statistics, an MS in math, a BS in math, and a BS in exercise science. I consider myself an accidental academic (opinions are my own). I am a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

U.S. Hispanic Population by Age & Generation

Tue, 27 Oct 2026 19:01:54 GMT

Last Thursday’s QTRS included Figure 1 below and got me thinking. Hispanic household wealth is low, but this group is unique in the U.S. because many members are recent immigrants. The question is how many Hispanics in the U.S. are immigrants, and, in particular, we want to know that by age. Wealth takes time to build, and I would expect that historically it takes a few generations to build that wealth.

Before we move to the next figure, here is a quiz question. Hispanics aged 40-49 are what percentage 1st generation (immigrants), 2nd generation (at least one parent is an immigrant), and 3rd generation plus (both parents are citizens). Are they about about equally represented? More 1st than 3rd? Reversed? Etc.

Figure 1: From Black Wealth Takes a Nosedive (10/13/2026)

Figure 2, data from IPUMS, answers the question. There are more 1st-generation Hispanics aged 40-49 than there are 2nd- and 3rd-generation Hispanics combined. Overall, for ages 30 and up, first-generation Hispanics make up 30.7% of the total, while the 2nd and 3rd generations account for 9.3% and 11.2%, respectively. In other words, 60% of the Hispanic population aged 30 and older are immigrants.

It isn’t surprising their wealth is low, and while I can’t say how much this accounts for the differences compared to Whites and Asians, it certainly accounts for some of it.

Figure 2: Data from IPUMS.

What is also interesting about Figure 2 is that we should expect a generational shift in the Hispanic population. The 20-29 age group has second generation as a majority, and the 0-19 age group has third generation as almost equal to second generation.

While searching for information, I came across two other graphs that are worth sharing, in addition to Figure 2, which is the main graph today. The first, Figure 3, is from the Pew article Key Facts About U.S. Latinos (10/22/2025). The data rule know the distribution, not just summary statistics (formerly know the distribution, not just the mean and median). Figure 3 is technically correct, but it is misleading and does not clearly tell the story of the Hispanic population. Of the 67% that are U.S.-born, almost half are children. That matters.

Figure 3: From the Pew article Key Facts About U.S. Latinos.

The second graph (table actually) Figure 4, comes from the 2019 paper Financial Security and Immigrants’ Legal Status: An Analysis of Net Worth in the United States. It points out that household net worth is higher for US-born than foreign-born households, with one exception—the Black population, which is probably a story for another day. However, given the high percentage of immigrant Hispanic adults, any comparison of household wealth is misleading if you don’t account for this fact.

Figure 4: From Financial Security and Immigrants’ Legal Status: An Analysis of Net Worth in the United States.

Reference

IPUMS Data: Sarah Flood, Miriam King, Renae Rodgers, Steven Ruggles, J. Robert Warren, Daniel Backman, Etienne Breton, Grace Cooper, Julia A. Rivera Drew, Stephanie Richards, David Van Riper, and Kari C.W. Williams. IPUMS CPS: Version 13.0 [dataset]. Minneapolis, MN: IPUMS, 2025. https://doi.org/10.18128/D030.V13.0

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QTRS October 22, 2026

Thu, 22 Oct 2026 19:01:33 GMT

As I see it . . .

Jeff Selingo is a higher ed guru, author, thought leader, and whatnot, and he’s on the board of my college. I pay attention to his newsletter, and this got my attention this week.

The Southern school story is wearing thin. Pandemic-era social media fed teenagers a steady diet of undergrads living mostly normal lives on Southern campuses, especially in the SEC. Six years later, some admissions leaders elsewhere are tired of hearing about it.
An enrollment vice president at a private college in the Mid-Atlantic told me at my booth in the exhibit hall that the narrative has crowded out what should matter in a college search. “Fit is too focused on social, almost to the exclusion of everything else,” he said. Part of it is frustration. His college has missed its enrollment and revenue targets two years running.
Counselors see it too. Keeon Gregory, dean of college counseling at Greensboro Day School, said the “three Fs” drive too many searches: football, friends, and food. “None of those things tells us much about the academic experience or the support students will need in their first year,” Gregory said during a session I moderated on the first-year experience.

There has been a trend of students in northern states going to college in southern states. It seems they do better on “football, friends, and food,” and students aren’t paying enough attention to “academic experience” and “student support.” This isn’t surprising to me and makes a lot of sense, as there isn’t much to differentiate schools academically or in areas of student support, so why not focus on the three Fs?

As I see it, there are only two areas that really differentiate schools academically: student profile and size. In any given classroom, the median student’s abilities largely set the expectations. You will learn more in calculus at Cornell than at Ithaca College, not because the professor is better, but because the students are prepared to do more. In the end, the colleges a student is admitted to into are likely to provide very similar classroom expectations, and even if one is somehow better academically, there is no real way to prove it.

The other factor is the size of the school or the program a student is in. The bigger the program, the more classes one will have to choose from. The one tradeoff here is that bigger schools tend to have more students in classrooms, and when it comes to student support, you’ll likely get less of it at a bigger school. But schools of similar size are likely to have similar amounts of support for students.

This isn’t to say there are no differences, but colleges are more alike than different. There is a logic to focusing on the three Fs, as most students don’t want monastic experience, and it seems to me that an SEC college is more fun to attend, as “fun” really summarizes the three Fs.

Northern colleges losing students to the south need to ask themselves, “Is your college a fun place to be, or are you overly focused on safety?” To me, there is a real tension between safety and fun that mirrors the political divide. The left is more focused on safety. To me, a student who goes south is saying they would rather take a little more risk, have fun, and have a little less safety.

I’ll end with one extreme example at my college. Years ago they outlawed chalking. This activity is where you write stuff on walkways with chalk. It might be about a party, or a viewpoint, or just something stupid and fun. Apparently, we decided some chalking messages upset some students, and we needed to stop it. Eliminating hurt feelings is part of the safety the left wants. Going to college there doesn’t seem fun to me.

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Let’s go to some data.

Household wealth

Two graphs from the article Black Wealth Takes a Nosedive (10/13/2026). The first shows that Hispanics managed to increase their wealth by 18%, while Blacks went down 25% from 2022 to 2025. Where does this leave the groups’ overall wealth?

The answer is in figure 2. As always, the order is the same. Asians crush everyone else with a household wealth of $677 thousand, double the White value of $332 thousand. Hispanics come in a far third at $80 thousand, but still double the Black value of $37 thousand. Why did Hispanics make gains and Blacks didn’t, according to the author?

Here is what the author said.

The Trump administration’s priority for race-targeted policy is helping White people. The administration is channeling its resources toward addressing discrimination against White men although by race Black people are the primary target for discrimination. The administration’s refugee policy is focused on bringing White South Africans to the United States and ignoring all of the truly needy people in the world.
Black Americans are not likely to receive any help from the Trump administration in addressing this decline in wealth. They will have to turn elsewhere, to state and local governments and nonprofit organizations.

So, Trump is helping White people, yet their wealth gain is only a third, and they have less than half the wealth of Asian people. Meanwhile, Hispanics made gains. I’m having trouble with the logic here. What this has to do with refugee policies is also beyond me. I don’t believe any president has this type of impact on the wealth changes of individual groups over a couple of years. You need to show me some serious data to convince me.

What I do know is that Asian Success isn’t an Accident (9/10/2024) and that successful habits follow the same race patterns as wealth. Maybe it’s time I update the Asian success post.

EV sales decline

From the EIA.

There are a couple of points in the post worth noting.

Growth of hybrid electric vehicle sales has slowed this quarter as the average transaction price for a new vehicle passed $50,000—the first time this price has been reached so far this year, according to Kelley Blue Book.

$50,000 is an expensive car for most people. This has been a key problem with EVs; the upfront cost is too high.

Battery electric vehicles have historically been more popular in the U.S. luxury vehicle segment, which accounted for 12% of the total U.S. light-duty vehicle sales in 3Q26. However, sales in this segment are also declining. In 3Q26, battery electric vehicles accounted for 12% of luxury light-duty vehicle sales, down from 31% in 3Q25 prior to the expiration of the clean vehicle tax credits.

Now a second graph of theirs.

The clean vehicle credits were largely going to wealthy people that could afford an EV. The rise in battery electric vehicle sales from 2021 to 2025 in the top graph was due to wealthy people. This trend was never sustainable.

Graph of the week

From the IEA. The graph here is from their newsletter, which doesn’t have a link. A version of this graph is at the link, but this one is nicer.

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QTRS Oct 15, 2026

Thu, 15 Oct 2026 19:02:52 GMT

As I see it . . .

One of the things you don’t do when teaching statistics classes is use sports data as examples. Too many students have no interest in knowledge of any particular sport. That’s probably good advice for my posts here. So, let me talk about baseball. Specifically, my thoughts on the upcoming collective bargaining and the owners desire for salary caps.

For those that don’t know, the current contract between players and owners expires Dec 1, 2026. Owners will lock out the players as they negotiate a new contract. The big sticking point is that the owners want a cap on how much each team can spend on players. MLB is unique in not having a salary cap, and the owners think such a measure is necessary for competitive balance. Players will say that the owners want the cap to make more money.

As I see it, a salary cap will make baseball less compelling. In the current league championship series, nearly 11 million viewers watched game one between the Dodgers and the Brewers, while about 3 million viewers tuned in for the Guardians vs. the Rays. I suspect that a large portion of those 11 million viewers are rooting against the Dodgers. Why? Because the Dodgers’ payroll exceeds the total of the other three teams. People love to see Goliath fall.

If there were a salary cap, there wouldn’t be an evil empire, currently the Dodgers and formerly the Yankes, to root against. The Dodgers are down 0 to 3, and I bet viewership on tonight’s game 4 will be high. In fact, it’s higher than the world series if the Dodgers don’t make it.

Now, the playoff viewership gain may not offset the regular season loss due to spending. To me, this situation improves with a salary floor, which is also on the table.

The morale of today’s rant is to never underestimate people’s desire to see others fail. It might be more powerful than wanting to see people succeed.

Full disclosure, I’m a lifelong Mets fan, currently a wannabe Evil Empire.

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Let’s go to some data.

Gallup on Education

Two figures from the recent Gallup poll on higher education (10/1/2026). The first shows the decline in the percentage of people who view college as very important. It was 70% in 2014 and is now at 31%. That’s a major collapse in 12 years.

What’s really astonishing is how little higher education has done in response. From my perspective, the response has mostly been to grumble about how people don’t understand the value, along with return on investment arguments and complaints about Republican attacks. In fact, some people looking at this chart will think to themselves that the drop is mostly from Republicans. Well, let’s go to the second figure.

The breakdowns show declines for all groups. From 2019 to 2025/2026, the decline among men and women is only 2 points apart. Democrats declined 3 points more than Republicans. Yes, women and Democrats still see college as very important more, but the declines in the figure above are from everyone.

Worse, there is not a single subgroup above 50%; in fact, one group is at 47% (Hispanic adults) and the rest are 40% or lower. Higher education should be panicking, but we change really slowly, and in this case, too slowly. Thoughts on this next week.

Impressive poverty decline

From Our World in Data (10/13/2026), we have this chart showing poverty in China and Indonesia. Impressive decline. How? The second graph below is one that should have been included with this one.

You raise the standard of living and get people out of poverty by using more energy. The people in poverty in those countries don’t care how you get the energy. They aren’t worried about being green when they can’t feed themselves.

Single motherhood

Lots of interesting graphs in the IFS article Single Mothers Are Getting Older (9/14/2026) and I’ll share this one. I consider this a strange dynamic. What I do know is that there is strong evidence that kids do better, on average, with two parents, and that Asian kids have the highest percentage of living with two parents.

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Medical Device Spending by Country

Tue, 13 Oct 2026 19:03:05 GMT

I ran into a graph on X that listed MRI machines per million people by country. The point was that Canada had a low number of MRI machines per million people, while the US had a high number, which suggests that Canada’s health is bad. That got me curious, and you today’s post.

It turns out that the World Health Organization (WHO) keeps counts of eight different medical devices. The one caveat with the data is that the most recent data for any device and country is 2021, while a good portion of the data is between 2013 and 2017, with a few as old as 2010. But, in any given year, the data is machines per million people, so the comparisons are reasonable even if the years don’t match up.

Now, even if comparing medical devices by country doesn’t excite you, today’s post is a good example of the data rule: normalize properly and ask, “Per what?” Let’s go to the data.

Figure 1 shows the count of medical devices by country. The US has, by far, more medical devices per million people than all other countries. Interestingly, of the eight devices WHO counts, mammography is the machine that dominates the list. The countries at the tail end that don’t list as having any are probably data collection issues.

As for Canada, it is in the middle of the road. Most countries have some form of universal coverage; Japan and Greece, 2 and 4 on the chart, included. I’d argue that counting machines is only one way to compare countries, and given that machines aren’t free, it makes sense to compare money spent.

Figure 1: Data from the World Health Organization (WHO) .

I used Gemini to get a typical cost of each piece of equipment, and this is what I used: Magnetic Resonance Imaging (MRI) $1,800,000, Computed Tomography (CT) units $450,000, Positron Emission Tomography (PET / PET-CT) $1,200,000, Gamma Camera / Nuclear Medicine (SPECT) $275,000, Radiotherapy Units (Category Average) $3,000,000, Mammography Units (3D Tomosynthesis) $280,000, Linear Accelerator (LINAC) $3,200,000, and Telecobalt Unit $650,000.

Notice that mammography units are low-cost compared to other equipment, making it easier to own more. Figure 2 shows spending on equipment per million people. Notice how Japan jumped to the number 2 spot as they outspend even the US on MRIs. The spend on mammography units isn’t as much as it looks like in Figure 1.

Figure 2: Data from the World Health Organization (WHO) .

In order to buy equipment, you have to have the money to spend as a society. MRI machines at nearly $2 million a pop aren’t cheap. We should normalize based on GDP. Figure 3 is the spending on medical equipment as a percentage of GDP. All of a sudden the US spend on equipment doesn’t look so special. Greece really invests in medical equipment, and Turkey jumps to the second spot. Canada really doesn’t spend on medical equipment, but that isn’t necessarily because of universal health care, as Greece has it and is in the top spot. In fact, all the top spenders as a percent of GDP have it. Comparing the number of medical machines between Canada and the US as a slam against universal coverage is really nonsense.

Figure 3: Data from the World Health Organization (WHO) .

I made two extra graphs for those interested. Figures 4 and 5 are the same as Figures 1 and 2 but without mammography units. They are such a big category that I took it out to better compare the other seven. Based on count, Figure 4, the US falls to the second spot, with Japan buying more of the other seven per million people than the US.

Figure 4: Data from the World Health Organization (WHO) .

Figure 5 is the percent of GDP, and the US comes in at 11. The interesting thing to me is the cost of MRI machines (blue). They are expensive, and countries have enough of them to take up more than 0.2 point of GDP. Who knew?

Figure 5: Data from the World Health Organization (WHO) .

I really do get curious about stuff, and now you know more about medical equipment purchases. Cool, right? So, why haven’t you subscribed? Hey, I have to push once in a while.

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Please tell me if you believe I expressed something incorrectly or misinterpreted the data. I'd rather know the truth and understand the world than be correct. I welcome comments and disagreement. I encourage you to share article ideas, feedback, or any other thoughts at briefedbydata@substack.com.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

Class of 2026 SAT Scores

Tue, 06 Oct 2026 19:00:48 GMT

The College Board reports SAT results by sex and race in its annual report. Today we look at the results from the 2025-2026 school year in their report, the 2026 SAT Suite of Assessments Annual Report. Let’s get right to the data.

Figures 1 and 2 are the distributions of male and female scores for math and reading/writing. The numbers above the bars are counts, while the bar heights are percentages. Since the number of male and female test takers is close—960,612 and 975,491, respectively—this doesn’t change the relationships.

In Figure 1, we see males score higher on the math portion of the SAT. There are about 70% more males in the 700-800 range than females and 17% more in the 600-690 range. This explains at least in part why there are more males in math-based STEM fields.

Figure 1: Data from the College Board’s 2026 SAT Suite of Assessments Annual Report.

In Figure 2, the reading/writing portion of the SAT, I was surprised that males edged out females in the top two score categories. Their distributions are much closer in reading/writing than in math.

Figure 2: Data from the College Board’s 2026 SAT Suite of Assessments Annual Report.

Moving to the distribution by race, Figures 3 and 4 are the math scores. In Figure 3, the purple bar in the 700-800 range represents Asians. Of Asians, 37% take the SAT and score above 700, and another 30% score in the 600-690 range. In the 700-800 range, the next closest group are those that identify as two or more races at 11%, well under a third of Asians. Even among White test takers, only 8% score in the 700-800 range. It really is amazing. How does this scenario play out when we consider college admissions? To answer that, we look at Figure 4, which shows the counts.

Figure 3: Data from the College Board’s 2026 SAT Suite of Assessments Annual Report.

Because the races constitute a much different number of SAT test takers and the population in general, Figure 4, which is the number of students in each category, looks much different than Figure 3. Even though Asians constitute about 6% of the U.S. population, they dominate the 700-800 category. If you combine African American, Hispanic, Two or More Races, and White, you get only 6,325 more scores above 700 than the Asians. Based on this, one would expect that your top colleges would be about half Asian. Meanwhile, one would expect very few African Americans and Hispanics and even fewer White students than Asian students.

Figure 4: Data from the College Board’s 2026 SAT Suite of Assessments Annual Report.

Moving to the reading/writing portion of the SAT, we have Figures 5 and 6. Here again, Asians excel. 24% of Asian test takers score above 700, while another 33% score from 600 to 690. In fact, the distributions by race in Figure 5 are very similar to those in Figure 3. Still, we’ll look at counts.

Figure 5: Data from the College Board’s 2026 SAT Suite of Assessments Annual Report.

We finish off with the number of students in each score range by race in Figure 6. Here, there are actually more White students in the 700-800 range than Asian students, but again, given that Asians constitute about 6% of the population, it is astonishing they are so close.

Figure 6: Data from the College Board’s 2026 SAT Suite of Assessments Annual Report.

Overall, we see the same type of ranking as usual. Asians do the best, followed in order by White, Hispanic, and African American (College Board naming). Ivy League and elite schools largely pull from the 700-800 students, which is why Asians make up a disproportionate amount. In fact, their percentage in most cases is lower than one might expect based on SAT scores.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS Oct 1, 2026

Thu, 01 Oct 2026 19:01:32 GMT

As I see it . . .

There is no shortage of chatter about grade inflation and the abilities of current students. A college math department is somewhat unique in that it sees a large percentage of students across campus in its classes and a corresponding range of abilities. The writing department likely comes in a close second, but the range of abilities may not be as stark or obvious given the nature of math as being clearly right or wrong.

What is often overlooked in discussions about student performance, or the lack thereof, is the connection to executive functions. Gemini gives an official definition of executive functions as having three core components: working memory, inhibitory control (self-control), and cognitive flexibility (mental set shifting). There are then four higher-order executive functions: planning and prioritization, organization, time management, and self-monitoring (evaluating your own performance in real-time and making adjustments as needed.) These higher-order skills are necessary for academic success and for success in general.

As I see it, the difference between a calculus class and a lower-level math class is not just the ability to do the math but the stark difference in executive function skills. What’s the connection? Gemin tells me this:

The connection between executive function (EF) and academic success is exceptionally strong—in many developmental and educational studies, measures of executive function are even better predictors of early school readiness and long-term academic achievement than IQ.

Interestingly, without asking about math, this came up in Gemini’s response:

Math and STEM Performance: Math relies heavily on multi-step procedural working memory. A single dropped negative sign or forgotten intermediate step often derails an entire calculation, heavily taxing working memory and self-monitoring.
Test Performance: Timed testing environments demand rapid mental shifting, emotional regulation under pressure, and pacing—all direct outputs of prefrontal cortex functioning.

As I’ve been thinking about the issue for some time now, this all seems obvious. The problem I see in higher education is that we aren’t doing anything to improve executive function skills, yet we think we can fix years of not learning math in a semester. Part of Gemini’s respones included:

Crucially, executive functions are malleable. Unlike fixed intellectual markers, these cognitive skills can be developed, strengthened, and supported through structured routines, external scaffolding (like graphic organizers, visual checklists, and broken-down tasks), and meta-cognitive training.

If these skills are malleable, that implies that they can also become worse too. In many ways, I think K-12 and college are not only not improving these skills but also worsening them. In many ways we are allowing students to foster poor executive function skills.

Colleges, at least those that aren’t at the top of the food chain, that want to boost retention and graduation rates would be wise to invest in programming to improve executive function skills, along with across-the-board corresponding classroom expectations. This likely entails educating the faculty on how their role is in improving executive function skills. Lowering expectations and not looking to improve root issues to academic success make higher education more of a fraud than anything, and I would go further and say passing students along and graduating them with poor executive function skills is criminal.

At the end I’ll post what Gemni had to say about classroom strategies to improve executive function skills for those interested.

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The left-right view of the world

This graph comes from the Survey Center on American Life post Young Women Are the Most Likely to Believe that Men Are at the Root of Their Problems. (9/22/2026)

The differences between team D and team R here are stark, especially in the 18-29 age group. How is it that 18-29-year-old Republican women were the second lowest here while the 18-29-year-old Democratic women are by far the highest? This is nuts.

FIRE 2027 Free Speech Report

The graph here from the report refers to speakers you don’t like. I suppose the slight drop here is encouraging, but I still see this as a big problem both in action and in the attitude of students, and it isn’t just a leftist thing, as the report notes:

Finally, for the second year in a row, a majority of students opposed allowing each of the six controversial speakers included in the survey — three liberal and three conservative — to speak on campus.

EIA graph of the week

We’ll just keep using fossil fuels as long as they’re available.

The spinning CD

EF follow-up

For those curious, below is what Gemini gave me about classroom strategies to improve executive function skills. I’m no expert here and just following my curiosity. I can’t say how accurate these statements are, but they seemed worth noting.

Strategies to support and scaffold executive function (EF) generally fall into two categories: external scaffolding (modifying the environment or task to reduce cognitive load) and internal skill-building (teaching students how to manage these processes independently).

Here are practical, evidence-based strategies organized by the specific EF domain they target, followed by general classroom or study frameworks.

1. Scaffolding Working Memory

Because working memory has a strict capacity limit, the goal is to offload mental storage into the external environment.

Externalize Information: Use visual anchors, anchor charts, formula sheets, or step-by-step problem templates so students don’t have to hold instructions and rules in their heads simultaneously.
Chunk Information: Break complex multi-step assignments or directions into single, digestible chunks. Give one step at a time rather than a four-step sequence verbally.
Encourage “Brain Dumps”: Before starting a complex test or essay, have students write down key formulas, dates, or ideas on a scratch pad immediately so they free up working memory “RAM” for the actual problem-solving.
Use Dual-Coding: Combine verbal explanations with visual diagrams or written outlines so information enters through multiple sensory channels.

2. Scaffolding Inhibitory Control & Sustained Attention

Attention and self-control are finite resources that deplete over long periods of cognitive work.

Micro-Breaks & Pacing: Build intentional cognitive rest periods into study sessions or class periods (e.g., the Pomodoro technique: 25 minutes of focus followed by a 5-minute reset).
Friction Reduction (Removing Distractions): Physically remove temptations—put phones in another room, close extra browser tabs, or use noise-canceling headphones.
Self-Talk and “Stop-Think-Act”: Teach students explicit pause routines before diving into a difficult task or reacting to frustration. Naming the friction (”This problem looks frustrating, let’s look at what we do know”) helps bridge the emotional brain and the prefrontal cortex.

3. Scaffolding Cognitive Flexibility

When students get stuck or frustrated by a change in problem style, flexibility helps them pivot.

Error Analysis Routines: Instead of penalizing mistakes, treat them as data. Prompt students to ask: “What assumption did I make here that worked in the last problem but failed in this one?”
Multiple Solution Paths: Encourage students to solve a problem or prove a concept in more than one way. This breaks the rigidity of relying on a single rote algorithm.
Metacognitive Prompts: Use cue cards that ask: “What’s a different way to look at this?” or “If plan A isn’t working, what is plan B?”

4. Supporting Organization, Planning, & Time Management

Higher-order tasks require making invisible timelines visible.

Visual Timers & Time Tracking: Use visual countdown timers (like Time Timer) so students can see time elapsing rather than just reading numbers on a clock, which helps build realistic time-estimation skills.
Backward Mapping: For long-term projects or essays, start at the final deadline and work backward on a calendar, assigning mandatory milestone dates for outlines, rough drafts, and revisions.
Templates and Checklists: Provide standardized layout templates for note-taking (like Cornell notes) or organizing written work to eliminate the cognitive paralysis of staring at a blank page.

Implementation Principle: Fading Scaffolds

The ultimate goal of executive function support is independence. When introducing a new scaffold (like a detailed problem-solving template or a backward-planning calendar), provide high support initially. Over time, gradually fade that support so the student internalizes the routine and builds the neural pathways to do it on their own.

Are you looking to apply these strategies in a specific context—such as designing materials for independent study, managing a classroom environment, or supporting a specific age group?

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Female/Male Time Use

Tue, 29 Sep 2026 19:02:02 GMT

In mid-August the BLS posted Time spent in personal care activities averaged 9.8 hours per day in 2025, including a stacked bar chart of time use for women and men. Stacked bar charts are hard to read, but it got me curious about the supposed narrative of males not doing enough around the house, which falls under the data rule: Doubt something everyone knows is true. Oh, and if the BLS headline has you scratching your head, note that personal care includes sleeping.

Today’s data comes from the BLS America Time Use data portal and is time use for those 18 and over for females and males. The data is the daily average over the entire year, and so, for example, hours worked won’t be 8 or so, as the workweek gets averaged over weekends and days off, plus the data includes people that don’t work or work only part-time.

We start with Figure 1, which is just working hours plus travel for work and housework. Since 2005, males have worked more hours than females and have done less housework, but when you add the two together, males do more overall. This conclusion would seem to be sensible, as if you are working more, you have less time to do housework. Interestingly, the gap here between females and males has narrowed. In 2005, males spent about an hour more per day on housework and work, including travel. By 2025 that gap is now only about half an hour more for males.

Figure 1: Data from the BLS America Time Use data portal.

One curiosity about the time use data is that there is a work category that doesn’t include work-related travel, such as the commute to work. If you want to close the gap between males and females in Figure 1, you might use work only and get Figure 2. This might be one on purpose or simply not realizing that there is a work including travel category. Still, combining work and housework, males do more even if you don’t include traveling for work, which it seems you should.

Figure 2: Data from the BLS America Time Use data portal.

Ok, you say, but we all know that if you add in making and cleaning up after meals along with caring for children, then women certainly do more. Figure 3 would suggest otherwise. It is basically a tie, with some years male slightly higher and other females slightly higher. This seems like simply the noise in the data.

Now, it is the case that women do more childcare and meals, but again, this seems to make sense as they are home more. It isn’t as if working more hours isn’t contributing to the household.

Figure 3: Data from the BLS America Time Use data portal.

Do males really not help out around the house? Figure 4 looks at caring for children, interior and exterior maintenance, repair and decoration, as well as lawn and garden care. If you look at those four categories, it is again a tie with men doing more of the maintenance and lawn care and women doing more childcare.

Figure 4: Data from the BLS America Time Use data portal.

I’ve selected categories that caught my attention and seemed worth comparing. Figure 4 is particularly interesting, as the categories are very different. Childcare is a daily activity, whereas all the maintenance and lawn care are weekend jobs. This makes sense: if men work more, they have less daily time on workdays but make up for it on weekends. Yet, I can see how this can come off as men not holding their own around the house on a daily basis if a lot of their work is done on the weekend.

At the same time, would women want to swap roles here? I don’t think so. I’m guessing they’d rather take care of kids than cut the grass and paint the house. In fact, the roles make sense in that on average men can get physical work done faster than women. From a household efficiency standpoint Figure 4 is what you would expect.

With all this said, time use is going to vary a lot based on where and how one lives. There are no lawns to cut if you live in an apartment and no childcare if you don’t have children. These are averages across the population, but it does suggest that men do and have done their share, but in a different way. I look forward to comments on this one and the inevitable unsubscribe.

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I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS Sept 24, 2026

Thu, 24 Sep 2026 19:02:15 GMT

As I see it . . .

In looking at the PISA scores by country this week, it is clear that achievement is decreasing in almost all countries and that the 10th percentile scores are decreasing faster. Why is the obvious question? One commonality is smartphones and technology use in general. Of course, we don’t know if smartphones are causing some or part of the decline because we don’t have experiments. Defenders of smartphones with just enough statistics knowledge will chant, “Correlation isn’t causation.” True, but. . .

As I see it, one shouldn’t always wait for experiments to prove causation before acting. Instead, consider the related type I and type II errors and their consequences. If the null hypothesis is that smartphones are fine and the alternative is that learning decreases, then what are the possible errors here? A type I error is that I reject the null hypothesis when we shouldn’t. In other words, we conclude that smartphones cause learning harm when they don’t. A type II error occurs when we accept the alternative hypothesis while the null hypothesis is actually true. We conclude that smartphones decrease learning when they don’t. Which one is worse?

Do we ban smartphones in schools or not then? We really want to avoid a type I error which would be leaving smartphones in schools when they are doing harm. A type II error would have us ban smartphones when they weren’t causing a problem. Each error has potential harms. The type I is obvious: decreased learning. In the type II case, we have to ask whether taking smartphones away when they weren’t a problem would have negative consequences. I don’t see any undue harm by taking smartphones out of schools.

In this case, the errors are not symmetric. I really don’t want to make a type I error, and I can live with making a type II error. Banning smartphones in schools is smart policy right now. Beyond learning, there is evidence that smartphones have other downsides. After Babel has a good summary in the post, Are Phone-Free Schools Working? (9/17/2026)

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Better in 1862?

A must-see post from the Library of Congress: School and Family Charts: Nurturing the Perceptive Faculties (Sept 2026).

With the school year off to a solid start, I wanted to use today’s post to highlight some of my favorite items in our popular graphic arts collection: the “School and Family Charts.” Originally released in 1862, this set of twenty-two charts was created by Marcius Willson, a leading textbook author, and N.A. Calkins, the superintendent of New York’s primary schools, and published by Harper & Brothers, known for the popular magazine Harper’s Weekly. The charts must have had lasting appeal, as they were reprinted many times. The Library’s set was copyrighted in 1890.

Here are two (I couldn’t decide on just one) of the eleven charts. Learning materials of this quality seem more inspiring to me than most of what I see today. The LOC post includes commentary about learning and how to use the materials.

Education revenue and spending

Two charts worth knowing from Do Elite Universities Really Need This Much Money? (8/25/2026)

Note here that administrative spending per student for the Ivy League exceeds the total spending of the bottom four institution types by a factor of 2 (ok, not quite 2 for State Flagships).

Rings to roofs

The Rings to Roofs dashboard has an abundance of compelling charts. Here is one of them. The point here is that a reduction in marriage rates changes the demand for housing. Two single people occupy two housing units, whether homes or rentals, whereas a married couple occupies only one. They estimate that returning to 2000 marriage rates would fix 18% of the housing shortage.

An aging world

On the way to population decline, we get a shift in old and young people. The Census Bureau makes the point in their article By 2060, U.S. Population Will Be Younger Than Almost Half the World’s Countries Despite Continued Growth of Older Adults (9/3/2026)

Challenges for an Aging World
The report covers cross-national comparisons on access to healthcare and social care, employment, retirement, volunteering, poverty, living arrangements and other age-related issues.
Among key findings:
Labor Force. Between 2012 and 2022, labor force participation among adults 65 and over fell in high‑income countries but rose in low- and middle-income countries.
Poverty. Among Organisation for Economic Co-operation and Development (OECD) countries in 2020, older adults in the United States (21.6%) and South Korea (40.5%) faced some of the highest poverty rates.
Caregiving. In many OECD countries, 3 out of 5 caregivers age 50 and over were women. Some high-income countries are beginning to compensate older caregivers to offset the health and financial stresses of caregiving.
Volunteering. More than 50% of the older population did volunteer work in the United Kingdom and New Zealand, compared to less than 10% in Ukraine, Guatemala and Cape Verde.

The spinning CD

New from Tape Five. Tape Five is defined as electro swing, and their new album is ok. Still, they deserve more love, so I’m including one of my favorites from a past album, Tonight Josephine! Give both a listen and expand your music range.

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Country PISA Percentile Results

Tue, 22 Sep 2026 19:01:31 GMT

Last week I looked at the 10th percentile, mean, and 90th percentile PISA results for the OECD. Generally speaking, declines at the 10th percentile for reading and math are worse than at the 90th percentile. But means can come about in many ways, so the data rule “know the distribution, not just the mean and median” applies. Today we’ll look at four graphs: the 10th and 90th percentiles for math and reading by country.

In selecting the countries, I went with only those that had data for all PISA years, with two exceptions. The UK didn’t have 2003 data for math or 2000 and 2003 data for reading. The US didn’t have 2006 data for reading. Both are included.

There is a lot that might be said about these graphs overall and specific countries. I’ll provide highlights and look forward to your thoughts in the comments. Let’s go to the data, which comes from the NAEP PISA IDE portal.

Figure 1 starts us off with the 10th percentile for math. For countries above the OECD mean, everyone has declined in the last two cycles, and to some extent, this decline started even earlier. Even the top three countries—Hong Kong, Japan, and Korea—showed declines. A few below did hold or improve a bit, but nothing to write home about. Notice that, for example, the US and Germany are below the OECD 10th percentile mean.

Figure 1

Figure 2 (note that the y-axis scale differs from Figure 1) shows the 90th percentile for math. Notice that Japan and Korea improved in the last two testing cycles, although Japan is still shy of the 2012 pre-smartphone peak. Why is a good question here? They dropped from 2012 to 2015 but are recovering. Do they manage smartphones in the school and at home somehow?

We see a general decline for those above the OECD mean. Indonesia, despite gains at the 10th percentile, easier to do given their low scores; they didn’t manage that at the 90th percentile despite low scores.

Figure 2:

Moving to reading, Figure 3 is the 10th percentile graph. Here we see across-the-board declines since 2012, except for a few low-scoring countries. This evidence goes to my hypothesis that smartphones hurt the low achievers more than the high achievers. I doubt COVID is an issue here, as the declines started sooner and the trend largely continues from 2018 to 2022. The 90th percentile story is different.

Figure 3:

Figure 4 is the 90th percentile for reading. Interestingly, the US is at the top here but barely above the OECD mean in the 10th percentile. There are declines here, but they are less drastic and less consistent.

Figure 4:

What do I think I know? First, Figure 5, which I showed last week, hides the complexity of PISA scores.

Figure 5:

For all the talk about reading issues in the US, the top students are doing as well as ever. I’d like quartiles, not just the 10th and 90th percentiles, but the distribution of scores by country seems to be skewing more toward the bottom. This, to me, is a bigger concern than some lower scores at the top end. Still, scores are decreasing in almost all countries that I’m presenting here, which are mostly OECD countries. I’ll stop here and look forward to other thoughts in the comments.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS Sept 17, 2026

Thu, 17 Sep 2026 19:02:00 GMT

As I see it . . .

Jared Cooney Horvath at Digital Delusions gives two definitions related to using AI that are clarifying.

When experts use a tool to make performance easier, we call this cognitive offloading: and it works because established expertise allows the user to maintain control over the tool.
. . . cognitive outsourcing: when a tool is used to perform the very process a person is meant to be learning.

As I see it, the use of AI, whether in education or business, should be articulated as cognitive offloading or cognitive outsourcing. If the AI is being used for something the person is supposed to learn, cognitive outsourcing, then it shouldn’t be used to complete the task. This is a majority of the education system. Horvath says it well in his article:

Carpenters aren’t better at construction than I am because they can swing a hammer any better than I can. They are better because they deeply understand carpentry – those material, structures, and principles that make swinging a hammer meaningful in the first place.
K-12 does not exist to ensure children know how to operate the tools of today: it exists to ensure that, when confronted with the unpredictable tools of tomorrow, they’ll have something meaningful to do with them.
Operating AI is easy (some might say trivial). Developing the knowledge, judgement, imagination, and expertise required to use it meaningfully is extraordinarily difficult.
That’s the work of education.

I don’t see the matter as simply an issue in education. Do businesses really want to hire new employees, have them do everything with AI, and not learn about their business? That doesn’t seem smart to me, but I can see the allure of quick productivity gains hiding the potential long-term losses in knowledge and later innovation.

This framework helps us think about AI use, but it now requires individuals, educators, and businesses to think carefully and articulate what should be learned and what to cognitively offload or outsource. I don’t see this happening in higher education. I see two camps forming. The first camp believes that AI is the future, and we have to teach students how to use it. This argument seems silly to me, as students are already using it. The other camp believes it should never be used. What I’m not seeing so far is a clear rationale for when, how, and why to use AI. Minimally, as I’ve said before, students should learn how and when to use AI to cognitively offload, in other words, to use AI to be more efficient at what they already know how to do.

One overarching concern I have related to AI and what we should learn is that I think we confuse learning content and gaining skills. I’ll use programming as an example. One can learn programming so they can, well, program. That’s the content. I do think learning programming improves logical thinking skills, attention to detail, and other skills. You can outsource the programming to complete the content part, but you don’t gain the skills. In education and business, the skills gained from learning a task are as important, if not more so, than the content. I’d argue the more skills you gain throughout life, the more you can learn and adapt to the “unpredictable tools of tomorrow.”

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Let’s go to some data.

How hot was Aug 2026?

August 2026 was a record for the month and will likely be officially classified as an El Niño month. If you are curious about ENSO classification, you can read this from NOAA.

Here is the long-term trend. Note that Aug 2026 is one of the higher historical anomalies. As El Niño gets going, we should expect a round of record anomalies in the coming months.

The NOAA page for Aug 2026 has this fun graphic; actually, they’ve always had them, I just decided to add it here.

This is why data is important

The paper (hat tip to the Nuzzo letter), A Dramatic Underestimate of the Performance Gap Between Elite Male and Female Athletes (Nov 2025), illustrates an important fact, and it isn’t the difference between males and females but how common “knowledge” can be so off. Here is the key chart.

Participants were asked for the male age that matches the world record for professional women in the events shown in the figure. About 5% got it right. In most cases, about 70% were off by at least 4 years. A quarter or more were off by at least 9 years.

This study included only 300 participants: “A sample of 300 adults was obtained from the company Prolific, an opt-in platform for participants who complete studies in return for payment.” Thus it is a small study that may not be representative of the U.S. population based on the survey methods.

Still, this illustrates a key point. We look at data because quite often our views or “facts” about the world are wrong, and we are basing our options, our voting choices, and policy on incorrect information. This behavior isn’t purposeful; we are all shaped by the world around us, but we could be more critical of what we think we know. A good use of AI is to do quick checks on what we think is true, although AI isn’t foolproof either.

If you are curious, here are the record times.

Ignoring men

Climate change is warming the planet, and working in extreme heat for outdoor workers is and will be more of an issue. So, good on American Inequality for writing the article No Right to Shade: How Extreme Heat Falls on America’s Workers (8/19/2026). Now, this is all they say about who these workers are:

Farmworkers, construction crews, postal workers, roofers, and delivery drivers are disproportionately Latino and immigrant, and a significant share are undocumented or working on temporary visas. That status shapes everything about how heat risk lands on migrant and immigrant farmworkers. Workers who fear retaliation, job loss, or immigration enforcement are far less likely to report a missed water break or push back on an unsafe pace, even when they recognize the early signs of heat illness in themselves or a coworker. Piece-rate pay (where more work means more money), common in agriculture, adds its own pressure: workers are paid by the bucket or the row, not the hour, which quietly punishes anyone who stops to rest or drink water.

Let me help a bit using the same source they use. (DAFW is days away from work.) That’s 80% males. If it were 80% females, I’m sure we’d hear about that. This type of bias doesn’t help credibility. It also doesn’t help build a coalition to support your cause.

I also have to point out this complete chart fail in the article. Three issues. The graph is just stuck in the article and not referenced. The second is the data rule: Normalize properly; ask, “Per what?” Don’t compare raw counts; this should be a percentage of workers, or better workers in occupations impacted by heat. If you can’t do that, please at least mention it. The bet is that there are more workers, so the percentage is going down, not up. Finally, the 38% in the title is highly misleading unless you actually look at the graph. That 38% is almost all from 2020 to 2023. The last four years have been flat. Did climate change stop? Say something about what is or might be going on here.

On marriage

From the IFS (8/21/2026).

Because married adults consistently report being happier than their unmarried peers, the sheer number of young men forgoing marriage could be adding to the happiness crash now unfolding among young adults across America.

The spinning CD

A cover by Tape Five.

LOC - Today in History

https://www.loc.gov/collections/today-in-history

Nasa visualization studio

https://svs.gsfc.nasa.gov/

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PISA Results

Tue, 15 Sep 2026 19:01:53 GMT

The buzz this past week or so has been the new 2025 PISA data. You might have come across Figure 1, which is from the OECD Summary page. Note that this is OECD-23, not the full 38. The 23 are the long-standing members, but when you scroll over the image, the U.S. isn’t on the list. My main issue goes to my data rule “know the distribution, not just the mean and median.”

Figure 1: From the OECD Summary page.

If you are a regular reader, you know that the lower percentiles in NAEP 12th grade reading and math scores in the U.S. have declined faster. The NAEP PISA IDE portal includes the 10th and 90th percentiles, and so let’s look at those.

First up is math in Figure 2, which shows the results for the full OECD. For reference, a standard deviation in PISA scores is 100. Since 2018 the 90th percentile dropped 17 points, while the 10th percentile dropped 27 points, or a 62% larger drop, while the man dropped 24 points. The drop at the lower end of scores is influencing the mean, although it isn’t dramatic. Still, this makes the mean in Figure 1 a little misleading.

We shouldn’t ignore the steady decline since 2003, with a 10-point drop from 2003 to 2018 for the 10th percentile and a 17-point drop for the 90th percentile.

It is worth noting that the 2013 smartphone date doesn’t appear to be the beginning of a decline. In the U.S. NAEP scores, the lower percentile result showed this. Here the drop is only a few points from 2012 to 2018.

What about reading?

Figure 2. Data from the NAEP PISA IDE portal.

Figure 3 is more compelling. The 10th percentile shows a clearer drop starting with 2012. The drop from 2012 to 2025 is 43 points, almost half a standard deviation. The 90th percentile doesn’t start dropping until 2015, with a drop of 22 points from 2015 to 2025. Something different seems to be happening at the bottom and top end that doesn’t show up if you just look at the mean. This is similar to the U.S. NAEP reading and math scores.

Figure 3: Data from the NAEP PISA IDE portal.

My working hypothesis is that the smartphone generally has a greater impact on the lower-performing students that might be starting to catch up to the top end, although I’m open to other reasons for the decline since 2018. I ruled out COVID when looking at the NAEP U.S. scores. This is aggregate data across countries, and there may be differences between countries that hide trends. Next week I’ll look at some country-level data.

Note: I gave up on the science scores, as the NAEP PISA IDE portal was abysmally slow.

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I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

Classroom Connections Sept 12, 2026

Sat, 12 Sep 2026 10:05:14 GMT

Classroom connections are less about immediate application and more about me pointing out resources. I believe that there is a lot of amazing math, statistics, and data out there that might be used in math classrooms and is also intriguing to the curious. Simultaneously, when someone inquires about the applications of math, consider these numerous examples.

Some of these examples may require some effort to be classroom-ready, and some of the material has appeared in previous QTRS posts. I’m ordering the content roughly based on the level of math. Please tell me if you or someone you know uses any of these suggestions in the classroom or has a relevant idea (email me at thomas.pfaff@sustainabilitymath.org). I encourage you to leave a comment, as your feedback motivates me to continue this work, or send me an email if you find these classroom connection posts useful. Similarly, if you have an opinion or concept that is relevant, please share it in the comments. Please share, like, subscribe, and comment.

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Resources

Podcast: The Recent Chalk and Talk, Math Fact Crisis, Two Years Later with Brian Poncy (8/28/2026), is an excellent listen:

In this episode, Anna is joined by returning guest Dr. Brian Poncy to discuss math fact fluency and whether improving students’ fluency with basic number operations leads to better overall math achievement.

Materials for the Facts on Fire mentioned in the podcast. In general, Chalk and Talk episodes are valuable for anyone teaching math or related subjects.

Data: I’ve been adding real-world data sets to my Teaching Real Data repository. You can sort the data by potential uses, and I’ve incorporated notes and metadata.

Animations: I’ve posted my statistics animations in one location and my calculus animations.

If you have statistics or calculus animation ideas, then let me know.

Two recent books worth reading: Instructional Illusions (Sept 2025) and Digital Delusions (Dec 2025).

Census Bureau

The Census Bureau’s Statistics in Schools continually adds new material. They include data, activities, and teacher notes.

5-minute population pyramid activities.

TigerWeb

The TIGERweb, TIGERweb Decennial, and TIGERweb Economic Census web-based applications allow the users to visualize our TIGER (Topologically Integrated Geographic Encoding and Referencing database) data. The applications allow users to select features and view their attributes, to search for features by name or geocode, and to identify features by selecting them from a map. The TIGERweb, TIGERweb Decennial, and TIGERweb Economic Census applications provide a simple way to view our TIGER data without having to download the data.

Census Infographics & Visualizations “Explore Census data with infographics and visualizations covering a broad range of topics.” Graphics can be sorted by topic and are updated regularly. Great for QL courses and other areas that want to add some data to their courses. Here is one from 9/10/2026.

Basic graphs to modeling

The BLS article What makes a job better? Survey evidence from job changers has a range of uses.

This article uses Survey of Household Economics and Decisionmaking (SHED) data to explore the role of changes in job characteristics in determining self-assessed job quality. The analysis includes individuals who started a new job between 2021 and 2023. We determine that changes in pay and benefits alone incorrectly predict self-assessed changes in overall job quality 30 percent of the time.

Interpreting charts such as this one:

Interpreting correlations

Modeling or inspiring students to learn math to understand all this.

Geometry?

I’m not sure where one might use this two-part series from the Library of Congress Engineering a Way for Fish (3/19/2026) and Cross-Cutting Concepts in Conservation: Implementing a Way for Fish (5/7/2026), but it is interesting enough to mention. A few teasers.

Invite students to explore the engineering design of one example of a fishway, a fish ladder, through careful observation of the top-view schematic below.

Print copies of the image for students and ask them to share what they see. What shapes do they notice? What patterns stand out? Ask them to label the dam and the fish ladder and determine the direction of river flow. Engineers often curve dams toward the current to increase structural strength.
Next, ask students to trace where fish would enter the fishway when migrating upstream and where they would enter when moving downstream. Direct attention to the overall “V” shape of the ladder. Why might engineers use angled or stepped designs?
Pair the schematic with a historical photograph of the fish ladder. What new questions do students have?

Statistics

The paper Climate Change Impacts on the Phenology of Laurentian Great Lakes Fishes (8/19/2025) has numerous statistically interpretable data for basic stats courses. The graph here (Figure 4a) makes sense without the caption, for example.

First, we found that typically the majority of species were arriving earlier year over year, consistent with the rising water temperatures (Figure 4a). For example, both northern pike and yellow perch had a shift toward earlier arrivals throughout the study period (Figure 4a). There were a few exceptions; for instance, bigmouth buffalo and freshwater drum (both native) and white perch (non-native) arrived later toward the last few years of the study (Figure 4a).

Example of reported statistics.

Overall, the predicted first Julian day of native fishes was earlier over time by over 10 days across the study period (Figure 4c). The interaction between the arrival of non-native species and year was significant (F = 3.33 and p = 0.04), whereby the predicted Julian day was earlier across years, which was in alignment with the warming water temperatures (Figure 4c).

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS Aug 10, 2026

Thu, 10 Sep 2026 19:01:07 GMT

As I see it . . .

I’ll start off by noting that today’s rant is more me thinking out loud than anything else. Take it for what it’s worth.

I’ll start by saying that I take all student behavior that faculty find perplexing as the result of an educational system that allowed or even encouraged such behavior. It isn’t the fault of the student.

Now, I would argue that I can put a pile of math homework in front of someone who doesn’t know math, and they could do a reasonable job of ordering the homework based on grades in the class.

It would be easier if I could just show a few pictures, but I can’t do that. So, imagine we have homework done on a clean piece of paper, no frills or wrinkles, and the problems ordered nicely down the page. Imagine another homework assignment torn out of the spiral notebook, with frills and wrinkles, problems partially labelled and unclear, and problems scattered across the page. One suggests that care was put into the work, and the other not so much. One suggests careful thought about work, and the other not so much. This is not an issue of handwriting but one of how much thought, order, and effort were put into the work. Why the difference?

As I see it, the difference here isn’t one of cognitive ability, IQ for short, but one of learned behavior. In some instances, the student really just doesn’t care, but in plenty they care, and they have been allowed to do shoddy work. For example, they often do things in a rushed, last-minute way and struggle to stay organized. I would argue that at least some of this behavior is the fault of the educational system and doesn’t promote executive functions.

In my 25 years, I’ve seen a continued lowering of expectations somewhat accelerated by COVID and issues of mental health. Homework deadlines are flexible—so flexible that some faculty will accept a semester’s worth of homework in the last week of class. We aren’t going to fight with students to submit organized homework; hey at least they did it. I assume, but I don’t know, that at least some high schools function the same way.

I don’t think this “flexibility” is helping students. Education is about content, but it is also about developing useful skills and positive habits; the latter two also help with learning content.

I think we need a better understanding of what actually helps students develop executive function and what acceptable flexibility doesn’t lead to bad habits. My take is that our current flexibility is doing more harm than good. Let me know your thoughts in the comments.

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More on coal

One comment I received about the coal post on Tuesday was that without regulation and the environmental movement, the U.S. would be burning much more coal. Take it for what it is worth, but Gemini had this to say:

Economic research from energy economists and the U.S. Energy Information Administration (EIA) generally attributes roughly 70–80% of coal's decline to market forces (primarily cheap gas) and 20–30% to environmental regulations and policy.

I’ll put this issue on my to-do list to try to understand this dynamic better and to see if it is true, but I thought it was worth noting.

Data center update

From Our World in Data. (9/1/2026)

Natural gas exports

From the EIA (9/1/2026). A reader commented on the relationship between natural gas and coal. One part of that puzzle is what the U.S. is exporting. Europe has targets to get rid of all coal plants, but that would be harder without LNG imports from the U.S.

U.S. Pipelines

One of the things that make coal attractive for lower-income companies is the need for less infrastructure. Trucks and trains can move coal around. Gas and liquids are better with pipelines, and here is how many liquid pipeline projects the U.S. has completed in the last 15 years from the EIA.

The article doesn’t give the miles of pipelines, but here is one example they note:

Enterprise’s 550-mile, 600,000 barrel per day (b/d) natural gas liquids (NGL) pipeline originates in West Texas from the Delaware and Midland basins and connects to Enterprise’s fractionation complex in Chambers County in Texas.

On the natural gas front we have this graph again from the EIA.

As an aside, I often get curious when writing, and what was supposed to be something short ends up a little longer. One more graph here is a map of all pipelines in the U.S. from the National Pipeline Mapping System (NPMS). At the link the map is interactive, and you can zoom in on areas. I’d like this map animated where it shows the pipelines added each year.

Smartphone use

Fun fact: I don’t and never had a cell phone or smartphone. Two graphs from the Pew article About half of Americans say they spend too much time on their smartphone (9/1/2026) that suggest I’m the sane one.

One positive here is that at least the 18-29 group seems to know they are spending far too much time on phones. Can they or will they change behaviors?

The impact on sleep here is particularly serious. I think the negative of the smartphone outweighs any positives, although maybe at this point if I got one, I’d have a better sense of how to use it.

The spinning CD

Every now and then I run into a song I hadn’t heard in a long time and am reminded of how good it was. You get a classic today

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Coal Consumption

Tue, 08 Sep 2026 19:01:06 GMT

Sometimes I’m not sure what makes me choose what data to explore in any given week. This is one of those weeks. Why coal? I’m not sure, but with the talk of super El Niño leading to climate change, coal consumption got into my head. Coal is a big contributor to atmospheric CO₂. We’ll look at coal consumption going back to 1965 through 2025 with data from the Energy Institute. Let’s go to the data.

Figure 1 is the total coal consumption for the world in exajoules. Three observations. Coal consumption increased again in 2025. The impact of Covid is seen in the graph. Coal consumption increased from 95 exajoules in 1999 to 161 exajoules in 2013, a 70% increase. The natural question is how? Was this a bunch of countries increasing consumption or just a few?

Figure 2: Data from the Energy Institute.

Figure 2 groups countries according to their OECD membership (Organisation for Economic Co-operation and Development—a group of 38 advanced, high-income countries). OECD countries’ coal use flattened by 1990 and has been decreasing since 2008. This trend isn’t entirely surprising. Coal is the easiest source of energy to get started with for lower-income countries. Still, the non-OECD countries increased their coal consumption starting in 2000 and now use almost three times as much as the OECD countries ever did. Keep in mind this is total use, no per capita.

Figure 2: Data from the Energy Institute.

Dialing down further, Figure 2 looks at coal consumption by region. In 2025, almost all of the coal consumption is from the Asia Pacific. The increase in coal consumption starting around 2000 is entirely in the Asia Pacific, even as other regions have decreased their coal use. The other regions have been decreasing or have increased by negligable amounts. One more step.

Figure 3: Data from the Energy Institute.

In 2025, China and India accounted for 83% of South Asia’s coal consumption and 70% of the world’s consumption. The majority of the world’s growth that began in 2000 is from China, with some help from India. Figure 4 has these two countries plus the U.S. for context. The rest of the world could completely stop using coal, but if China and India don’t, we would only drop from 166 exojoules to 115 exojoules. Also note that what the U.S. does relative to coal consumption really doesn’t matter much.

Figure 4: Data from the Energy Institute.

No big conclusions here. I really just become curious about something and dig through the data until I understand it well. I don’t see China and India dropping consumption anytime soon, and while the narrative about all the solar panels in China is nice, anyone who talks about that without mentioning China’s coal use isn’t being honest.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS Sept 3, 2026

Thu, 03 Sep 2026 19:02:10 GMT

As I see it . . .

What got my attention that led to the post on Tuesday is this from the Atlantic article Is the College Backlash a Mirage?

Despite the reported skepticism of higher education, enrollment in four-year colleges and universities is growing. These institutions awarded 2 million bachelor’s degrees in 2023, compared with 1.6 million in 2010, and the fraction of 25-year-olds with a bachelor’s degree has steadily increased for the past 15 years.

As I noted on Tuesday, the number of degrees conferred is not the correct metric to demonstrate that enrollment is growing. To decide whether there is college backlash or not, you need to look at the percentage of high school graduates that go to college, as I did in the post.

As I continually come across misuse of data in the media, I wonder why this happens. One explanation is that it is purposefully misleading. It may be that the author here knows full well that what they are saying is not only incorrect but also effectively misinformation, which is ironic as a place like The Atlantic is very much against misinformation. This reasoning would suggest that the editor is in on it too. I tend to, but not always, believe this isn’t the explanation. I think there are two key factors involved.

First is that the average journalist has little data training. Maybe they have something along the lines of a first-year introductory statistics course, which isn’t much. Thinking in terms of data, one might say critical data thinking skills, takes more than just a course and include curiosity and habits to think beyond surface data that develop over time.

Second, they are activists first, not analysts. The author likely thinks very favorably about higher education. They came across the number of degrees conferred, which confirms their priors, and you get the article (full disclosure: I couldn’t read the full article, so maybe something better was done, but either way the second paragraph shouldn’t be so wrong). No critical thinking necessary; another bit of irony as those with degrees are convinced they are great critical thinkers.

As I see it, this isn’t just some pet peeve of mine but a serious problem with journalism. Articles like the one in The Atlantic either erode trust or, more likely, simply confirm what readers want to hear. All this type of journalism does is split people into camps.

Worse, you can’t solve problems you don’t know exist. It is all too simple to read the headline and a couple of paragraphs of the article and come away thinking there is no college problem and ignore the “backlash.” That would be a mistake.

First, as I noted in my post, the percentage of high school students going to four-year colleges dropped noticeably from 2023 to 2024. This could just be noise, but it is enough to make one pause. We’ll have to wait to see the 2025 data, but the “backlash” could be real; the data leaves that open.

Second, the “backlash” makes it take some time to show up in the data. Students already in the college pipeline in high school won’t change course easily. But students starting high school might decide on a different path. It will also take time for high school to offer other paths. Big systems and culture change slowly at first.

Lastly, the “backlash” may well open the doors to other forms of credentialism, which is a big part of the market colleges have cornered. It takes time to develop such systems, but if entrepreneurs see an opening, they are more likely to put effort into disrupting higher education. I can see a company developing proctored tests, like the SAT or AP exams, for people to demonstrate they have skills and knowledge without going to college.

The point here is, wishing away a problem with misused data, such as the Atlantic article, does the left no good. In this case, the misleading use of data is frustrating, and journalism needs to do better (I won’t hold my breath). At the same time, the topic also frustrated me. I do believe higher education is important and can be valuable, but it isn’t at its best at the moment. Let’s not pretend otherwise.

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Let’s go to some data.

Read of the week

If you are interested in the grid and the impact of solar and wind, read If Grid Utilization is Good, Wind and Solar Are Bad. Wind and solar advocates say we need to use the grid more efficiently—their own plans would do the opposite (8/29/2026) from the Energy Bad Boys on Substack.

The short version, I think, is that building up the grid to add solar and wind lowers grid utilization, which increases electricity prices. The analogy I’m working with is that a factor used only 40 hours a week produces a more expensive product than one used 24/7. That’s why there are night shifts at factories. Here is a key graph.

As a side note: Higher education’s utilization rate is really low.

Research surprise of the week

I talk about adapting to climate change, as so far we are doing nothing to stop it, but I’m not sure how we end up adapting to this (thanks JH): Scientists detect a surprising shift in human blood as atmospheric CO₂ rises (8/15/2026)

Rising carbon dioxide in the atmosphere may be leaving a measurable imprint inside the human body. Researchers analyzing more than two decades of U.S. health data found that blood bicarbonate levels have climbed about 7% since 1999, while calcium and phosphorus have declined—changes that closely track increasing atmospheric CO2.

The research uses NHANES data, which I’m familiar with and have used, lending extra credibility to the results for me. I’m now on the lookout for reports of physiological changes in humans and animals that might be linked to rising CO₂.

Graph of the week

I haven’t done one of these in a while, and I always wonder if folks appreciate this as I do. This one is from the paper Diffuse and regionally structured domestication of the common fig (Ficus carica L.) in the Mediterranean Basin (4/2/2026) in the journal Horticultural Research.

Caption:

Population genetic structure in cultivated and spontaneous fig trees. Population genetic structure inferred with STRUCTURE at K = 4 based on 14 nuclear SSR markers in 949 individuals sampled across 14 countries, including F. carica, F. carica subsp. rupestris, and F. colchica. (a) Relative average membership coefficient per sampling site to each genetic cluster. White-bordered pie charts denote spontaneous figs (sp), and black-bordered pie charts denote cultivated figs (cv). Pie wedges represent the mean proportion of ancestry assigned to each STRUCTURE cluster within a site. (b) STRUCTURE bar plot showing individual membership coefficients inferred at K = 4. Each vertical bar represents a single fig tree, and colors correspond to the inferred genetic clusters.

EV data

From the World Population Review Newsletter (9/3/2026). First up is a graph of the percentage of EVs on the road.

I appreciate that they note:

Worth sitting with: the gap between "leading the sales charts" and "actually replacing the fleet" is enormous—it takes years for high sales shares to translate into a meaningfully electrified stock of cars already on the road.

What they don’t mention is that Norway spent some of its oil revenue to heavily subsidize EVs in a way that most countries can’t. That is why they are tops in the next graph:

These are good sales, but if you want an all-or-mostly all-electric fleet, and the article doesn’t clearly distinguish the type of EV, you have to sell more than 30% EVs. For example, the mean age of a U.S. car is almost 13 years. If EVs were 100% of sales, it would take more than 13 years to have an all-electric fleet.

The spinning CD

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Is the College Backlash a Mirage?

Tue, 01 Sep 2026 19:00:26 GMT

I don’t have a subscription to The Atlantic, but I can read the first two paragraphs of the article The College Backlash Is a Mirage: Americans are more pessimistic than ever about the value of a degree—but enrollment keeps going up, and that is all I need. Here is the second paragraph.

If you were to judge, instead, by the choices that Americans are actually making, you might draw a different conclusion. Despite the reported skepticism of higher education, enrollment in four-year colleges and universities is growing. These institutions awarded 2 million bachelor’s degrees in 2023, compared with 1.6 million in 2010, and the fraction of 25-year-olds with a bachelor’s degree has steadily increased for the past 15 years. Even as Americans tell pollsters that college isn’t worth it, their behavior suggests that they still recognize the value of a degree for themselves and their children. And they’re correct to do so.

Before we get to the data, let’s deal with a little logic. The number of bachelor’s degrees awarded is not evidence that “enrollment in four-year colleges and universities is growing.” Anyone paying attention to higher education knows that grade inflation is real and that colleges have a strong desire to retain students in order to pay their bills. This means they graduate a higher percentage of students. Worse, comparing 2010 to 2023 (last year in the NCES data) hides some inconvenient facts.

Let’s go to the data and look into degrees conferred, enrollment, and the metric that really matters (skip to the end if you can’t wait). The data is from the National Center for Education Statistics.

Figure 1 is the number of degrees conferred. The Atlantic article refers only to four-year schools, but I added in the work done at two-year colleges. Yes, the number of bachelor’s degrees awarded in 2023 is more than in 2010 but has also gone down three years in a row. I’m not sure why 2010 is the comparison year. Why not 2000, as that is the year the degrees conferred started growing? Either way, if your metric for people valuing college is degrees conferred, which makes no sense, you have to explain why the three-year drop, which actually would imply, based on the authors’ flawed logic, that enrollment started to drop four years before 2021 or 2017. Of course, some of this drop might be due to COVID, but you can’t just pretend it doesn’t exist, I suppose, unless you are an Atlantic author.

Figure 1: Data from the National Center for Education Statistics table 318.40.

Two more points on Figure 1. It is interesting that two-year degrees have been flat since 2010. I was also concerned that the data in Figure 1 contains for-profit colleges, and maybe that has some impact. This question gets you Figure 2, which removes for-profit college graduates.

The pattern for four-year degrees doesn’t change, but for two-year degrees it does. Two-year degrees without for-profit colleges increased, which means the for-profit two-year degrees decreased.

Figure 2: Data from the National Center for Education Statistics table 318.40.

We already know that the Atlantic article must be nonsense. Not only is the logic flawed, but they also ignore a decrease in the number of degrees conferred. But why not look at actual enrollment data? The NCES has that data, and you can see it in Figure 3.

Ah, since 2010, four-year college enrollment has been flat. Growth stopped in 2010, dropped in 2020 due to COVID, and only grew a little in 2023. Well, that doesn’t fit the article’s narrative, and so it makes sense to just ignore it, at least in the first two paragraphs; maybe they bring it up later in the article. Regardless, if you are going to tell me enrollment is growing, then you should give me enrollment data; when you don’t, I figure you are trying to deceive me.

Figure 3: Data from the National Center for Education Statistics table 303.70.

It is worth pointing out that since 2010, while four-year college enrollment was flat, two-year college enrollment was growing. I would say that this trend is an argument that America has lost some faith in the four-year degree. Those students could have chosen to go to four-year colleges and didn’t for whatever reason; cost is likely one of them.

Still, enrollment isn’t exactly evidence that America has lost faith in college. Consider the data rule: Normalize properly; ask, “Per what?” The metric we need is the percentage of high school graduates that chose to go to college. College enrollment is dependent on the pool of those that graduate high school. This isn’t perfect, as folks can enter college at a later stage in life, but it’s a good indicator. The NCES has this data, and it is in Figure 4.

The NCES didn’t start collecting data separately for 2- and 4-year colleges until 2013. Since 2013, the percentage of high school students attending a four-year college has remained flat, with a noticeable drop from 2023 to 2024 landing lower than any year in the short history of that data. Is this drop a sign of the start of something or normal variation? We’ll see, but it certainly doesn’t suggest that higher education is getting a ringing endorsement, and saying “enrollment in four-year colleges and universities is growing” to suggest that demand for college is up is simply wrong. It would be fair to say that despite the pessimism about college, the percentage of high school graduates going to four-year colleges has been stable, although the 2024 data is concerning.

Figure 4: Data from the National Center for Education Statistics table 302.20.

The drop in the total percentage starting in 2018 is due to two-year colleges. The drop there is noticeable and suggests some loss in faith in the two-year degree, although the economy has greater influence there. If there are jobs, it is easy to do that and then get a two-year degree.

The verdict. It would be generous to call the Atlantic article misleading. It really is just BS. The writer is a higher education supporter and wants to write something positive. The thing is, enrollment really isn’t up at four-year colleges, and degrees conferred have actually been down for three years. The positive is that the percentage going to a four-year college is flat, but there’s a concerning drop in 2024 that reaches the lowest value in the data, suggesting the pessimism narrative may be having an impact. None of this is so bad that we can say society has given up on higher education. At the same time, none of this is a ringing endorsement either. Will the pessimism result in another decline in the percentage attending? If so, the pessimism may have real consequences. If not, and it ticks up, then we basically have the status quo, which suggests the pessimistic narrative is having no effect.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

Animating Age of Death Scenarios

Tue, 25 Aug 2026 19:03:38 GMT

In last week’s post you got the best estimate for your expected age of death, but the SSA has an optimistic and pessimistic scenario. We need to explore those cases, and to up my game a bit, I created two animations: one for females and one for males. For those interested, the R file that creates the animations is posted on my GitHub site, and the links to the data can be found in the R code. Let’s go to the data.

Figure 1: Data from the SSA.

Figure one is the female expected age of death given an age in the associated year. All three scenarios are presented. First, note that life expectancy goes up, even in the pessimistic case. I have three key observations, but you may have others so leave them in the comments

The differences are large. Consider age 60. In the optimistic scenario, the expected age of death for females reaches well over 95, while the pessimistic scenario is about 8 years lower.
Watch the kink from age 0 to 1. The steeper the slope, the more one gains in life expectancy from getting through that year. Historically getting to age 1 was a big deal. In 1900, females had a 12% chance of dying before age 1, while in the optimistic case in 2100, that reduces to 0.0471%. For the optimistic scenario, age 0 to 1 becomes essentially flat. The expectations appear to be real improvements in infant mortality over the pessimistic scenario, which still has that kink in the curve.
The age of death curve for the optimistic scenarios becomes essentially flat from age 0 to about 70. Historically, we gained on the age of death for every year we lived, but in the future, death rates will be decreasing. For example, in 1900, a 10-year-old female had a 0.26% chance of dying before age 11. In 2100, the optimistic scenario sees this rate drop to 0.0075%. That’s what the flattening of the line shows. Note that as one gets older, death rates go up, and getting through a year raises your expected age of death.

Figure 2 is the same graph but for males. The observations above hold for this graph. The one observation I note is that for the optimistic scenario the male age of death is very close to that for females at birth, whereas for the best estimate there is still a noticeable gap at birth of a few years.

Figure 2: Data from the SSA.

One final observation is that animations are useful for how things change over time. Notice how the lines rise faster from about 1900 to 1950 and then slow even more as we approach 2100. These projections show how much progress occurred in the early 20th century and that life expectancy progress is slowing.

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Bio

I am a tenured mathematics professor at Ithaca College (PhD in Math: Stochastic Processes, MS in Applied Statistics, MS in Math, BS in Math, BS in Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations, and I’m open to job offers (a full vita is available on my faculty page).

QTRS August 20, 2026

Thu, 20 Aug 2026 19:01:40 GMT

As I see it . . .

Last week’s QTRS started a short discussion with readers gregvp and jk in the comments. If you are interested in AI issues, it is worth checking out. After that discussion I’m going to amend my thoughts on AI and education. Generally, I think AI shouldn’t be allowed in most courses, but there should be a senior-level course on using AI in your discipline. This is still, in my mind, the easiest and most doable approach at the moment, but not necessarily the best.

A deeper policy would really start to examine the purpose of courses, especially required courses for a major. Let me provide a couple of examples.

A student who is not a comp sci major is required to take a one-semester programming course. Why? Do they just need to learn some programming for short programming tasks in the major? If so, maybe they just need a vibe coding class, but that is a completely unique course and not a prerequisite for further courses in programming.

What if this course requirement is actually intended to build logical thinking skills and attention to detail and is less about the programming skills? In other words, the focus is less on the content and more on the skills developed while learning the content. If so, it shouldn’t be using AI.

As another example, I teach 100-level introductory statistics courses that other majors require. In my courses, students have to learn R. Students aren’t always happy about these requirements. I’m well aware that the majority of the students won’t ever use R again. My point in using it, beyond the fact that you really should learn some software to do statistics if you are required to take a statistics course, is that students improve their skills during the learning process.

As I see it, this distinction between skills learned during a course and the content is ignored. This issue is largely due to the focus on student learning outcomes pushed by accreditation. Worse, it is often the case that majors require courses outside the department but then never use the content in their courses.

From my math department perspective, this happens for statistics and calculus courses. How do I know they don’t get used? Well, some departments list a math requirement as either statistics or calculus, and neither is a prerequisite to future courses. In other words, courses don’t require it, and since students have one or the other, a future class won’t have a common background to build on. Some students will have statistics and some calculus. Beyond this, a single course in programming, statistics, or calculus isn’t enough to do much with the content.

I would argue that content is more easily forgotten than skills. I would argue that over four years of college, students should gain numerous skills, including time management, attention to detail, reading comprehension, etc., and that these skills are developed in different courses with different content. In fact, in last week’s QTRS, I included a chart listing the skills required for various occupations.

This doesn’t mean content is unimportant, but we need to think more carefully about what students acquire not from one course but from the collection of courses they take. If a student takes a course for content, then they should use that content in other courses. In some cases, maybe AI is used, such as for simple programming. If this isn’t the case, then maybe the skills developed are more important than the content. In these cases, AI shouldn’t be used.

The problem with all this is that it requires much more careful consideration of the role of courses and how they connect to other courses and programs. Professional programs do this type of work on some level, but liberal arts programs do little, and they need it. My cynical bet is that none of these changes will happen and AI will be used in a haphazard fashion throughout courses and programs.

One last point from the comments discussion. People in higher ed really need to talk more with those in industry to figure out what they are doing with AI. The comments from gregvp and jk included some interesting ideas that I certainly hadn’t thought of.

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More bad pr for EVs

The problem with the article They were told to park outside. Then their cars burst into flames (8/17/2026) by the Washington Post, but it doesn’t say which types of cars are more likely to combust. This is why they are told to park outside: so that when they do catch fire, they don’t burn down buildings. Let’s start with the chart of the total number of recalls.

It’s easy to assume all these recalls are for EVs, since the issue is electronics. Gemini provided me with this table to clarify the issue:

The problem isn’t with BEVs. ICE cars have some problems, but the big issue is with hybrids. I call this a PR problem for electric vehicles because hybrids are the best-selling of the electric versions. Here is data from the EIA.

My bet is that this problem will dissuade people from buying hybrids or EVs for two reasons. First, they will equate the problem with electric vehicles in general. Second, they brought a hybrid as a compromise and will move back to ICE instead of moving to an EV. Of course, these problems will get resolved, but it will be a setback for hybrids.

The value of oil

Here is a graph from Our World in Data (8/18/2026) and a question. Should Guyana have stayed a low-income country and not developed its oil resources? I don’t see how any country would make that decision.

You might reasonably ask if only a few are enjoying the riches in Guyana. Here is what Our World in Data has to say.

It’s too early to see the full effects of this, and hard to measure how far the oil boom has translated into better living standards in the country. Official poverty estimates, for example, have not been published since production began. But there is early evidence of the government channeling oil revenue toward citizens, for instance, through cash grants for every adult, free tuition at public universities, and increasing health spending.

Oil has been good for the people of Guyana. Just like it has been good to other countries, such as Norway.

Natural gas record for U.S.

This graph from the EIA speaks for itself. Just like Guyana and everyone else in the world, we will use fossil fuels because they are so valuable.

The spinning CD

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