Question

Environment

a. After collecting the average (mean) global temperatures for each of the most recent 100 years, we want to construct the graph that is most appropriate for these data. Which graph is the best?

b. After collecting the average (mean) global temperature and the amount of carbon monoxide emissions for the most recent 100 years, we want to construct a graph to investigate the association between those two variables. Which graph is the best?

c. An investigation of carbon monoxide sources includes motor vehicles, furnaces, fires, coal-burning power plants, and tobacco smoke. If we want to construct a graph that illustrates the relative importance of these sources, which graph is the best?

Short answer

a. A time-series graph will be the most appropriate to represent the average global temperature over 100 years.

b. A scatterplot will be the most appropriate graph to identify the association between the given two variables.

c. A Pareto chart will be the most appropriate graph to depict the various sources of carbon monoxide.

Step-by-step solution

Given information

Three different types of data are required to be depicted using an appropriate graph.

Discuss the choice of graph

Different types of graphs are constructed to represent different kinds of data.

The analysis of the data becomes easy and meaningful if the correct graphical representation is used to display the data values.

Identify the appropriate graph for time-based data

a.

Here, the average global temperatures are recorded over 100 years, which are to be represented through a graph.

When data values vary over time (months/years), a time-series graph is the most suitable to represent the data.

It best describes the variation/trend in the values that occurs over time.

Thus, a time-series graph will be the most appropriate graph to depict the average temperatures.

Identify the appropriate graph for determining the association 

b.

Here, it is required to investigate the relationship between the average global temperatures and the amount of carbon monoxide emissions.

When the association/relationship between a pair of variables is required to be identified, a scatterplot can be constructed.

The pattern of the observations on the plot is examined to identify if a relationship exists between the two variables.

Thus, a scatterplot will be the most appropriate graph to depict the association between the above two variables.

Identify the appropriate graph for comparing the relative frequency 

c.

Here, five different sources of carbon monoxide emissions are provided. The relative importances of the five sources are required to be determined through a graph.

When the categories of a variable are given, a bar chart is plotted. Precisely, if the relative frequencies are required to be compared for different categories, a Pareto chart is very useful.

The lengths of the bars describe the frequency of each category and help to identify the most frequently occurring category.

Thus, a Pareto chart will be the most appropriate graph to depict the proportion of emissions for each of the five different sources.