A Quick Review of Graphs

You’ll see a lot of graphs in the pages ahead—don’t let it scare you. You encounter graphs every time you scroll through your news feed: charts for election results, opinion polls, sales figures, health outcomes, and just about anything else. Apps on your phone might supply you with graphs to show how many steps you took last week, how much you spent over the past month on different types of goods, or how many books you read last year. When you were applying to college, you probably consulted graphs that showed the range of entrance exam scores for first-year students at schools you were eyeing to see how you measured up.

We live in a time when data are cheap and plentiful, and so many aspects of our lives are quantified. Graphs make sifting through all of it a lot easier. Economics can make you a more effective user of all of that data. To start, here’s a quick refresher to walk you through some familiar graphs, with useful tips on how to read them. Along the way, we’ll remind you of some of the basic tools and language you’ll use to work through them.

Graphs That Break Down Numbers

▲ Pie Charts When you want to break down a total into its component slices, pie charts can provide an easy way to show each of the parts that comprise the whole.

Data from: U.S. Bureau of Labor Statistics.

The data from the graph are as follows:

Lowest-income quintile: $18,900; Second quintile: $46,300; Middle quintile: $75,800; Fourth quintile: $115,800; and Highest-income quintile: $245,000. A callout pointing to the data in the horizontal axis reads, Remember a quintile is one fifth.

▲ Analyzing Distributions When you want to see how an economic statistic—say, income—is distributed across the population, it can be helpful to divide the data up into smaller, equal-sized segments. In economics you’ll come across lots of data that has been broken down into fifths, segments that we call quintiles. This breakdown reveals the dispersion in outcomes across the population—a fact often obscured by measures like the median or mean. Bar charts like this one use quintiles to show that the poorest fifth of the population get by with an average annual income of less than $20,000, while the richest fifth enjoys an average income of nearly a quarter of a million dollars.

Data from: U.S. Census Bureau.

The data from the graph are as follows:

Lowest-income quintile: $18,900; Second quintile: $46,300; Middle quintile: $75,800; Fourth quintile: $115,800; and Highest-income quintile: $245,000. A callout pointing to the data in the horizontal axis reads, Remember a quintile is one fifth.

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Graphs That Show Comparisons

Most of the graphs you encounter are designed to visualize numbers, give them scale, and provide opportunities to make comparisons.

▲ Bar Chart and Dot Plot Sometimes you’ll want to compare data for different categories. One of the most common ways to visualize and compare data across different categories is with a bar chart. For example, a bar chart can show you, for particular levels of education, the median earnings of the person with that amount of education. Each bar in Panel A represents a category of education—like college graduate—and the height of the bar shows the median earnings of a person with that level of education. It’s easy to see that people with more education generally have higher earnings.

An even simpler way to represent data across categories is with a dot plot, as shown in Panel B. It’s an even simpler way to visualize and compare data across different categories. A dot plot shows different values for different groups, plotting the data along a single axis to show how different variables rank along a particular scale. Instead of the height of the bars showing you the median earnings of each education category, there is a dot on the dot plot. Both bar charts and data plots can be used to show the same information, so which way do you prefer to see the data?

Data from: U.S. Bureau of Labor Statistics.

Text above the graph reads, Figure 3, Highly Educated People Earn More Money.

Panel A: A Bar Chart

Median annual earnings in 2017

The data from the graph are as follows:

High school dropout: $25,200; High school graduate: $32,300; Associate’s degree: $40,300; Bachelor’s degree: $53,900; Master’s degree: $70,400; and Professional degree: $100,300.

Text below this graph reads, Data from U.S. Bureau of Labor Statistics. A callout pointing to this text reads, Data are only as good as their source. Be sure to take a look at where the numbers come from.

The text on the right side, beside the graph reads,

Panel B: A Dot Plot

Median annual earnings.

The data in this dot plot are linked to the data from the bar chart. A upward vertical arrow has dots with the following labels (from bottom to top): High school dropout; High school graduate; Associate’s degree; Bachelor’s degree; Master’s degree; and Professional degree. Dashed lines from these dots are connected to the top of the respective bars in the bar chart. A callout pointing to the top of the arrow reads, The median is the middle value-meaning that half of the people in each category earn more than this, and half earn less. That’s different from the mean, which is what you get when you add up all the data, and then divide the sum by the total number of people with that amount of education.

A boring spreadsheet of numbers like this:

▲ Time-Series Graphs Often, you’ll want to look at how a certain indicator or data point changes over time. Plot time on the horizontal axis and your data (in this case, the percentage of the population who complete high school and college) along the vertical axis, and voila:

The column headers read, Year, Share who completed high school, and Share with a Bachelor’s degree.

The data from the table reads as follows:

Row 1. Year: 1940; Share who completed high school: 38.1 percent; Share with a Bachelor’s degree: 5.9 percent.

Row 2. Year: 1950; Share who completed high school: 52.8 percent; Share with a Bachelor’s degree: 7.7 percent.

Row 3. Year: 1960; Share who completed high school: 60.7 percent; Share with a Bachelor’s degree: 11.0 percent.

Row 4. Year: 1970; Share who completed high school: 75.4 percent; Share with a Bachelor’s degree: 16.4 percent.

Row 5. Year: 1980; Share who completed high school: 85.4 percent; Share with a Bachelor’s degree: 22.5 percent.

Row 6. Year: 1990; Share who completed high school: 85.7 percent; Share with a Bachelor’s degree: 23.2 percent.

Row 7. Year: 2000; Share who completed high school: 88.1 percent; Share with a Bachelor’s degree: 29.1 percent.

Row 8. Year: 2010; Share who completed high school: 88.8 percent; Share with a Bachelor’s degree: 31.7 percent.

Row 9. Year: 2017; Share who completed high school: 92.5 percent; Share with a Bachelor’s degree: 35.7 percent.

… becomes a clear time-series graph. The years become the horizontal axis, now for each column B and C, plot the data along the vertical axis for each year and connect the dots. Viola! You have a pretty graph that makes it much easier to take in the big finding—educational attainment has risen over time.

Data from: National Center for Education Statistics.

The text above the graph reads, Figure 4, Educational Attainment has risen over time. The graph shows two curves, one representing High school graduates and the other representing college graduates.

The approximated data from the graph is as follows: In 1900, 3 percent of the people aged 25 and above were college graduates, while 14 percent were high school graduates. In 1940, 7 percent of the people aged 25 and above were college graduates, while 26 percent were high school graduates. In 1980, close to 25 percent of the people, aged 25 and above were college graduates, while 72 percent were high school graduates. In 2017, about 36 percent of the people aged 25 above are college graduates, while 90 percent are high school graduates. Both lines keep increasing gradually over the years.

A callout referring to the values along the horizontal axis reads, Check the date range to make sure you’re getting the big picture, not just a blip of data. A callout referring to the vertical axis reads, Pay attention to the (bold) scale: (end bold) Zooming in on the numbers can make data appear more erratic. The text below the graph reads, Data from: National Center for Education Statistics.

Graphs That Show Relationships

In economics, we are concerned not just with numbers describing different outcomes, but with relationships between different outcomes. The coordinate system enables you to display two sets of data on a single graph. This simple setup forms the skeleton of many of the graphs you will encounter in economics; it’s also one that you’re probably familiar with from middle school math class. You can plot one measure on the horizontal axis, and a second measure on the vertical, so each data point shows a pair of outcomes for an individual person, state, or country.

▲ Scatterplot You can plot individual data points on a coordinate graph to create a scatterplot. This simple graph helps you to see the range of responses and see if any patterns emerge. For example, we can plot the average happiness of people in a country and each country’s average income. Americans rated their level of life satisfaction on average to be about 7 on a scale of 1–10; and their average annual income is about $56,000 per person. The black dot below represents those two numbers—it shows the average level of happiness and income for people in the United States. The other dots represents another country’s averages. Looking at all the dots, you can see that richer countries are generally happier countries. There’s a relationship there.

The text above the scatterplot reads, Figure 5, People in High-Income Countries are more satisfied with their lives. A whole cluster of dots is between the points 0 and $50,000 along the horizontal axis and 3 and 8 along the vertical axis. The point labeled U S A is at (55,000, 7.8). Some dots are also plotted in the following points (68,000, 6), (67,500, 6.1), (75,000, 6.8), and (80,000, 6.5). All data in the graph are approximate.

An asterisk is beside the graph and text beside the asterisk reads, Remember. Scatterplots show (Italics) all (end Italics) the underlying data and so reveal the (bold) shape (end bold) of the (bold) relationship (end bold) between two variables.

▲ The stylized graphs of economics One thing you’ll graph a lot in economics is the relationship between the price of stuff and the quantity of stuff people will buy or sell at different prices. The demand curve, a fundamental tool in economics, shows the quantity of stuff that people will buy at different prices. The demand curve always shows price on the vertical axis and quantity on the horizontal axis.

The text above the table and the graph reads, How many avocados does Lukia buy each week?

The table gives the following data:

Price of avocados: $0.50; Quantity of avocados: 5;

Price of avocados: $1.00; Quantity of avocados: 4;

Price of avocados: $1.50; Quantity of avocados: 3;

Price of avocados: $2.00; Quantity of avocados: 2;

Price of avocados: $2.50; Quantity of avocados: 1;

The line graph plots Quantity of avocadoes per week along the horizontal axis and Price per avocado along the vertical axis. The graph shows a curve with a negative slope extending between (1, 2.50) and (5, 0.50). Three points are plotted on the line at (2, 2.00), (3, 1.50), and (4, 1.00) respectively. Text accompanying the point (1, 2.50) reads, At a price of $2.50, Lukia buys one avocado. Text accompanying the point (2, 2.00) reads, $2.00 (rightward arrow) 2 avocados. Text accompanying the point (3, 1.50) reads, $1.50 (rightward arrow) 3 avocados. Text accompanying the point (4, 1.00) reads, $1 (rightward arrow) 4 avocados. Text accompanying the point (5, 0.50) reads, $0.50 (rightward arrow) 5 avocados. An asterisk is beside the graph and the text beside this asterisk reads, In economics, price will always go on the vertical axis, quantity will go on the horizontal.

The demand curve will almost always slope down from top left to bottom right, reflecting the idea that when something becomes cheaper, people buy more of it. For example, when avocados are priced at $2.50 each, Lukia will only buy one. But when they are on sale for $0.50, she’ll buy five, and eat avocado toast all week long.

This graph demonstrates a negative relationship between quantity and price—you can see this because the line tilts downward as you look from left to right. If the line tilted upward from left to right, you’d be looking at a positive relationship.

In economics you’ll want to look at not just the direction of the line, but the steepness of it. This is called the slope. You calculate the slope along a straight line by looking at two points on the line, and dividing the vertical change by the horizontal change. In simple terms, it’s rise over run. In mathematical terms, it’s

The equation reads, Slope equals Change in the value on the vertical axis over Change in value on the horizontal axis equals Delta y over Delta x equals rise over run.

A note reads, Hint: The little triangle (Delta) is the Greek symbol delta. It’s used as a shorthand for ‘change’ -in this case, a change in value.

In the chapters ahead, you’ll see lots of stylized graphs like this. We’ll take the time to walk you through each one, and provide a quick refresher on how to do all the calculations that come up in this book as we get to them.

A Relationship Is Not The Same Thing as Cause and Effect

Sometimes you’ll look at a graph, and you’ll see a very clear relationship between two variables. For example, if you compare the volume of ice cream produced in the United States over time with the number of airline miles flown in the same time period, you’ll see a clear relationship:

Text above the graph reads, Figure 7, Ice Cream Production Rises and Falls with Air Travel.

An asterisk is beside the graph and the text beside the asterisk reads, (bold) Remember: (end bold) Correlation doesn’t imply causation. The graph has two curves, one representing Airline miles flown and the other representing Ice cream production.

The approximated data from the graph reads as follows: In January 2016, the airline miles flown was close to 0 percent, which then dropped to negative 5 percent by the next few months, before increasing again, to reach as high as 32 percent by the July of 2016. Eventually this number came down to about negative 7 percent by January 2017, only to increase again and reach as high as 38 percent by the June of 2017. Again there is a drop, reaching negative 3 percent by January 2018, only to increase again and reaching about 42 percent by the mid of 2018.

In January 2016, ice cream production was at 0 percent, then increased to about 56 percent by the mid of 2016, only to drop to about negative 4 percent by January 2017. It then again rose to about 40 percent a few months later, had a slight drop to about 36 percent to only increase again to 41 percent by the mid of 2017. Then a gradual fall began, making it fall to about negative 9 percent by January 2018. The ice cream production eventually gained momentum, reaching as high as 43 percent by the April of 2018, only to have a short drop to about 38 percent by June 2018.

You probably wouldn’t infer that the presence of airplanes flying overhead leads people to eat more ice cream. Lots of variables are related, but that doesn’t mean that one causes the other. There are other omitted variables—like the fact that people tend to go on vacation in the summer, and also eat more ice cream in the summer—that are related to both of these outcomes.

It’s also possible to think you’ve identified a cause-and-effect relationship, but to get it backward. If you compared airline miles flown with, say, time students spend in school, you would probably conclude that families tend to schedule vacations during school breaks. But if you conclude that kids don’t go to school in the summer or during the winter holidays because they’re traveling, you’ve reversed the causality.

Both cases should make you wary about drawing conclusions whenever you look at data, be it in a textbook like this one or a news story: The fact that two things are related, or correlated, doesn’t mean one causes the other. As the saying goes, “correlation does not imply causation.”