91Ó°ÊÓ

Eighty adults were asked to watch a 30 -minute infomercial until the presentation ended or until boredom became intolerable. The following table lists the frequency distribution of the times that these adults were able to watch the infomercial. $$ \begin{array}{lc} \hline \begin{array}{c} \text { Time } \\ \text { (minutes) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Adults } \end{array} \\ \hline 0 \text { to less than } 6 & 16 \\ 6 \text { to less than } 12 & 21 \\ 12 \text { to less than } 18 & 18 \\ 18 \text { to less than } 24 & 11 \\ 24 \text { to less than } 30 & 14 \\ \hline \end{array} $$ Draw two histograms for these data, the first without truncating the frequency axis. In the second case, mark the frequencies on the vertical axis starting with 10 . Briefly comment on the two histograms.

Briefly explain the concept of cumulative frequency distribution. How are the cumulative relative frequencies and cumulative percentages calculated?

The following table, reproduced from Exercise 2.14, gives the frequency distribution of the number of credit cards possessed by 80 adults. $$ \begin{array}{lc} \hline \text { Number of Credit Cards } & \text { Number of Adults } \\ \hline 0 \text { to } 3 & 18 \\ 4 \text { to } 7 & 26 \\ 8 \text { to } 11 & 22 \\ 12 \text { to } 15 & 11 \\ 16 \text { to } 19 & 3 \\ \hline \end{array} $$ a. Prepare a cumulative frequency distribution. b. Calculate the cumulative relative frequencies and cumulative percentages for all classes. c. Find the percentage of these adults who possess 7 or fewer credit cards. d. Draw an ogive for the cumulative percentage distribution. e. Using the ogive, find the percentage of adults who possess 10 or fewer credit cards.

The following table, reproduced from Exercise 2.15, gives the frequency distribution of ages for all 50 employees of a company. $$ \begin{array}{lc} \hline \text { Age } & \text { Number of Employees } \\ \hline 18 \text { to } 30 & 12 \\ 31 \text { to } 43 & 19 \\ 44 \text { to } 56 & 14 \\ 57 \text { to } 69 & 5 \\ \hline \end{array} $$ a. Prepare a cumulative frequency distribution table. b. Calculate the cumulative relative frequencies and cumulative percentages for all classes. c. What percentage of the employees of this company are 44 years of age or older? d. Draw an ogive for the cumulative percentage distribution. e. Using the ogive, find the percentage of employees who are age 40 or younger.

What advantage does preparing a stem-and-leaf display have over grouping a data set using a frequency distribution? Give one example.

The following data give the money (in dollars) spent on textbooks by 35 students during the \(2009-10\) academic year. $$ \begin{array}{lllllllll} 565 & 728 & 470 & 620 & 345 & 368 & 610 & 765 & 550 \\ 845 & 530 & 705 & 490 & 258 & 320 & 505 & 457 & 787 \\ 617 & 721 & 635 & 438 & 575 & 702 & 538 & 720 & 460 \\ 540 & 890 & 560 & 570 & 706 & 430 & 268 & 638 & \end{array} $$ a. Prepare a stem-and-leaf display for these data using the last two digits as leaves. b. Condense the stem-and-leaf display by grouping the stems as \(2-4,5-6\), and \(7-8\).

What is a stacked dotplot, and how is it used? Explain.

Create a dotplot for the following data set. $$ \begin{array}{llllllllll} 1 & 2 & 0 & 5 & 1 & 1 & 3 & 2 & 0 & 5 \\ 2 & 1 & 2 & 1 & 2 & 0 & 1 & 3 & 1 & 2 \end{array} $$

The following data give the numbers of television sets owned by 40 randomly selected households. $$ \begin{array}{rrrrrrrrrr} 1 & 1 & 2 & 3 & 2 & 4 & 1 & 3 & 2 & 1 \\ 3 & 0 & 2 & 1 & 2 & 3 & 2 & 3 & 2 & 2 \\ 1 & 2 & 1 & 1 & 1 & 3 & 1 & 1 & 1 & 2 \\ 2 & 4 & 2 & 3 & 1 & 3 & 1 & 2 & 2 & 4 \end{array} $$ a. Prepare a frequency distribution table for these data using single-valued classes. b. Compute the relative frequency and percentage distributions. c. Draw a bar graph for the frequency distribution. d. What percentage of the households own two or more television sets?

The following data give the amounts spent on video rentals (in dollars) during 2009 by 30 households randomly selected from those who rented videos in 2009. $$ \begin{array}{rrrrrrrrr} 595 & 24 & 6 & 100 & 100 & 40 & 622 & 405 & 90 \\ 55 & 155 & 760 & 405 & 90 & 205 & 70 & 180 & 88 \\ 808 & 100 & 240 & 127 & 83 & 310 & 350 & 160 & 22 \\ 111 & 70 & 15 & & & & & & \end{array} $$ a. Construct a frequency distribution table. Take \(\$ 1\) as the lower limit of the first class and \(\$ 200\) as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. What percentage of the households in this sample spent more than \(\$ 400\) on video rentals in \(2009 ?\)