Lesson 4: Graphics in the Media

class: center, middle, inverse, title-slide

.title[
# Lesson 4: Graphics in the Media
]
.author[
### Fei Ye
]
.date[
### May, 2024
]

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## Unit 5D: Graphics in the Media

*Primary Source:* PPT for the book "Using & Understanding Mathematics".

---

## Graphics Beyond the Basics

- A **multiple bar graph** has two or more sets of bars that allow comparison between two or more data sets. All the data sets must have the same categories so that they can be displayed on the same graph.
- In cases for which data categories are quantitative, a **multiple line chart** is often a better choice.
- A **stack plot** shows different data sets stacked upon one another. Data can be stacked in both bar charts and line charts.

---

## Sample Multiple Bar Graph

![](data:image/png;base64,#img/image-20200818141459191.png)

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## Sample Line Graph

![](data:image/png;base64,#img/image-20200818141512396.png)

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## Example: Education Pays

What general messages are revealed by the graphs in the previous two slides? Comment on how the use of the multiple bar and line graphics helps convey these messages.

**Solution:** The bar graph conveys two clear messages.

- people with greater education have significantly higher median incomes
- for equivalent levels of educational attainment, women still earn much less than men.
- No matter what the unemployment rate (at least over the time period shown) is, unemployment has always been significantly lower for more highly educated people.

---

## A Stack Plot

The following stack plot shows the breakdown of average student budgets at different types of institutions.

![](data:image/png;base64,#img/image-20200818141528195.png)

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## Example: Trends in Health Data (1 of 2)

What was the death rate for cardiovascular disease in 1980? Discuss the general trends visible on this graph.

![image-20200818141543350](data:image/png;base64,#img/image-20200818141543350.png)

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## Example: Trends in Health Data (2 of 2)

**Solution:** For 1980, the cardiovascular wedge extends from about 180 to 620 on the vertical axis, so its thickness is about 440. Therefore, the death rate in 1980 for cardiovascular disease was about 440 deaths per 100,000 people.

- The downward slope of the top wedge shows that the overall death rate from these four diseases decreased substantially from 800 deaths per 100,000 in 1900 to about 434 in 2011.
- The gradual disappearance of the tuberculosis wedge shows that this disease was once a major killer, but has been nearly wiped out since 1960.
- The widening and then narrowing of the cardiovascular wedge shows that the death rate for this disease grew in the first few decades shown, but has declined in recent years.
- The cancer wedge shows that the cancer death rate rose steadily until the mid-1990s, but has dropped somewhat since then.

---

## Practice: Comparing College Expenses

The expenses of on semester for two college students are shown in the table below.

1. Which type of statistical graph would you like to use to compare the expenses.

2. What can you conclude about their expenses?

| Student\Expense | Transport | Food | Books | Tuition | Misc |
| --------------- | -------------- | ---- | ----- | ------- | ---- |
| Student 1       | $600           | $350 | $250  | $3,200  | $300 |
| Student 2       | $750           | $280 | $150  | $2,950  | $400 |

---

## Graphs of Geographical Data

We are often interested in geographical patterns in data. The figure below shows one common way of displaying geographical data. This type of graph is known as color-coded map.

.pull-left[
  ![](data:image/png;base64,#img/image-20200818141603609.png)
]

.pull-right[In this case, the map shows trends in energy use per capita (per person) in different states. The actual data values are shown in small print with each state, while the color coding shows the binned categories listed in the legend.]

---

## Contour Map

.row[
.left-col[
Contour maps are commonly seen in weather forecast. The following figure shows the temperate of US at a certain time.
]
.right-col[
![](data:image/png;base64,#img/image-20200818141615187.png)
]
]

---

## Example: Interpreting Geographical Data (1 of 2)

Use the figure to answer the following question.
.pull-left[
What geographical characteristics are common to states with the lowest energy usage per person?
]
.pull-right[
![resize , 120%](data:image/png;base64,#img/image-20200818141603609.png)
]

--
**Solution:** The color coding shows that the states in the lowest category of energy use per person are all either warm-weather states (CA, AZ, FL, and HI) or states in the more densely populated regions of the northeast (NY, NH, CT, MA, and RI).

---

## Example: Interpreting Geographical Data (2 of 2)

Use the figure to answer the following question.
.pull-left[
Were there any temperatures above 80F in the United States on the date shown in the contour map? If so, where?
]
.pull-right[
![](data:image/png;base64,#img/image-20200818141615187.png)
]

--
**Solution:** The 80 contour passes through southern Florida, so the parts of Florida south of this contour had a temperature above 80.

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## Practice: Covid-19 Map

The figure shows the latest confirmed Covid-19 cases by states in US. What information do you get from this color-coded map of Covid-19?

[![:resize , 52%](data:image/png;base64,#img/Covid19Sep20.png)](https://www.theguardian.com/world/ng-interactive/2020/jul/15/covid-19-coronavirus-us-map-latest-cases-state-by-state)

---

## Three-Dimensional Graphics

Computer software makes it easy to give almost any graph a three-dimensional appearance.

- Allow us to describe data sets of 3-variables.

- However, can be difficult to read the data precisely.

- Three-dimensional graphics therefore tend to work best when they are interactive (online), so that figures can be rotated or viewed from different perspectives.

---

## Example: Three-Dimensional Carbon Dioxide Emissions

Based on the figure, about when did China surpass Russia in total carbon dioxide emissions?

![:resize , 50%](data:image/png;base64,#img/image-20200818141649980.png)

**Solution:** China surpassed Russia in total emissions sometime between 1990 and 1995.

---

## A Few Cautions about Graphics

- Perceptual distortions:  Many graphics are drawn in a way that distorts our perception of them.

- Watch the scales:  It can be visually deceptive if you do not study the scales carefully.

- Percentage change graphs:  Graphs that show percentage change can be misleading unless you interpret them with great care.

- Pictographs:  Pictographs are graphs embellished with additional artwork. The artwork may make the graph more appealing, but can also distract or mislead.

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## Perceptual Distortion

The lengths of the dollars to the right represent the data, but your eyes tend to focus on the area.

![:resize , 30%](data:image/png;base64,#img/image-20200818141732503.png)

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## Different Vertical Scales

Both graphs show the same data, but they look very different because their vertical scales have different ranges.

![](data:image/png;base64,#img/image-20200818141747452.png)

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## Different Horizontal Scales

It appears that the world population has been rising linearly. However, the time intervals on the horizontal axis are not uniform in size.

![](data:image/png;base64,#img/image-20200818141800608.png)

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## Practice: Read carefully

Compare the two graphs below showing support for same-sex marriage rights from a poll taken in December 2008. What would you conclude based on each graph?

![](data:image/png;base64,#img/WrongVerticalScale.png)

.small[Source: Math in Society by David Lippman]