Solved: A frequency distribution lists the ________ of

Problem 1AYU Define raw data in your own words.

Problem 2AYU A frequency distribution lists the ________ of occurrences of each category of data, while a relative frequency distribution lists the ________ of occurrences of each category of data.

Problem 3AYU In a relative frequency distribution, what should the relative frequencies add up to?

Problem 4AYU What is a bar graph? What is a Pareto chart?

Problem 5AYU Flu Season The pie chart shown, the type we see in USA Today, depicts the approaches people use to avoid getting the flu. ________________ (a) What is the most common approach? What percentage of the population chooses this method? ________________ (b) What is the least used approach? What percentage of the population chooses this method? ________________ (c) What percentage of the population thinks flu shots are the best way to beat the flu?

Problem 6AYU Cosmetic Surgery This USA Today-type chart shows the most frequent cosmetic surgeries for women in 2009. By Anne R. Carey and Suzy Parker, USA Today (a) If women had 1.35 million cosmetic surgeries in 2009, what percent were for tummy tucks? ________________ (b) What percent were for nose reshaping? ________________ (c) How many surgeries are not accounted for in the graph?

Problem 7AYU Internet Users The following Pareto chart represents Internet users in the top 10 countries as of June 2010. (a) Which country had the most Internet users in 2010? ________________ (b) Approximately how many Internet users did the United Kingdom have in 2010? ________________ (c) Approximately how many more users were in China than in Germany in 2010? ________________ (d) How might this graph be misleading?

Problem 9AYU Divorce The following graph represents the results of a survey, conducted in May 2010, in which a random sample of adult Americans was asked, “Please tell me whether you personally believe that in general divorce is morally acceptable or morally wrong.” (a) What percent of the respondents believe divorce is morally acceptable? ________________ (b) If there were 240 million adult Americans in 2010, how many believe that divorce is morally wrong? ________________ (c) If Gallup claimed that the results of the survey indicate that 8% of adult Americans believe that divorce is acceptable in certain situations, would you say this statement is descriptive or inferential? Why?

Problem 8AYU Poverty Every year the U.S. Census Bureau counts the number of people living in poverty. The bureau uses money income thresholds to define poverty, so noncash benefits such as Medicaid and food stamps do not count toward poverty thresholds. For example, in 2009 the poverty threshold for a family of four with two children was $21,756. The bar graph represents the number of people living in poverty in the United States in 2009, by ethnicity. (a) How many whites were living in poverty in 2009? ________________ (b) Of the impoverished, what percent were Hispanic? ________________ (c) How might this graph be misleading?

Identity Theft Identity fraud occurs when someone else’s personal information is used to open credit card accounts, apply for a job, receive benefits, and so on. The following relative frequency bar graph represents the various types of identity theft based on a study conducted by the Federal Trade Commission. (a) Approximately what percentage of identity theft was loan fraud (such as applying for a loan in someone else’s name)? (b) If there were 10 million cases of identity fraud in 2008, how many were credit card fraud (someone uses someone else’s credit card to make a purchase)?

Made in America In a poll conducted July 27-29, 2010, a random sample of 2163 adults (aged 18 and over) was asked, “When you see an ad emphasizing that a product is ‘Made in America’, are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?” The results of the survey are presented in the side-by-side bar graph. (a) What proportion of 18- to 34-year-old respondents are more likely to buy when made in America? What proportion of 35- to 44-year-old respondents are more likely to buy when made in America? (b) Which age group has the greatest proportion who are more likely to buy when made in America? (c) Which age group has a majority of respondents who are less likely to buy when made in America? (d) What is the apparent association between age and likelihood to buy when made in America?

Problem 12AYU Desirability Attributes In a poll conducted July 27-29, 2010, a random sample of 2163 adults (aged 18 and over) was asked, “Given a choice of the following, which one would you most want to be?” The results of the survey are presented in the side-by-side bar graph. (a) What proportion of males would like to be richer? What proportion of females would like to be richer? ________________ (b) Which attribute do females desire more than males? ________________ (c) Which attribute do males prefer over females two-to-one? ________________ (d) Which attribute do males and females desire in equal proportion?

College Survey In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat belt when riding in a car driven by someone else?” The frequencies were as follows: (a) Construct a relative frequency distribution. (b) What percentage of respondents answered “Always”? (c) What percentage of respondents answered “Never” or “Rarely”? (d) Construct a frequency bar graph. (e) Construct a relative frequency bar graph. (f) Construct a pie chart. (g) Suppose that a representative from the Centers for Disease Control says, “52.7% of all college students always wear a seat belt.” Is this a descriptive or inferential statement?

College Survey In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat belt when driving a car?” The frequencies were as follows: Response Frequency I do not drive a car 249 Never 118 Rarely 249 Sometimes 345 Most of the time 716 Always 3093 (a) Construct a relative frequency distribution. (b) What percentage of respondents answered “Always”? (c) What percentage of respondents answered “Never” or “Rarely”? (d) Construct a frequency bar graph. (e) Construct a relative frequency bar graph. (f) Construct a pie chart. (g) Compute the relative frequencies of “Never,” “Rarely,” “Sometimes,” “Most of the time,” and “Always,” excluding those that do not drive. Compare with those in Problem. What might you conclude? (h) Suppose that a representative from the Centers for Disease Control says, “2.5% of the college students in this survey responded that they never wear a seat belt.” Is this a descriptive or inferential statement? College Survey In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat belt when riding in a car driven by someone else?” The frequencies were as follows: Response Frequency Never 125 Rarely 324 Sometimes 552 Most of the time 1257 Always 2518 (a) Construct a relative frequency distribution. (b) What percentage of respondents answered “Always”? (c) What percentage of respondents answered “Never” or “Rarely”? (d) Construct a frequency bar graph. (e) Construct a relative frequency bar graph. (f) Construct a pie chart. (g) Suppose that a representative from the Centers for Disease Control says, “52.7% of all college students always wear a seat belt.” Is this a descriptive or inferential statement?

Problem 15AYU Use the Internet? The Gallup organization conducted a survey in which 1025 randomly sampled adult Americans were asked, “How much time, if at all, do you personally spend using the Internet—more than 1 hour a day, up to 1 hour a day, a few times a week, a few times a month or less, or never?” The results of the survey were as follows: (a) Construct a relative frequency distribution. ________________ (b) What proportion of those surveyed never use the Internet? ________________ (c) Construct a frequency bar graph. ________________ (d) Construct a relative frequency bar graph. ________________ (e) Construct a pie chart. ________________ (f) A local news broadcast reported that 37% of adult Americans use the Internet more than 1 hour a day. What is wrong with this statement?

Problem 16AYU Dining Out In a poll taken in April 2010, a sample of 521 adults was asked, “How often do you dine out?” The results of the survey are given in the table on the following page. (a) Construct a relative frequency distribution. ________________ (b) What proportion of those surveyed dine out once or twice a week? ________________ (c) Construct a frequency bar graph. ________________ (d) Construct a relative frequency bar graph.

Problem 17AYU Texting A survey of U.S. adults and teens (ages 12–17) was administered by Pew Research April 29-May 30, 2010, to determine the number of texts sent in a single day. (a) Construct a relative frequency distribution for adults. ________________ (b) Construct a relative frequency distribution for teens. ________________ (c) Construct a side-by-side relative frequency bar graph. ________________ (d) Compare the texting habits of adults and teens.

Problem 18AYU Educational AttainmentOn the basis of the 2009 Current Population Survey, there were 94.5 million males and 102 million females 25 years old or older in the United States. The educational attainment of the males and females was as follows: (a) Construct a relative frequency distribution for males. ________________ (b) Construct a relative frequency distribution for females. ________________ (c) Construct a side-by-side relative frequency bar graph. ________________ (d) Compare each gender’s educational attainment. Make a conjecture about the reasons for the differences.

Problem 19AYU Dream Job A survey of adult men and women asked, “Which one of the following jobs would you most like to have?” The results of the survey are shown in the table. (a) Construct a relative frequency distribution for men and women. ________________ (b) Construct a side-by-side relative frequency bar graph. ________________ (c) What are the apparent differences in gender as it pertains to this question?

Problem 20AYU Car Color DuPont Automotive is a major supplier of paint to the automotive industry. A survey of 100 randomly selected autos in the luxury car segment and 100 randomly selected autos in the sports car segment that were recently purchased yielded the following colors. (a) Construct a relative frequency distribution for each car type. ________________ (b) Draw a side-by-side relative frequency bar graph. ________________ (c) Compare the colors for the two car types. Make a conjecture about the reasons for the differences.

Problem 21AYU Olympic Gold Medals in Hockey The table shows the gold © medal winners in hockey in the Winter Olympics since 1920. (a) Construct a frequency distribution. ________________ (b) Construct a relative frequency distribution. ________________ (c) Construct a frequency bar graph. ________________ (d) Construct a relative frequency bar graph. ________________ (e) Construct a pie chart.

Problem 22AYU Bachelor Party In a survey conducted by Opinion Research, participants were asked, “If you had an ‘X-rated’ bachelor party, would you tell your fiancé all, edit details, or say nothing?” The following data are based on their results. (a) Construct a frequency distribution. ________________ (b) Construct a relative frequency distribution. ________________ (c) Construct a frequency bar graph. ________________ (d) Construct a relative frequency bar graph. ________________ (e) Construct a pie chart.

Problem 23AYU Favorite Day to Eat Out A survey was conducted by Wakefield Research in which participants were asked to disclose their favorite night to order takeout for dinner. The following data are based on their results. (a) Construct a frequency distribution. ________________ (b) Construct a relative frequency distribution. ________________ (c) If you own a restaurant, which day would you purchase an advertisement in the local newspaper? Are there any days you would avoid purchasing advertising space? ________________ (d) Construct a frequency bar graph. ________________ (e) Construct a relative frequency bar graph. ________________ (f) Construct a pie chart.

Blood Type A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown: (a) Construct a frequency distribution. (b) Construct a relative frequency distribution. (c) According to the data, which blood type is most common? (d) According to the data, which blood type is least common? (e) Use the results of the sample to conjecture the percentage of the population that has type O blood. Is this an example of descriptive or inferential statistics? (f) Contact a local hospital and ask them the percentage of the population that is blood type O. Why might the results differ? (g) Draw a frequency bar graph. (h) Draw a relative frequency bar graph. (i) Draw a pie chart.

Foreign Language According to the Modern Language Association, the number of college students studying foreign language is increasing. The following data represent the foreign language being studied based on a simple random sample of 30 students learning a foreign language. (a) Construct a frequency distribution. (b) Construct a relative frequency distribution. (c) Construct a frequency bar graph. (d) Construct a relative frequency bar graph. (e) Construct a pie chart.

President’s State of Birth The following table lists the presidents of the United States (as of October 2010) and their state of birth. (a) Construct a frequency bar graph for state of birth. (b) Which state has yielded the most presidents? (c) Explain why the answer obtained in part (b) may be misleading.

Highest Elevation The following data represent the land area and highest elevation for each of the seven continents. (a) Would it make sense to draw a pie chart for land area? Why? If so, draw a pie chart. (b) Would it make sense to draw a pie chart for the highest elevation? Why? If so, draw a pie chart.

Problem 28AYU StatCrunch Survey Choose a qualitative variable from the Sullivan StatCrunch survey data set and summarize the variable. Click here for Survey ----> StatCrunch Survey

Stat Crunch Survey Choose a qualitative variable from the Sullivan StatCrunch survey data set and summarize the variable by gender. What are the differences, if any, in the value of the variable for males and females?

Putting It Together: Online Homework Keeping students engaged in the learning process greatly increases their chance of success in a course. Traditional lecture-based math instruction has been giving way to a more student-engaged approach where students interact with the teacher in class and receive immediate feedback to their responses. The teacher presence allows students, when incorrect in a response, to be guided through a solution and then immediately be given a similar problem to attempt. A researcher conducted a study to investigate whether an online homework system using an attempt-feedback- reattempt approach improved student learning over traditional pencil-and-paper homework. The online homework system was designed to increase student engagement outside class, something commonly missing in traditional pencil-and-paper assignments, ultimately leading to increased learning. The study was conducted using two first-semester calculus classes taught by the researcher in a single semester. One class was assigned traditional homework and the other was assigned online homework that used the attempt-feedback-reattempt approach. The summaries on the next page are based on data from the study. (a) What is the research objective? (b) Is this study an observational study or experiment? (c) Give an example of how the researcher attempted to control variables in the study. (d) Explain why assigning homework type to entirely separate classes can confound the conclusions of the study. (e) For the data in the table, (i) identify the variables, (ii) indicate whether the variables are qualitative or quantitative, and (iii) for each quantitative variable, indicate whether the variable is discrete or continuous. (f) What type of variable is letter grade? What level of measurement is letter grade? Do you think presenting the data in a table from A to F would be a better representation of the data than presenting it in a graph? (g) What type of graph is displayed? (h) Could the data in the graph be presented in a pie chart? If so, what is the “whole”? If not, why not? (i) Considering the students with no prior college experience, how might the table and the graph generate conflicting conclusions?

Problem 31AYU When should relative frequencies be used when comparing two data sets? Why?

Suppose you need to summarize ordinal data in a bar graph. How would you arrange the categories of data on the horizontal axis? Is it possible to make the order of the data apparent in a pie chart?

Describe the circumstances in which a bar graph is preferable to a pie chart. When is a pie chart preferred over a bar graph? Are there circumstances in which a pie chart cannot be drawn, but a bar graph could be drawn? What are these circumstances?

Consider the information in the chart shown next, which is in the USA Today style of the graph. Could the information provided be organized into a pie chart? Why or why not?