A selection of graphs from The New York Times featured in “What’s Going On in This Graph?”
ASSOCIATION (relationship between two or more variables)
a. Women Marathoners’ Running Times (scatter plot)
b. World Leader Ages (modified scatter plot)
c. Climate Friendly Electric Cars (scatter plot)
d. Global Life Expectancy and Health Expenditures (connected scatter plot)
e. Solving Gun Murders (scatter plot)
f. Vaccination by Country (bubble scatter plot)
g. International Optimism (scatter plot)
h. Serena Williams’s Record and Legacy (scatter plot)
TIME
a. Voting Shifts (time series)
b. World Cities’ Air Pollution (time series)
c. Covid Herd Immunity (time series)
d. How We Spent Our Time During the Pandemic (slope chart)
e. Covid Hospitalizations (time series)
f. Olympic Gymnastics Routine (connected time series)
g. Pandemic Price Changes (time series)
h. Supply Chain Delays (flowchart)
i. Weddings (time series step graph)
j. Extreme Temperatures (stacked time series)
k. U.S. Population Dynamics (time series)
l. Teen Health-Related Behaviors (time series)
m. Serena Williams’s Record and Legacy (time series)
n. Tree Rings and Climate (stacked area time series)
o. Calling for Climate Action (stacked area time series)
p. Immigrant Economic Mobility (stacked area times series)
q. Temperature Trends (high-low time series)
r. “Tripledemic” (line time series)
s. Global Temperature Change (time series)
t. LeBron James (Time series step graph)
u. Earthquakes (bubble time series)
v. The Anthropocene (time series)
w. Price of Eggs (time series)
x. Baseball Has Changed (line time series)
COMPARING CATEGORIES
a. Essential Workers (bar chart)
b. How We Spent Our Time During the Pandemic (bar chart)
c. U.S. Well-Being Compared Internationally (dot plot)
d. First Vaccinated (bubble chart)
e. Mortality by Race (bar mekko chart)
f. Diversity in Professional Sports (segmented bar graph)
g. Smoking and Income (bar chart)
h. Vaccination Roadblocks (radar graph)
i. Post-Pandemic Jobs (bar chart)
j. Covid in Prisons (connected dot plot)
k. The Pandemic Changed How We Spent Our Time (grouped bar chart)
l. College Essays (bar chart)
m. Global Success Factors (bar chart)
n. Refugees From Ukraine (infographic)
o. Inflation in Words (word cloud)
p. Serena Williams’s Record and Legacy (infographic)
q. Americans Moving (stacked bar graph)
r. Immigrant Economic Mobility (bubble graph)
s. Senate Representation by State (infographic)
t. Russian Trade (radial comparison graph)
u. Online College (segmented bar graph)
v. Social Connections (bar chart)
PARTS TO WHOLE
a. Instant Mastery (infographic)
b. Gas-to-Electric Vehicle Turnover (waffle chart)
c. President Biden’s Economic Plan (Part-to-Whole chart)
d. SNAP ‘Thrifty Food Plan’ (segmented pie chart)
e. Global Carbon Emissions (treemap & segmented bar graph)
f. Clean Energy Metals (stacked bar graph)
g. Where $5 Trillion of Federal Pandemic Stimulus Money Went (treemap & donut map)
h. Free Speech (segmented bar chart)
i. Immigrant Economic Mobility (infographic)
j. Paying College Athletes (segmented bar graph)
k. Russian Trade (treemap)
l. Words Used (segmented bar graph)
MAPS
a. Covid-19 Cases in America (bubble map & choropleth map)
b. Climate Threats (choropleth)
c. 2020 Presidential Election Maps (tile map and choropleth map)
d. U.S. Air Pollution (choropleth map)
e. Recent U.S. Development (map)
f. Global Climate Risks (map)
g. Growing Zones (map)
h. New Normal U.S. Precipitation (choropleth)
i. 2020 Census Redistricting (cartogram)
j. Wind and Solar Power (map)
k. U.S. Population Diversity Shift (map)
l. U.S. Asian Population (map)
m. Extreme Temperatures (bubble map)
n. Endangered Biodiversity (choropleth)
o. Train Derailments (bubble map)
p. Sex Education (tilegram)
OTHER
a. Supply Chain Delays (flowchart)
b. Drawing Voting Maps (infographic)
c. Olympics Medal Count (heatmap)
d. March Madness Bracket (tree diagram)
Definitions:
Total Immunity: Share of people who have been vaccinated plus the estimated share of people who have recovered from infection.
Vaccine Immunity: Share of people who are fully vaccinated.
Herd immunity range: 70 percent – 90 percent of people are immune to the virus either because of vaccinations or infection and recovery.
These four graphs show when the United States is predicted to reach herd immunity under different scenarios. Herd immunity occurs when enough people become immune to a disease to make its spread unlikely. Herd immunity can be achieved through vaccination or through natural infection.
The graphs were generated from a mathematical model using data as of Feb. 16, 2021, for the number of people who have been vaccinated and an estimate of the number of people who have been infected by Covid-19 and have recovered. Four scenarios are modeled:
Graph A: Maintaining the current supply of vaccinations and public precautions (masking and social distancing)
Graph B: Increasing the vaccine supply and maintaining public precautions
Graph C: Maintaining the vaccine supply with lifting some public precautions in the spring
Graph D: Maintaining vaccine supply and public precautions, but experiencing contagious variants
The model assumes that immunity lasts indefinitely and that vaccination prevents infection rather than just reducing the symptoms.
After looking closely at the graphs above (or at this full-size image), answer these four questions:
What do you notice?
What do you wonder?
What impact does this have on you and your community?
What’s going on in these graphs? Write a catchy headline that captures the graph’s main idea.
The questions are intended to build on one another, so try to answer them in order.
2. Next, join the conversation online by clicking on the comment button and posting in the box. (Teachers of students younger than 13 are welcome to post their students’ responses.)
3. Below the response box, there is an option for students to click on “Email me when my comment is published.” This sends the link to their response which they can share with their teacher.
4. After you have posted, read what others have said, then respond to someone else by posting a comment. Use the “Reply” button to address that student directly.
On Wednesday, March 10, teachers from our collaborator, the American Statistical Association, will facilitate this discussion from 9 a.m. to 2 p.m. Eastern time.
5. By Friday morning, March 12, we will reveal more information about the graph, including a free link to the article that included this graph, at the bottom of this post. We encourage you to post additional comments based on the article, possibly using statistical terms defined in the Stat Nuggets.
UPDATED: MARCH 11, 2021
The Reveal
With the objective of curtailing coronavirus as quickly as possible with the fewest number of deaths, researchers from PHICOR, headquartered at the City University of New York School of Public Health & Health Policy, modeled different scenarios for paths of total immunity and vaccine immunity.
Graph A: What would happen if we just proceeded as we are doing currently?
Graph B: What would happen if people were vaccinated more quickly?
Graph C: What would happen if public precautions, like masking and social distancing, were reduced?
Graph D: What would happen if more contagious coronavirus variants appeared?
The February 20, 2021 New York Times article “When Could the United States Reach Herd Immunity? It’s Complicated.” shows ten scenarios, four of which are included here. The outputs of the models for each scenario are the month that total immunity and vaccine immunity reaches the herd immunity threshold and the number of deaths prior to herd immunity.
What do we notice? Of the four graphs, the US would reach herd immunity earliest and the fewest people would die if more people are vaccinated sooner in the scenario depicted in Graph B. In Graph C, if we relax public precautions, the model predicts that the U.S. would reach herd immunity sooner, but many more people would die. Why would the U.S. reach herd immunity sooner? Fewer public precautions allow coronavirus to spread more quickly, resulting in more people either dying or recovering with immunity. In Graph D, if more contagious variants spread, the model predicts that the herd immunity threshold would increase to more than 70 percent and deaths could double or even more.
Not reaching herd immunity before the arrival of contagious variants may result in an unacceptable number of deaths. Go to the article to see models for additional scenarios involving the three variables: vaccine shots, public precautions and contagious variants. What would you recommend as a strategy?
Here are some of the student headlines that capture the stories of these graphs: “Have Vaccine and Patience. Will Travel.” by Mitch of Pennsylvania, “Four Paths to the Normal World—But at What Cost?” by Paul of Memphis, Tennessee, “Have You HEaRD? Herd Immunity Is Coming!” by Eliana of New York, “Having a Normal Summer Is Up to Us: Here Are the Stats” by Audrey of California, “What’s the Quickest Way to Reach Herd Immunity?” by Katie of Andover, Massachusetts, and “What’s More Important, Lives or Freedom?” by Juliana from North Carolina.
You may want to think critically about these questions:
Explain the relationship between each of the variables: number of shots per day, amount of public precautions and presences of contagious variants and the month that the herd immunity threshold is reached.
Explain the relationship between each of the variables: number of shots per day, amount of public precautions and presences of contagious variants and the number of deaths from the virus.
Of the four scenarios, which do you think is the best? Explain your reasoning.
What other variables besides number of shots per day, amount of public precautions and presences of contagious variants could affect the month that the herd immunity threshold is reached.
The next graph on recent land development in the United States will be released by Friday, March 12 with live-moderation on Wednesday, March 17. You can receive the 2020-2021 “What’s Going On In This Graph?” schedule by subscribing here to the Learning Network Friday newsletter. In the meantime, keep noticing and wondering.
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Stat Nuggets for “When Could the United States Reach Herd Immunity? It’s Complicated.”
5. What does the data show? What do you notice
(what story does it tell?)
6. Why is it telling the story you wrote in 5? What
do you wonder?
To see the archives of all Stat Nuggets with links to their graphs, go to this index.
TIME SERIES GRAPH
A time series graph shows how a numerical (quantitative) variable changes over time.
The Herd Immunity graphs each show two time series — the percentage of the U.S. population that have total immunity and vaccine immunity to Covid-19 according to the PHICOR model. The values through February 16, 2021 are actual values. Thereafter, they are projected values based on the assumptions of the model.
MATHEMATICAL MODEL
A mathematical model is a representation of a real-world problem used to gain qualitative and/or quantitative understanding, to predict future behavior, or to guide decision-making.
The Herd Immunity graphs are based on a mathematical model using data as of February 16, 2021 for the number of people who have been vaccinated and an estimate of the number of people who have been infected by Covid-19 and have recovered. The first graph shows the current situation. The other three graphs show what may be expected to happen under different situations. Each varies from the current situation by one of these variables: number of shots per week, type of public precautions and presence of variants. (See graphs for varying conditions.)
The model assumes that people take a full regiment of the vaccine, that immunity lasts indefinitely and that vaccination prevents infection rather than just reducing the symptoms. Also, the model assumes that the vaccine prevents infection against current and future coronavirus variants in 90 percent of those who are fully vaccinated, and that 80 percent of the population is ultimately fully vaccinated.
IMMUNITY
Total Immunity: People who have been vaccinated plus an estimate of the number of people who have been infected and have recovered.
Vaccine Immunity: People who are fully vaccinated and have immunity.
Herd immunity range: Range of the percentage of the population who have total immunity such that a contagious disease is unlikely to spread through the population.
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The graphs for “What’s Going On in This Graph? are selected in partnership with Sharon Hessney. Ms. Hessney wrote the “reveal” and Stat Nuggets with Roxy Peck, professor emerita, California Polytechnic State University San Luis Obispo, and moderates online with David Wilcox, statistics teacher at the Lawrenceville School in Lawrenceville, New Jersey.
