Chapter 2: Problem 31
Briefly explain how to prepare a dotplot for a data set. You may use an example to illustrate.
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Chapter 2: Problem 31
Briefly explain how to prepare a dotplot for a data set. You may use an example to illustrate.
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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 give the amounts (in dollars) spent on refreshments by 30 spectators randomly selected from those who patronized the concession stands at a recent Major League Baseball game. $$ \begin{array}{rrrrrrrr} 4.95 & 27.99 & 8.00 & 5.80 & 4.50 & 2.99 & 4.85 & 6.00 \\ 9.00 & 15.75 & 9.50 & 3.05 & 5.65 & 21.00 & 16.60 & 18.00 \\ 21.77 & 12.35 & 7.75 & 10.45 & 3.85 & 28.45 & 8.35 & 17.70 \\ 19.50 & 11.65 & 11.45 & 3.00 & 6.55 & 16.50 & & \end{array} $$ a. Construct a frequency distribution table using the less-than method to write classes. Take \(\$ 0\) as the lower boundary of the first class and \(\$ 6\) as the width of each class. b. Calculate the relative frequencies, and percentages for all classes. c. Draw a histogram for the frequency distribution. d. Prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions.
Stem-and-leaf displays can be used to compare distributions for two groups using a back-to-back stem-and-leaf display. In such a display, one group is shown on the left side of the stems, and the other group is shown on the right side. When the leaves are ordered, the leaves increase as one moves away from the stems. The following stem-and-leaf display shows the money earned per tournament entered for the top 30 money winners in the \(2008-09\) Professional Bowlers Association men's tour and for the top 21 money winners in the 2008 09 Professional Bowlers Association women's tour. $$ \begin{array}{r|c|l} \text { Women's } & & \text { Men's } \\ \hline 8 & 0 & \\ 8871 & 1 & \\ 65544330 & 2 & 334456899 \\ 840 & 3 & 03344678 \\ 52 & 4 & 011237888 \\ 21 & 5 & 9 \\ & 6 & 9 \\ 5 & 7 & \\ & 8 & 7 \\ & 9 & 5 \end{array} $$ The leaf unit for this display is 100 . In other words, the data used represent the earnings in hundreds of dollars. For example, for the women's tour, the first number is 08 , which is actually 800 . The second number is 11 , which actually is 1100 . a. Do the top money winners, as a group, on one tour (men's or women's) tend to make more money per tournament played than on the other tour? Explain how you can come to this conclusion using the stem-and-leaf display. b. What would be a typical earnings level amount per tournament played for each of the two tours? c. Do the data appear to have similar spreads for the two tours? Explain how you can come to this conclusion using the stemand-leaf display. d. Does either of the tours appears to have any outliers? If so, what are the earnings levels for these players?
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. $$ \begin{array}{llrlllllll} 23 & 17 & 34 & 26 & 18 & 33 & 46 & 42 & 12 & 37 \\ 44 & 15 & 22 & 19 & 28 & 32 & 18 & 39 & 40 & 48 \\ 16 & 11 & 9 & 24 & 18 & 26 & 31 & 7 & 30 & 15 \\ 18 & 22 & 29 & 32 & 30 & 21 & 19 & 14 & 26 & 37 \\ 25 & 36 & 23 & 39 & 42 & 46 & 29 & 17 & 24 & 31 \end{array} $$ Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.
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