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Section 1
Graphs, Pareto Diagrams, and Stemandleaf Displays
a. How long do you typically spend on grooming per day?b. How do you think you compare to the 50,000 college students in "Students, Here's Looking at You" on page $32 ?$c. How do you think you compare to all college students? What are the similarities? What are the differences?
Students in an online statistics course were asked how many different Internet activities they engaged in during a typical week. The following data show the number of activities:$$\begin{array}{rrrrrrrrrrrrrr}\hline 6 & 7 & 3 & 6 & 9 & 10 & 8 & 9 & 9 & 6 & 4 & 9 & 4 & 9 \\4 & 2 & 3 & 5 & 13 & 12 & 4 & 6 & 4 & 9 & 5 & 6 & 9 & \\11 & 5 & 6 & 5 & 3 & 7 & 9 & 6 & 5 & 12 & 2 & 6 & 9 & \\\hline\end{array}$$a. If you were asked to present these data, how would you organize and summarize them?b. How many different Internet activities did you engage in last week?c. How do you think you compare to the 40 Internet users in the sample above?
As a statistical graph the circle graph has limitations. Examine the circle graph in Figure 2.1 and the bar graph in Figure 2.2.a. What information do they both demonstrate?b. What information is shown in the circle graph that cannot be shown in the bar graph?c. "Generally speaking, the bar graph is a better choice for use than the circle graph." Justify this statement.
Results from a Self.com poll on "What is your top cold-weather beauty concern?" were reported in the December 2008 issue of Self magazine: Dry skin $-57 \%$ Chapped lips $-25 \% ;$ Dull hair $-10 \% ;$ Rough feet $-8 \%$a. Construct a pie chart showing the top cold-weather beauty concerns.b. Construct a bar graph showing the top cold-weather beauty concerns.c. In your opinion, does the pie chart in part a or the bar graph in part b result in a better representation of the information? Explain.
American Payroll Association got a big response to this question about company dress code: "The current dress code at my company is $\ldots "$Final results: a. A little too relaxed $-27 \%$b. A little too formal- $15 \%$c. Just right $-58 \%$Most people mentioned the importance of "comfort" in their explanations. The vast majority of respondents were very happy with their company's dress code or policy.a. Construct a circle graph depicting this information. Label completely.b. Construct a bar graph depicting this same information. Label completely.c. Compare the previous two graphs, describing what you see in each one now that the graphs have been drawn and completely labeled. Do you get the same impression about these people's feelings from both graphs? Does one emphasize anything the other one does not?
How much more young Americans, 17- to 28-year-olds, say they are willing to pay for an environmentally friendly vehicle was reported in a USA Today Snapshot on February 5,2009: A lot more $-11 \% ;$ Somewhat more $-$ $36 \% ;$ Slightly more $-33 \% ;$ Would not pay more $-20 \%$.a. Name the variable of interest.b. Identify the type of variable.c. Construct a pie chart showing how young Americans feel about paying for an environmentally friendly vehicle.d. Construct a bar graph showing how young Americans feel about paying for an environmentally friendly vehicle.e. In your opinion, which graph is the better representation of the information? Why? Explain.
The number of points scored by the winning teams on October $28,2008,$ the opening night of the $2008-2009$ NBA season, are listed below.$$\begin{array}{lccc}\hline \text { Team } & \text { Boston } & \text { Chicago } & \text { LA Lakers } \\\text { Score } & 90 & 108 & 96 \\\hline\end{array}$$a. Draw a bar graph of these scores using a vertical scale ranging from 80 to 110 .b. Draw a bar graph of the scores using a vertical scale ranging from 50 to $110 .$c. In which bar graph does it appear that the NBA scores vary more? Why?d. How could you create an accurate representation of the relative size and variation between these scores?
The American Community Survey gathers data for population, demographic, and housing unit estimates. The Census Bureau then uses the data to produce and disseminate official estimates of housing units for states and counties. The $2005-2007$ housing unit estimates for the town of Webster in New York State estimates are listed here.a. Construct a pie chart of this breakdown.b. Construct a bar graph of this breakdown.c. Compare the two graphs you constructed in parts a and $b ;$ which one seems to be the most informative? Explain why.
Cleaning behind furniture and washing windows top the list of spring-cleaning chores, according to the Soap and Detergent Association's (SDA) latest National Spring Cleaning Survey. International Communications Research (ICR) completed the independent consumer research study in January/February $2008 .$ The initial survey question was asked of 1013 American adults $(507 \text { men and } 506$ women).Question asked: Do you regularly engage in spring cleaning?$\begin{array}{cl}\text { Results: } & \text { Yes-77\% } \\ & \text { No-23\% }\end{array}$More women $(86 \%)$ than men (68\%) spring-clean.a. Construct and fully label a bar graph showing the results from all adults surveyed.b. Construct and fully label a bar graph showing the results comparing the women and men separately.c. Discuss the graphs in parts a and b, being sure to comment on how accurately, or not, the graphs picture the information.
Credit card companies sometimes provide their customers with a year-end summary. The year-end summary provides a comprehensive, easy-toread report summarizing the transactions into a several categories. Using table on the top of page 44 :a. Explain the meaning of the table entries of $\$ 64.02$ and $\$(100.55)$.b. Explain the meaning of the totals $\$ 1,159.19$ and $\$ 298.42$.c. Use a pie chart to display the year-end category totals using both dollar amounts and percentages. Be sure to label completely.d. Use a bar graph to display the monthly totals. Be sure to label completely.
A shirt inspector at a clothing factory categorized the last 500 defects as: $67-$ missing button; $153-$ bad seam; 258 - improperly sized; 22 - fabric flaw. Construct a Pareto diagram for this information.
Definitions of e-mail spam, or junk e-mail, typically include the idea that the e-mail is unsolicited and sent in bulk. Beginning in the early 1990 s the amount of email spam grew steadily until recently, with a total volume of over 100 billion e-mails per day in April $2008 .$ The amount being received has begun to decrease due to the use of better filtering software. As unbelievable as it might be, fewer than 200 spammers send about $80 \%$ of all spam. The chart below lists the percentage of e-mail spam relayed by each country in 2007.\begin{array}{lc}\text { Country } & \text { Percentage } \\\hline \text { Brazil } & 4.1 \\\text { China } & 8.4 \\\text { EU } & 17.9 \\\text { France } & 3.3 \\\text { Germany } & 4.2 \\\text { India } & 2.5 \\\text { Italy } & 2.8 \\\text { Poland } & 4.8 \\\text { Russia } & 3.1 \\\text { S Korea } & 6.5 \\\text { Turkey } & 2.9 \\\text { UK } & 2.8 \\\text { US } & 19.6 \\\hline\end{array}a. Construct a bar graph of this information with the percentages in declining order.b. Explain why a Pareto diagram of this information cannot be constructed.
A study completed by International Communications Research for the Soap and Detergent Association (SDA) lists the item Americans say they would be most willing to give up in order to be able to hire someone to do their spring cleaning. The most popular response was $\$ 100(29 \%),$ followed by dining out for a month $(26 \%),$ concert tickets $(19 \%),$ a weekend trip (9\%), and other ( $17 \%$ ).a. Construct a Pareto diagram displaying this information.b. Because of the size of the "other" category, the Pareto diagram may not be the best graph to use.Explain why, and describe what additional information is needed to make the Pareto diagram more appropriate.
What NOT to get them on Valentine's Day!a. Draw a bar graph picturing the percentages of "Presents not wanted."b. Draw a Pareto diagram picturing the "Presents not wanted."c. If you want to be $80 \%$ sure you did not get your Valentine something unwanted, what should you avoid buying? How does the Pareto diagram show this?d. If 300 adults are to be surveyed, what frequencies would you expect to occur for each unwanted item listed on the graphic?
The final-inspection defect report for assembly lineA12 is reported in a Pareto diagram.a. What is the total defect count in the report?b. Verify the $30.0 \%$ listed for "Scratch."c. Explain how the "cum \% for bend" value of $90.7 \%$ was obtained and what it means.d. Management has given the production line the goal of reducing their defects by $50 \% .$ What two defects would you suggest they give special attention to in working toward this goal? Explain.
Some cleaning jobs are disliked more than others. According to the July $17,2009,$ USA Today Snapshot on a survey of women by Consumer Reports National Research Center, the cleaning tasks women dislike the most are presented in the following Pareto diagram.a. How many total women were surveyed?b. Verify the $15 \%$ listed for "Cleaning refrigerator."c. Explain how the "cum \% for dusting" value of $80 \%$ was obtained and what it means.d. What three tasks would make no more than $75 \%$ of the women surveyed happy if those tasks were eliminated?
The American Time Use Survey presented at the beginning of the chapter outlined the time use of an average weekday for full-time university and college students.a. Construct a pareto diagram depicting the average time use for full-time college students.b. What activities seem to make up $75 \%$ of a college student's day?
The Office of Aviation Enforcement and Proceedings, U.S. Department of Transportation, posted this table listing the number of consumer complaints against top U.S. airlines by complaint category.a. Construct a Pareto diagram depicting this information.b. What complaints would you recommend the airlines pay the most attention to correcting if they want to have the most effect on the overall number of complaints? Explain how the Pareto diagram from part a demonstrates the validity of your answer.
The number of points scored during each game by a high school basketball team last season was as follows: 56,54,61,71,46,61,55,68,60,66,54,61$52,36,64,51 .$ Construct a dotplot of these data.
In a July $8,2009, U S A$ Today article titled "Couples saying 'I don't' to expensive weddings," the cutbacks may not be extending to the number of attendants. In a survey of recent weddings, the number of bridesmaids was as follows:a. Construct a dotplot of these data.b. What are the most common numbers of bridesmaids? How does the dotplot show this?
Shown below are the heights (in inches) of the basketball players who were the first-round picks by National Basketball Association professional teams for 2009.$$\begin{array}{llllllllll}\hline 82 & 86 & 76 & 77 & 75 & 72 & 75 & 81 & 78 & 74 \\77 & 77 & 81 & 81 & 82 & 80 & 76 & 72 & 74 & 74 \\73 & 82 & 80 & 84 & 74 & 81 & 80 & 77 & 74 & 78 \\\hline\end{array}$$a. Construct a dotplot of the heights of these players.b. Use the dotplot to uncover the shortest and the tallest players.c. What is the most common height and how many players share that height?d. What feature of the dotplot illustrates the most common height?
The table lists the median house selling prices for the 20 suburbs of Rochester. New York, as Iisted in the July $18,2009,$ Democrat \& Chronicle.a. Construct a dotplot of these data.b. Describe the distribution displayed by the dotplot found in part a.
Delco Products, a division of General Motors, produces commutators designed to be $18.810 \mathrm{mm}$ in overall length. (A commutator is a device used in the electrical system of an automobile.) The following sample of 35 commutator lengths was taken while monitoring the manufacturing process:$$\begin{array}{lllllll}\hline 18.802 & 18.810 & 18.780 & 18.757 & 18.824 & 18.827 & 18.825 \\18.809 & 18.794 & 18.787 & 18.844 & 18.824 & 18.829 & 18.817 \\18.785 & 18.747 & 18.802 & 18.826 & 18.810 & 18.802 & 18.780 \\18.830 & 18.874 & 18.836 & 18.758 & 18.813 & 18.844 & 18.861 \\18.824 & 18.835 & 18.794 & 18.853 & 18.823 & 18.863 & 18.808 \\\hline\end{array}$$Use a computer to construct a dotplot of these data values.
A computer was used to construct this dotplot below.a. How many data values are shown?b. List the values of the five smallest data.c. What is the value of the largest data item?d. What value occurred the greatest number of times? How many times did it occur?
Construct a stem-and-leaf display of the number of points scored during each basketball game last season:$$\begin{array}{ccccccc}56 & 54 & 61 & 71 & 46 & 61 & 55 & 68 \\60 & 66 & 54 & 61 & 52 & 36 & 64 & 51\end{array}$$
NO QUESTION
The amounts shown here are the fees charged by Quik Delivery for the 40 small packages it delivered last Thursday afternoon:$$\begin{array}{llllllllll}\hline 4.03 & 3.56 & 3.10 & 6.04 & 5.62 & 3.16 & 2.93 & 3.82 & 4.30 & 3.86 \\4.57 & 3.59 & 4.57 & 6.16 & 2.88 & 5.03 & 5.46 & 3.87 & 6.81 & 4.91 \\3.62 & 3.62 & 3.80 & 3.70 & 4.15 & 2.07 & 3.77 & 5.77 & 7.86 & 4.63 \\4.81 & 2.86 & 5.02 & 5.24 & 4.02 & 5.44 & 4.65 & 3.89 & 4.00 & 2.99 \\\hline\end{array}$$a. Construct a stem-and-leaf display.b. Based on the stem-and-leaf display, describe the distribution of the data.
One of the many things the U.S. Census Bureau reports to the public is the increase in population for various geographic areas within the country. The percent of increase in population for the 24 fastest-growing counties in the United States from July $1,2006,$ to July 1, $2007,$ is listed in the accompanying table.a. Construct a stem-and-leaf display.b. Based on the stem-and-leaf display, describe the distribution of the data.
Given the following stem-and-leaf display:a. What is the meaning of "Leaf Unit $=0.010^{\prime \prime} ?$b. How many data are shown on this stem-and-leaf display?c. List the first four data values.d. What is the column of numbers down the left-hand side of the figure?
A term often used in solar energy research is heating-degree-days. This concept is related to the difference between an indoor temperature of $65^{\circ} \mathrm{F}$ and the average outside temperature for a given day. An average outsidetemperature of $5^{\circ} \mathrm{F}$ gives 60 heating-degree-days. The annual heating-degree-day normals for several Nebraska locations are shown on the accompanying stem-and-leaf display constructed using MINITAB.a. What is the meaning of "Leaf Unit $=10^{\text {"'2 }}$b. List the first four data values.c. List all the data values that occurred more thanonce.