Practice these tips on the following graphs and answer the questions that follow. On this graph the individual data points are shown in blue (round symbols), and the trend line is shown in light blue. Use the trend lines to answer the questions.
Graph A
CO2
released by humans and the disappearance of Arctic sea ice
Annual Data
Trend
0
200
400
600
800
1000
1200
1400
1600
9
8
7
6
5
4
3
2
1
0
Area of Arctic Sea Ice (million km²)
Total Carbon Dioxide Released (gigatonnes)
In a recent study Dirk Notz and Julienne Stroeve examined the relationship between the total amount of carbon dioxide (CO2
) emitted by humans and the area of sea ice floating in the Arctic Ocean. They used data collected over 62 years, some of which are shown in the graph. The trend line indicates the average relationship they found between the total amount of CO2
released and the resulting area of sea ice in the Arctic Ocean, determined by a linear regression (the details of which are unimportant here!). Their results imply that the typical U.S. citizen, who releases 19 tons of CO2
annually (equivalent to the mass of three bull elephants), permanently melts over 600 square feet of sea ice every year, about the size of a typical small college classroom. To give a sense of scale in the graphs, one gigatonne (1 billion metric tons) is about the mass of a cube of water 3,300 feet on each side; 1 million km2
is about the area of Texas and New Mexico combined.
According to the graph, the variable shown on the Y-axis is gigatonnes .
The units for the variable on the X-axis are total carbon dioxide released .
There are two ways to view the information presented in Graph A to obtain new information. In one view, the graph can tell us the area of Arctic sea ice likely to exist given a total amount of carbon dioxide released. This view is convenient when you have or are given the total carbon dioxide released and want to know what its effect on the ice area will be. In the other view, the graph tells us the probable total carbon dioxide released given an area of Arctic sea ice. This view is convenient when you are given the area of sea ice and want to know how much carbon dioxide produced it.
For an example of the first view, assume the total carbon dioxide release was 530 gigatonnes. Then the likely area of sea ice would be 7.45 million km2
For an example of the second view, assume that you know that the area of Arctic sea ice is 6.0 million km2
. Using the graph, estimate the likely total carbon dioxide release:
400
900
1100
Graph doesn't show
850
The data presented by Notz and Stroeve can be represented by a downward-sloping straight line, as shown by the blue trend line on the graph. This trend implies a predictable relationship, or correlation, between the two variables on the graph. That is, according to this correlation, if at some time humans had emitted more carbon dioxide, there would be less sea ice in the Arctic Ocean.
Imagine that you enter an alternate universe where our laws of nature no longer apply, and read that two researchers, Eveorts and Zton, conducted a study of carbon dioxide release and area of Arctic sea ice. Data from their results are shown in Graph B .
Graph B
CO2
released by humans and the disappearance of Arctic Sea Ice
Annual Data
Trend
0
200
400
600
800
1000
1200
1400
1600
9
8
7
6
5
4
3
2
1
0
Area of Arctic Sea Ice (million km²)
Total Carbon Dioxide Released (gigatonnes)
Notice that this graph has an upward-sloping line, unlike the first graph, which has a downward-sloping line. This upward-sloping line indicates what kind of correlation in these (fictional) data?
At times of higher sea ice area, humans have emitted less total carbon dioxide.
At times of higher sea ice area, humans have emitted more total carbon dioxide.
The area of Arctic sea ice is independent of total carbon dioxide released.
The area of Arctic sea ice is independent of total carbon dioxide released.
The variable shown on the Y-axis of Graph A is gigatonnes.
The units for the variable on the X-axis of Graph A are total carbon dioxide released.
For an example of the second view, assuming that the area of Arctic sea ice is 6.0 million km2, based on the graph, the likely total carbon dioxide release would be around 900 gigatonnes.
In Graph B, the upward-sloping line indicates that there is a positive correlation between the area of Arctic sea ice and the total carbon dioxide released. This means that at times of higher sea ice area, humans have emitted more total carbon dioxide.
To answer the questions and interpret the graphs, we need to understand the information presented and how to read the graphs.
In Graph A, the Y-axis represents the variable "gigatonnes," which is the unit for the total carbon dioxide released. Therefore, the Y-axis represents the total carbon dioxide released by humans.
The X-axis represents the variable "total carbon dioxide released," which gives us the amount of carbon dioxide released by humans.
To obtain new information from the graph, we can consider two views:
1. The first view: Given the total carbon dioxide released, we can determine the likely area of Arctic sea ice. This view is useful when we have the total carbon dioxide released and want to know its effect on the sea ice area.
For example, if the total carbon dioxide release is 530 gigatonnes, we can look at the graph and find the corresponding area of sea ice. Based on the relationship shown in the graph, the likely area of sea ice would be 7.45 million km².
2. The second view: Given the area of Arctic sea ice, we can estimate the probable total carbon dioxide release. This view is useful when we are given the sea ice area and want to determine the amount of carbon dioxide produced.
For example, if we know that the area of Arctic sea ice is 6.0 million km², we can use the graph to estimate the likely total carbon dioxide release. Looking at the graph, we can see that the estimated total carbon dioxide release would be around 900 gigatonnes.
Now, let's move on to Graph B in the alternate universe.
In Graph B, the line is upward-sloping, unlike the downward-sloping line in Graph A. This upward-sloping line indicates a different correlation in these fictional data. It suggests that at times of higher sea ice area, humans have emitted more total carbon dioxide. This implies a positive correlation between the area of Arctic sea ice and the total amount of carbon dioxide released in this alternate universe.
To summarize:
- In Graph A, the Y-axis represents gigatonnes (total carbon dioxide released), and the X-axis represents the total carbon dioxide released.
- We can use Graph A to find the likely area of sea ice given the total carbon dioxide released and estimate the total carbon dioxide release given the area of sea ice.
- In Graph B, the upward-sloping line indicates that at times of higher sea ice area, humans have emitted more total carbon dioxide, suggesting a positive correlation between the two variables.