Question

For each of the five data sets described, answer the following three questions and then use Figure 2.2 (on page 48 ) to choose an appropriate graphical display for summarizing the data. 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 the 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 credit card debt of students at a college, the financial aid office asks each student in a random sample of 75 students about his or her amount of credit card debt. Data Set 2: To learn about how number of hours worked per week and number of hours spent watching television in a typical week are related, each person in a sample of size 40 was asked to keep a log of hours worked and hours spent watching television for one week. At the end of the week, each person reported the total number of hours spent on each activity. Data Set 3: To see if satisfaction level differs for airline passengers based on where they sit on the airplane, all passengers on a particular flight were surveyed at the end of the flight. Passengers were grouped based on whether they sat in an aisle seat, a middle seat, or a window seat. Each passenger was asked to indicate his or her satisfaction with the flight by selecting one of the following choices: very satisfied, satisfied, dissatisfied, and very dissatisfied. Data Set 4: To learn about where students purchase textbooks, each student in a random sample of 200 students at a particular college was asked to select one of the following responses: campus bookstore, off-campus bookstore, purchased all books online, or used a combination of online and bookstore purchases. Data Set 5 : To compare the amount of money men and women spent on their most recent haircut, each person in a sample of 20 women and each person in a sample of 20 men was asked how much was spent on his or her most recent haircut.

Short answer

Dataset 1: One numerical variable, a Histogram or Box plot. Dataset 2: Two numerical variables, a Scatter plot. Dataset 3: Two categorical variables, a Bar chart or Pie chart. Dataset 4: One categorical variable, a Bar chart or Pie chart. Dataset 5: One categorical and one numerical variable, a Side-by-side Box plot.

Step-by-step solution

Analysing Dataset 1

There is one variable in Dataset 1 which is the 'credit card debt' of students. The type of data is numerical as the 'credit card debt' is expressed in dollars. The purpose of the graphical display would be to summarize the data distribution, thus a Histogram or Box plot would be most appropriate for this case.

Analysing Dataset 2

There are two variables in Dataset 2: 'number of hours worked' and 'number of hours spent watching television'. These are numerical variables since they are expressed in hours. Since the purpose is to investigate the relationship between two numerical variables, a Scatter plot would be most suitable for this data set.

Analysing Dataset 3

In Dataset 3, we have two variables: 'seat type' and 'passenger satisfaction', which are categorical. The purpose of the graphical display would be to compare groups, as we need to see if satisfaction level differs based on seat type. Therefore, a Bar chart or Pie chart would be the most applicable.

Analysing Dataset 4

Dataset 4 comprises of one variable: 'place where textbooks are purchased'. This data is categorical. The purpose of the graphical display would be to summarize the data distribution. Hence, a Bar chart or Pie chart would work best for this scenario.

Analysing Dataset 5

In Dataset 5, we have two variables: 'gender' and 'amount spent on a haircut'. The 'amount spent on a haircut' is numerical whereas 'gender' is categorical. The purpose of the graphical display would be to compare groups - men and women. Consequently, a Side-by-side Box plot would be the most suited.