Visual Displays of Data and Graphics in the Media

Definition of a Multiple Bar Graph: A multiple bar graph is described as a simple extension of a regular bar graph. It utilizes two or more sets of bars to facilitate a direct comparison between two or more related data sets.
Requirement for Categories: To display data sets on the same graph, all data sets must share the same categories.
Application Example: Earnings and Education (Figure 3-11):
- Data Source: U.S. Census Bureau data for the pre-pandemic year 2019.
- Variables Tracked: The relationship among median earnings, level of educational attainment, and gender.
- Primary Findings:
  - Education Correlation: There is a significant positive correlation between education and income; people with higher educational attainment have noticeably higher median incomes. This is visually represented by the bars of each color becoming progressively longer as education level increases.
  - Gender Wage Gap: Across all educational categories, men earn more than women. This represents the well-known gender wage gap where women's earnings are approximately $70\%$ to $80\%$ of men's earnings. This is easily identifiable because the two bars in every category are of obviously different lengths.

Definition of a Multiple Line Chart: This chart follows the same basic logic as a multiple bar chart but utilizes lines instead of bars to show related data sets. These are particularly useful for showing trends over time.
Application Example: Overdose Deaths (Figure 3.13):
- Data Source: U.S. National Institutes of Health (2021 data listed as provisional estimates as of mid-2022).
- Specific Calculation Note: The sum of the individual drug lines on such a chart may be larger than the total number of overdose deaths. This occurs because some deaths involve more than one drug (e.g., cocaine laced with fentanyl), meaning those deaths are counted in multiple categories.
- Observed Trends (2020–2021):
  - There was a dramatic rise in the total number of overdose deaths during the start of the Covid-19 pandemic.
  - There was a corresponding dramatic rise in deaths involving synthetic opioids, primarily fentanyl.
- Hypothesized Causes: The increasing prevalence of fentanyl being ‐laced‑ into other illegal drugs and the social/economic impacts of the pandemic are cited as key potential causes for these increases.

Definition of a Stack Plot: A stack plot shows two or more related data sets simultaneously by stacking them vertically.
Common Applications:
- Student Budgets (Figure 3.14): Horizontal stacked bars can show the breakdown of average student costs (e.g., tuition, room and board, books) across different types of institutions.
- Global Energy Usage (Figure 3.15): A stack plot over time where each energy source (wood/biomass, coal, oil, natural gas, etc.) is represented by a color-coded region or ‐wedge.‑
Understanding Units and Scale in Energy Data:
- Energy Units: Energy usage is often measured in terawatt-hours ( $TWh$ ), which equals trillions of watt-hours.
- Contextual Comparison: One gallon of gasoline typically yields approximately $34,000\,\text{watt-hours}$ of energy.
How to Read a Stack Plot:
- Wedge Thickness: The thickness of any specific wedge at a given point in time represents the value for that specific category at that time.
- Total Value: The top line of the entire stack represents the total cumulative value of all categories combined.
- Calculating Specific Values: To find the value of a specific wedge (like oil usage), one must estimate the top and bottom levels of the wedge against the vertical axis and subtract the bottom value from the top value.

Core Data Observations from Figure 3.15:
- Total Energy Growth: Total global energy use doubled from slightly under $80,000\,\text{TWh}$ in 1977 to nearly $160,000\,\text{TWh}$ by 2019.
- Specific Usage Case: Oil usage in the year 2000 was estimated to be approximately $42,500\,\text{TWh}$ .
Challenges in Eliminating Carbon Emissions by 2050:
- Scaling Difficulty: As of 2019, non-carbon sources (the upper wedges) represented less than $10\%$ of total energy usage. To replace carbon sources entirely, the world would need to scale non-carbon production by a factor of more than 10.
- Rising Demand: Total energy use is rising substantially over time. By 2050, the world will likely require significantly more total energy than it does today, further increasing the scale at which non-carbon sources must be developed.

Geographical Patterns: Statistical data can be depicted by geographical region to show patterns across maps.
Color-Coded Maps (Figure 3.16):
- Maps can use color coding to display values by country or region.
- Example: Tracking agricultural yields for cereals (wheat, rice, corn). Higher yields indicate more productive land use where the same area of land produces more food.
Contour Maps (Figure 3.17):
- Definition: These maps use curvy lines (contours) to connect locations that have the same value (e.g., the same temperature).
- Interpretation of Contours:
  - Between any two contour lines, the value varies between the two temperatures listed on those lines.
  - Spacing and Rate of Change: Closely spaced contours indicate that the variable (temperature) is changing rapidly over a short distance. Widely spaced contours indicate more gradual changes.

Modern Data Visualization: Computers enable sophisticated graphics beyond traditional charts:
- Infographics: Poster-like visual summaries of various related data points.
- Computer Modeling: Interactive global maps showing real-time data, such as surface wind speeds and temperatures (Figure 3.18).
Critical Thinking and Statistics:
- The variety and complexity of modern graphics require the application of reasoning skills.
- Evaluation Steps: First, use reasoning to identify exactly what the graphic is attempting to show. Second, apply statistical understanding to determine if the underlying data appears reliable and if the visual representation is meaningful and accurate.