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Chapter 2: Problem 62

The article "Where College Students Buy Textbooks" (USA TODAY, October 14,2010 ) gave data on where students purchased books. The accompanying frequency table summarizes data from a sample of 1152 full-time college students. Construct a bar chart to summarize the data distribution. Write a few sentences commenting on where students are buying textbooks.

Short Answer

Expert verified
Based on the constructed bar chart, describe the trend in sources where students buy their textbooks.

Step by step solution

01

Construct the Bar Chart

Based on the frequency table provided, you will need to create a bar chart. For each category (store, website, etc.), create a vertical bar with a height proportional to the number of students who buy the textbooks at that source. You should also include labels for each category and the frequency count for each bar to make it easy for the reader to interpret the chart. Additionally, include a title for the chart, axis labels, and scale marks to indicate the number of students.
02

Comment on the Bar Chart

Now that the bar chart is complete, let's make some observations: - Determine which source(s) is the most popular for purchasing textbooks - Identify if there are any significant differences between different sources - Note any interesting or unexpected trends in the data For instance, if the bar chart shows that the majority of college students buy their textbooks online, this could indicate that students are looking for cheaper alternatives or convenience in purchasing textbooks online rather than going to a physical store. Also, if there are any sources with significantly low frequencies, it could imply that students are less likely to utilize that source for buying textbooks, which might be interesting to the college or that source. Keep in mind, the observations made from the bar chart are based on the sample data, and might not exactly represent the whole college student population.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bar Chart Construction
Bar charts are a simple yet powerful way to visualize categorical data. They help us see the frequency of each category at a glance. To construct a bar chart for student textbook purchases, you start by identifying the categories such as bookstores, online retailers, etc.
Each category will have its own vertical bar. The height of the bar represents the number of students who purchased from that category.
Make sure to include labels on each bar to clarify what it represents. Additionally, axis labels are crucial鈥攖hey help to understand what the numbers represent.
  • The vertical axis (Y-axis) typically indicates the frequency of purchases (e.g., number of students).
  • The horizontal axis (X-axis) lists the categories (e.g., bookstore, website).

Don鈥檛 forget to add a title to your chart. It provides context, so viewers instantly know what the chart is about. Good practice also involves including a scale to show the increments used for frequency counts.
Frequency Table Analysis
A frequency table is a tool used to show how often different values occur in a data set. It鈥檚 a way to organize raw data into a summary. This is especially useful for understanding large data sets鈥攍ike the one provided about college textbook purchases.
The table lists the sources where books are purchased and the number of students who bought textbooks from each.
Each row in the table corresponds to a specific source of textbooks.
  • The number next to each source is the frequency, indicating how many students made purchases there.
  • By studying these numbers, you can quickly see which sources are most or least popular.
  • Patterns or trends might become apparent, such as a high number of online purchases.

Frequency tables are not just about counting; they provide a compact way to analyze data before visualizing it with a chart. They are the foundation for creating more detailed analysis or visualizations.
Educational Data Interpretation
Interpreting data in an educational context involves analyzing information to draw conclusions or make observations. For the student textbook purchase data, interpretation means looking at where and how students prefer to buy textbooks.
This involves several tasks:
  • Identify which purchasing sources are used most frequently. High frequencies often suggest popularity or convenience.
  • Look for anomalies or surprising trends, such as an uncommon source being surprisingly popular or a typically popular source being ignored.

Using the bar chart, you can easily compare different purchasing sources at a glance. This comparison helps schools or bookstores understand student preferences, potentially adjusting their strategies accordingly.
Data interpretation should consider potential biases or sample limitations. Even well-collected data is only as good as the sample it represents鈥攚hich is often only a portion of a larger population.

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Most popular questions from this chapter

For each of the five data sets described, answer the following three questions and then use Figure 2.2 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.

The report "2013 International Bedroom Poll: Summary of Findings" describes a survey of 251 adult Americans conducted by the National Sleep Foundation (www.sleep foundation.org/sites/default/files/RPT495a.pdf, retrieved April 15,2017 ). Participants in the survey were asked how often they change the sheets on their bed and were asked to respond with one of the following categories: more than once a week, once a week, every other week, every three weeks, or less often than every three weeks. For this group, \(10 \%\) responded more than once a week, \(53 \%\) responded once a week, \(26 \%\) responded every other week, \(5 \%\) responded every three weeks, and \(6 \%\) responded less often than every three weeks. a. Use the given information to make a relative frequency distribution for the responses to the question. b. Summarize the given information by constructing a bar chart. c. The report also summarized data from 250 adults in Japan. For this group, \(11 \%\) responded more than once a week, \(30 \%\) responded once a week, \(22 \%\) responded every other week, \(9 \%\) responded every three weeks, and \(28 \%\) responded less often than every three weeks. Construct a comparative bar chart that will allow you to compare the response distributions for the U.S. sample and the Japan sample. Comment on similarities and differences between the distributions for these two countries.

The report "Trends in Education 2010: Community Colleges" (www.collegeboard.com/trends) included the accompanying information on student debt for students graduating with an AA degree from a public community college in 2008 . $$\begin{array}{|lc|}\hline \text { Debt } & \text { Relative Frequency } \\\\\hline \text { None } & 0.62 \\\\\text { Less than } \$ 10,000 & 0.23 \\ \text { Between } \$ 10,000 \text { and } \$ 20,000 & 0.10 \\\\\text { More than } \$ 20,000 & 0.05 \\\\\hline\end{array}$$ a. Use the given information to construct a bar chart. b. Comment on student debt for public community college graduates.

For each of the five data sets described, answer the following three questions and then use Figure 2.2 to select an appropriate graphical display. Question 1: How many variables are in the data set? Question 2: Are the variables in 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 reason parents believe their child is heavier than the recommended weight for children of the same age, each person in a sample of parents of overweight children was asked what they thought was the most important contributing factor. Possible responses were lack of exercise, easy access to junk food, unhealthy diet, medical condition, and other. Data Set 2: To compare commute distances for full-time and part-time students at a large college, commute distance (in miles) was determined for each student in a random sample of 50 full-time students and for each student in a random sample of 50 part-time students. Data Set 3: To learn about how number of years of education and income are related, each person in a random sample of 500 residents of a particular city was asked how many years of education he or she had completed and what his or her annual income was. Data Set 4: To see if there is a difference between faculty and students at a particular college with respect to how they commute to campus (drive, walk, bike, and so on), each person in a random sample of 50 faculty members and each person in a random sample of 100 students was asked how he or she usually commutes to campus. Data Set 5: To learn about how much money students at a particular college spend on textbooks, each student in a random sample of 200 students was asked how much he or she spent on textbooks for the current semester.

An exam is given to students in an introductory statistics course. Comment on the expected shape of the histogram of scores if: a. the exam is very easy b. the exam is very difficult c. half the students in the class have had calculus, the other half have had no prior college math courses, and the exam emphasizes higher-level math skills Explain your reasoning in each case.
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