There is now a new page that contains animations for concepts related to statistics and calculus. They are not sustainability related, but since I post materials for calculus and statistics and I have been playing with R, I decided to post these. There are 19 topics covered with 36 animations. In particular, if you teach calculus or statistics these animations may be helpful. So, go to the Animations page and take a look.

## Urban/Rural Red/Blue?

FiveThirtyEight has the interesting graph copied here from their article How Urban or Rural is Your State? And What Does That Mean For The 2020 Election? by Nathaniel Rakich (4/14/2020). How did they measure urbanization?

Essentially, we calculated the average number of people living within a five-mile radius of every census tract and took the natural logarithm to create an “urbanization index,” or a calculation of how urban or rural a given area is.

The article has a table of data that goes with the graph and they look at the 2020 election if urbanization dictated the outcome.

## What are people’s view of C-19?

The Pew article Worries About Coronavirus Surge, as Most Americans Expect a Recession – or Worse (3/26/2020) reports the results from a survey related to COVID-19. Most of it is not too surprising:

There is broad public agreement that the nation is confronting a crisis. Two-thirds of Americans – including majorities in all major demographic and partisan groups – say COVID-19 is a “significant crisis.”

But, then there is the graphic copied here. Ok, the partisan split on the news media and the President aren’t that surprising, while still quit stark. Interestingly, Dem/Lean Dem rank the top four categories consistently lower than Rep/Lean Rep. The CDC gets 10 percentage points lower and ordinary people 8 percentage points lower.

There are numerous charts of survey responses and the article has a methodology section with data.

## What is the distribution of people by age and race?

The Pew article, The most common age among whites in U.S. is 58, more than double that of racial and ethnic minorities by katherine Schaeffer (7/30/19) provides this graph of the distribution of age by race.

Whites had a median age of 44, meaning that if you lined up all whites in the U.S. from youngest to oldest, the person in the middle would be 44 years old. This compares with a median age of just 31 for minorities and 38 for the U.S. population overall.

U.S. Hispanics were also a notably youthful group, with a median age of 30. As a separate Pew Research Center report noted, Latinos have long been one of the nation’s youngest racial or ethnic groups, dating back to at least 1980.

The demographic differences leads to questions about studies that compare variables by race. If they don’t adjust for these differences they may be inaccurate. In general, a random sample of people will end up with an older cohort for whites and some variables are correlated with age.

## How much time do we spend on our phones?

The RescueTime blog post Screen time stats 2019: Here’s how much you use your phone during the workday? by Jory MacKay (3/21/2019) provides data on phone use. Note that

Let’s start with the high-level stats. When we looked at the data of 11,000 users who actively use the RescueTime app, we found that

most people,on average, spend 3 hours and 15 minutes on our phones.

So, the data comes from users of the RescueTime app and even though the sample size is large it is not a random sample. It is an interesting question if this sample of users is under users or over users of their phones. Still, the data is interesting.

And while a recent Deloitte survey found the average American checks their phone 47 times a day, our number was slightly higher.

We found that, onaverage, users check their phones 58 times a day with 30 check-ins happening during working hours (9am–5pm).

Most people spend about 1 minute and 15 seconds on their phone each time they pick them up.This meanswe’re losing 37.5 minutes a day during working hours to our phones(at a minimum).

The graph copied here is a representation of what those 37.5 minutes may look like. Why does this matter?

Psychologists have found that

even brief mental blocks created by shifting between tasks can cost as much as 40% of your productive time.And when it comes to our phones especially, it’s not just the switches themselves that interrupt our day, but the expectation of being interrupted.

In fact, a recent study in the

Journal of the Association for Consumer Researchfound thateven the presence of a turned off smartphone lowered our cognitive performance.In other words, just having your phone around undercuts your ability to do good work.

There are more graphs in the article and plenty of quantitative information for a stats or QL course.

## How do we visualize changing temperature distributions?

This recent video (3/29/19) by Robert Rohde shows how temperature distributions have changed. Each year the graph is a distribution of temperature anomalies. As noted “This essentially the same data that was previous shown as an animated map:” https://www.youtube.com/watch?v=JObGveVUz7k The video here is useful in any statistics or QL course and the two videos together provide an illustration of how to display data. The data is from Berkeley Earth.

## What is the state of Arctic Ice?

The melting season for Arctic Sea Ice has started with a quick drop in ice. The total ice is at a record low for this time of year (orange line in chart). But, how this plays out throughout the melting seasons is hard to predict based solely on past seasons. For instance, 2012 is the year of the record low (dashed line), but numerous seasons have been lower than 2012 at this time of year (2016 – yellow, 2015 – green, 2007 – blue shown here). Arctic Sea Ice extent is updated daily on the Charctic Interactive Sea Ice Graph by NSIDC. This graph allows the user to select years, download the image, and choose between Arctic and Antarctic ice extent. NSIDC posts the data and there is a project on both the Calculus and Statistics page using this data, as well as an interactive graph.

## What’s new at sustainabilitymath?

There are three more interactive graphs on the Interactive Graphs page for a total of five. One is Arctic Sea Ice extent by year for the months of March (high month), June, September (low month), and December, along with regression lines and residual plots (snapshot here). The other two represent the expected years to live at a given age. One of these is by race and gender, while the other is all females and males. Both graphs include a regression line and residual plot. The purpose of these graphs is to not only be interesting and informative, but to also be useful as classroom resource for projects or exercises.

## 0 to 6 or 1 to 7, Does it matter?

The Decoded/Pew Research Center article On a scale from 1 to 10, how much to the numbers really matter? by Jonathan Evans reports on their experiment using a 0 to 6 scale and 1 to 7 scale.

To carry it out, we randomly assigned respondents in France, Germany and the United Kingdom our political ideology question with one of two 7-point scales: either 0–6 or 1–7. The full question wording using our traditional 0–6 scale was this:

“Some people talk about politics in terms of left, center and right. On a left-right scale from 0 to 6, with 0 indicating extreme left and 6 indicating extreme right, where would you place yourself?”

Their graph copied here shows the results of this study. An explanation:

These outcomes suggest that when a scale is easily divided in half — for example, when the maximum value is 6 rather than 7 — it’s more likely for respondents to select the midpoint. Previous research has found that respondents are likely to assume that half the top endpoint is a scale’s midpoint, so when half the top endpoint is not an answer option (e.g., 3.5 on the 1–7 scale), respondents seeking the central point on the scale may sometime choose 3 (not the scale midpoint) and sometimes choose 4 (the actual scale midpoint). Those who received the 0–6 scale could more easily find the midpoint (3) by halving the top endpoint.

The article has other charts and links to methodology.

## What are the differences in the college aspirations of teens?

Pew reports results of a detailed survey in their article Most U.S. Teens See Anxiety and Depression as a Major Problem Among Their Peers — For boys and girls, day-to-day experiences and future aspirations vary in key ways by Juliana Menasce Horowitz and Nikki Graf (2/20/19). Here, we highlight college aspirations:

Girls are more likely than boys to say they plan to attend a four-year college (68% vs. 51%, respectively), and they’re also more likely to say they worry a lot about getting into the school of their choice (37% vs. 26%). Current patterns in college enrollment among 18- to 20-year-olds who are no longer in high school reflect these gender dynamics. In 2017, 64% of women in this age group who were no longer in high school were enrolled in college (including two- and four-year colleges), compared with 55% of their male counterparts.

There are also differences by parental education and economic class:

Among teens with at least one parent with a bachelor’s degree or higher, as well as those in households with annual incomes of $75,000 or more, about seven-in-ten say they plan to attend a four-year college after high school. By comparison, about half of teens whose parents don’t have a bachelor’s degree or with household incomes below $75,000 say the same.

The article has a number of other charts and a detailed methodology section (perfect for a stats course).