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How are the relative frequencies and percentages of categories obtained from the frequencies of categories? Illustrate with the help of an example.

In the past few years, many states have built casinos and many more are in the process of doing so. Forty adults were asked if building casinos is good for society. Following are the responses of these adults, where \(\mathrm{G}\) stands for good, B indicates bad, and I means indifferent or no answer. $$ \begin{array}{lllllllll} \text { B } & \text { G } & \text { B } & \text { B } & \text { I } & \text { G } & \text { B } & \text { I } & \text { B } & \text { B } \\ \text { G } & \text { B } & \text { B } & \text { G } & \text { B } & \text { B } & \text { B } & \text { G } & \text { G } & \text { I } \\ \text { B } & \text { G } & \text { B } & \text { B } & \text { I } & \text { G } & \text { G } & \text { G } & \text { B } & \text { B } \\ \text { I } & \text { G } & \text { B } & \text { B } & \text { B } & \text { G } & \text { G } & \text { B } & \text { B } & \text { G } \end{array} $$ a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of the adults in this sample said building casinos is good? d. What percentage of the adults in this sample said building casinos is bad or were indifferent? e. Draw a bar graph for the frequency distribution. f. Draw a pie chart for the percentage distribution. g. Make a Pareto chart for the percentage distribution.

The following data show the method of payment by 16 customers in a supermarket checkout line. Here, \(\mathrm{C}\) refers to cash, CK to check, \(\mathrm{CC}\) to credit card, \(\mathrm{D}\) to debit card, and \(\mathrm{O}\) stands for other. $$ \begin{array}{llllllll} \text { C } & \text { CK } & \text { CK } & \text { C } & \text { CC } & \text { D } & \text { O } & \text { C } \\ \text { CK } & \text { CC } & \text { D } & \text { CC } & \text { C } & \text { CK } & \text { CK } & \text { CC } \end{array} $$ a. Construct a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. Draw a pie chart for the percentage distribution.

How are the relative frequencies and percentages of classes obtained from the frequencies of classes? Illustrate with the help of an example.

A local gas station collected data from the day's receipts, recording the gallons of gasoline each customer purchased. The following table lists the frequency distribution of the gallons of gas purchased by all customers on this one day at this gas station. $$ \begin{array}{lc} \hline \text { Gallons of Gas } & \text { Number of Customers } \\ \hline 0 \text { to less than } 4 & 31 \\ 4 \text { to less than } 8 & 78 \\ 8 \text { to less than } 12 & 49 \\ 12 \text { to less than } 16 & 81 \\ 16 \text { to less than } 20 & 117 \\ 20 \text { to less than } 24 & 13 \\ \hline \end{array} $$ a. How many customers were served on this day at this gas station? b. Find the class midpoints. Do all of the classes have the same width? If so, what is this width? If not, what are the different class widths? c. Prepare the relative frequency and percentage distribution columns. d. What percentage of the customers purchased 12 gallons or more? e. Explain why you cannot determine exactly how many customers purchased 10 gallons or less. f. Prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions using the given table.

The following data give the one-way commuting times (in minutes) from home to work for a random sample of 50 workers. $$ \begin{array}{llllllllll} 23 & 17 & 34 & 26 & 18 & 33 & 46 & 42 & 12 & 37 \\ 44 & 15 & 22 & 19 & 28 & 32 & 18 & 39 & 40 & 48 \\ 16 & 11 & 9 & 24 & 18 & 26 & 31 & 7 & 30 & 15 \\ 18 & 22 & 29 & 32 & 30 & 21 & 19 & 14 & 26 & 37 \\ 25 & 36 & 23 & 39 & 42 & 46 & 29 & 17 & 24 & 31 \end{array} $$ a. Construct a frequency distribution table using the classes \(0-9\), \(10-19,20-29,30-39\), and \(40-49 .\) b. Calculate the relative frequency and percentage for each class. c. Construct a histogram for the percentage distribution made in part b. d. What percentage of the workers in this sample commute for 30 minutes or more? e. Prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions using the table of part a.

The following data give the number of turnovers (fumbles and interceptions) made by both teams in each of the football games played by a university during the 2014 and 2015 seasons. $$ \begin{array}{lllllllllllll} 2 & 3 & 1 & 1 & 6 & 5 & 3 & 5 & 5 & 1 & 5 & 2 & 1 \\ 5 & 3 & 4 & 4 & 5 & 8 & 4 & 5 & 2 & 2 & 2 & 6 & \end{array} $$ a. Construct a frequency distribution table for these data using single-valued classes. b. Calculate the relative frequency and percentage for each class. c. What is the relative frequency of games in which there were 4 or 5 turnovers? d. Draw a bar graph for the frequency distribution of part a.

The following table gives the frequency distribution for the numbers of parking tickets received on the campus of a university during the past week by 200 students. $$ \begin{array}{cc} \hline \text { Number of Tickets } & \text { Number of Students } \\ \hline 0 & 59 \\ 1 & 44 \\ 2 & 37 \\ 3 & 32 \\ 4 & 28 \\ \hline \end{array} $$ Draw two bar graphs for these data, the first without truncating the frequency axis and the second by truncating the frequency axis. In the second case, mark the frequencies on the vertical axis starting with 25\. Briefly comment on the two bar graphs.

The following data give the times (in minutes) taken by 50 students to complete a statistics examination that was given a maximum time of 75 minutes to finish. $$ \begin{array}{llllllllll} 41 & 28 & 45 & 60 & 53 & 69 & 70 & 50 & 63 & 68 \\ 37 & 44 & 42 & 38 & 74 & 53 & 66 & 65 & 52 & 64 \\ 26 & 45 & 66 & 35 & 43 & 44 & 39 & 55 & 64 & 54 \\ 38 & 52 & 58 & 72 & 67 & 65 & 43 & 65 & 68 & 27 \\ 64 & 49 & 71 & 75 & 45 & 69 & 56 & 73 & 53 & 72 \end{array} $$a. Prepare a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order. b. Prepare a split stem-and-leaf display for the data. Split each stem into two parts. The first part should contains the leaves 0 ,

The following data give the one-way commuting times (in minutes) from home to work for a random sample of 50 workers. $$ \begin{array}{llrlllllll} 23 & 17 & 34 & 26 & 18 & 33 & 46 & 42 & 12 & 37 \\ 44 & 15 & 22 & 19 & 28 & 32 & 18 & 39 & 40 & 48 \\ 16 & 11 & 9 & 24 & 18 & 26 & 31 & 7 & 30 & 15 \\ 18 & 22 & 29 & 32 & 30 & 21 & 19 & 14 & 26 & 37 \\ 25 & 36 & 23 & 39 & 42 & 46 & 29 & 17 & 24 & 31 \end{array} $$ Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.