Question

For each of the five data sets described, answer the following three questions and then use Figure 2.2 (on page 48 ) to select an appropriate graphical display. Question 1: How many variables are in the data set? Question 2: Is the data set categorical or numerical? Question 3: Would the purpose of a graphical display be to summarize the data distribution, to compare groups, or to investigate the relationship between two numerical variables? Data Set 1: To learn about the heights of five-year-old children, the height of each child in a sample of 40 five-year-old children was measured. Data Set 2: To see if there is a difference in car color preferences of men and women, each person in a sample of 100 males and each person in a sample of 100 females was shown pictures of a new model car in five different colors and asked to select which color they would choose if they were to purchase the car. Data Set 3: To learn how GPA at the end of the freshman year in college is related to high school GPA, both high school GPA and freshman year GPA were determined for each student in a sample of 100 students who had just completed their freshman year at a particular college. Data Set 4: To learn how the amount of money spent on a fast-food meal might differ for men and women, the amount spent on lunch at a particular fast-food restaurant was determined for each person in a sample of 50 women and each person in a sample of 50 men. Data Set 5: To learn about political affiliation (Democrat, Republican, Independent, and so on) of students at a particular college, each student in a random sample of 200 students was asked to indicate his or her political affiliation.

Short answer

Data Set 1: One numerical variable, purpose is to summarize data distribution, best graphical display is histogram or box plot. \n Data Set 2: Two categorical variables, purpose is to compare groups, best graphical display is bar chart or pie chart. \n Data Set 3: Two numerical variables, purpose is to investigate relationship, best graphical display is scatterplot. \n Data Set 4: One categorical and one numerical variable, purpose is to compare groups, best graphical display is side by side box plots or multi-series histograms. \n Data Set 5: One categorical variable, purpose is to summarise data distribution, best graphical display is bar chart or pie chart.

Step-by-step solution

Analyze Data Set 1

This dataset contains a single variable (height) and is numerical. The purpose of a graphic would be to summarize the data distribution of heights among five-year-olds. Possible graphics could be histogram or box plot.

Analyze Data Set 2

This dataset contains two variables (gender and color preference), and is categorical. Here, the purpose of a graphical display would be to compare groups (men vs women). Possible graphics could be bar chart or pie chart.

Analyze Data Set 3

This dataset contains two numerical variables (high school GPA and college freshman GPA). The purpose of the graph would be to investigate the relationship between them. A scatterplot would most fit this purpose.

Analyze Data Set 4

This data set contains two variables (gender and lunch expense), one categorical and one numerical. The purpose here is to compare groups (men vs women). Side by side box plots or multi-series histograms can be used.

Analyze Data Set 5

The dataset contains one variable (political affiliation) and is categorical. The purpose here would be to summarize the data distribution. A bar chart or pie chart would fit this purpose.