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# 8.6: Review Questions

Difficulty Level: At Grade Created by: CK-12

Answer the following questions and show all work (including diagrams) to create a complete answer.

1. In the table below, match the following types of graphs with the types of variables used to create the graphs.
Type of Graph Type of Variable
a. Histogram _____ discrete
b. Stem-and-leaf plot _____ discrete
c. Broken-line graph _____ discrete
d. Bar graph _____ continuous
e. Pie chart _____ continuous
1. In the table below, match the following types of graphs with the types of variables used to create the graphs.
Type of Graph Type of Variable
a. Broken-line graph _____ qualitative
b. Bar graph _____ numerical
c. Pie chart _____ categorical
d. Stem-and-leaf plot _____ quantitative
e. Histogram _____ numerical
1. Jack takes a pot of water at room temperature (22C)\begin{align*}(22^\circ \text{C})\end{align*} and puts it on the stove to boil (100C)\begin{align*}(100^\circ \text{C})\end{align*}, which takes about 5 minutes. He then takes a cup of this water, adds a package of hot chocolate, and mixes it up. He places the cup on the counter to cool for 10 minutes to 40C\begin{align*}40^\circ \text{C}\end{align*} before having his first sip. After 30 minutes, the hot chocolate is now at room temperature. Thomas is making chocolate chip cookies. He mixes all of the ingredients together at room temperature, which takes him about 5 minutes, and then places the cookies in the oven at 350C\begin{align*}350^\circ \text{C}\end{align*} for 8 minutes. After cooking, he takes them off the pan and places them on a cooling rack. After 15 minutes, the cookies are still warm (about 30C\begin{align*}30^\circ \text{C}\end{align*}), but he samples them for taste. After 30 minutes, the cookies are at room temperature and ready to be served. Draw a broken-line graph for each set of data. Label the graphs to show what is happening.
2. Scott is asked to track his daily video game playing. He gets up at 7 A.M. and plays for 1 hour. He then eats his breakfast and gets ready for school. He runs to catch the bus at 8:25 A.M. On the bus ride (about 35 minutes), he plays his IPOD until arriving for school. He is not allowed games at school, so he waits for the bus ride home at 3:25 P.M. When he gets home, he does homework for 1 hour and plays games for 1 hour until dinner. There are no games in the evening. Michael gets up at 7:15 A.M., eats breakfast, and gets ready for school. It takes him 30 minutes to get ready. He then plays games until he goes to meet the bus with Scott. Michael is in Scott’s class, but he has a free period from 11:00 A.M. until 11:45 A.M., when he goes outside to play a game. He goes home and plays his 1 hour of games immediately, and he then works on his homework until dinner. He, like Scott, is not allowed to play games in the evening. Draw a broken-line graph for each set of data. Label the graphs to show what is happening.
3. The following graph shows the gasoline remaining in a car during a family trip east. Also found on the graph is the gasoline remaining in a truck traveling west to deliver goods. Describe what is happening for each graph. What other conclusions may you draw?
4. Mr. Dugas, the senior high physical education teacher, is doing fitness testing this week in gym class. After each test, students are required to take their pulse rate and record it on the chart in the front of the gym. At the end of the week, Mr. Dugas looks at the data in order to analyze it. The data is shown below: Girls7088807676778972727672757780766868827860646465818484797870Boys768887868570767070798082828283848585788185\begin{align*}& \text{Girls} \qquad 70 \quad 88 \quad 80 \quad 76 \quad 76 \quad 77 \quad 89 \quad 72 \quad 72 \quad 76 \quad 72 \quad 75 \quad 77 \quad 80 \quad 76 \quad 68 \quad 68\\ & \qquad \qquad 82 \quad 78 \quad 60 \quad 64 \quad 64 \quad 65 \quad 81 \quad 84 \quad 84 \quad 79 \quad 78 \quad 70\\ &\text{Boys} \qquad 76 \quad 88 \quad 87 \quad 86 \quad 85 \quad 70 \quad 76 \quad 70 \quad 70 \quad 79 \quad 80 \quad 82 \quad 82 \quad 82 \quad 83 \quad 84 \quad 85\\ & \qquad \qquad 85 \quad 78 \quad 81 \quad 85\end{align*} Construct a two-sided stem-and-leaf plot for the data and compare the distributions.
5. Starbucks prides itself on its low line-up times in order to be served. A new coffee house in town has also boasted that it will have your order in your hands and have you on your way quicker than the competition. The following data was collected for the line-up times (in minutes) for both coffee houses: Starbucks2026262719121216121517208  8 18Just Us Coffee171615101610102920222212132415\begin{align*}& \text{Starbucks} \qquad \qquad 20 \quad 26 \quad 26 \quad 27 \quad 19 \quad 12 \quad 12 \quad 16 \quad 12 \quad 15 \quad 17 \quad 20 \quad 8 \ \quad \ 8 \ \quad 18\\ & \text{Just Us Coffee} \qquad 17 \quad 16 \quad 15 \quad 10 \quad 16 \quad 10 \quad 10 \quad 29 \quad 20 \quad 22 \quad 22 \quad 12 \quad 13 \quad 24 \quad 15\end{align*} Construct a two-sided stem-and-leaf plot for the data. Determine the median and mode using the two-sided stem-and-leaf plot. What can you conclude from the distributions?
6. The boys and girls basketball teams had their heights measured at practice. The following data was recorded for their heights (in centimeters): Girls171170176176177179162172160157155168178174170155155154164145171161Boys168170162153176167158180181176172168167165159185184173177167169177\begin{align*}& \text{Girls} \qquad 171 \quad 170 \quad 176 \quad 176 \quad 177 \quad 179 \quad 162 \quad 172 \quad 160 \quad 157 \quad 155\\ & \qquad \qquad 168 \quad 178 \quad 174 \quad 170 \quad 155 \quad 155 \quad 154 \quad 164 \quad 145 \quad 171 \quad 161\\ & \text{Boys} \qquad 168 \quad 170 \quad 162 \quad 153 \quad 176 \quad 167 \quad 158 \quad 180 \quad 181 \quad 176 \quad 172\\ & \qquad \qquad 168 \quad 167 \quad 165 \quad 159 \quad 185 \quad 184 \quad 173 \quad 177 \quad 167 \quad 169 \quad 177\end{align*} Construct a two-sided stem-and-leaf plot for the data. Determine the median and mode using the two-sided stem-and-leaf plot. What can you conclude from the distributions?
7. The grade 12 biology class did a survey to see what color eyes their classmates had and if there was a connection between eye color and sex. The following data was recorded:
Eye color Males Females
Blue 5 5
Green 6 8
Brown 3 4
Hazel 4 3

Draw a double bar graph to represent the data, and draw any conclusions that you can from the resulting chart.

1. Robbie is in charge of the student organization for new food selections in the cafeteria. He designed a survey to determine if 4 new food options would be good to put on the menu. The results are shown below:
Fish burgers 10 5
Vegetarian pizza 7 18
Brown rice 23 9
Carrot soup 20 20

Draw a double bar graph to represent the data, and draw any conclusions that you can from the resulting chart.

1. The guidance counselor at USA High School wanted to know what future plans the graduating class had. She took a survey to determine the intended plans for both boys and girls in the school’s graduating class. The following data was recorded:
Future Plans Boys Girls
University 35 40
College 27 22
Military 23 9
Employment 10 5
Other/unsure 5 10

Draw a double bar graph to represent the data, and draw any conclusions that you can from the resulting chart.

1. International Baccalaureate has 2 levels of courses, which are standard level (SL) and higher level (HL). Students say that study times are the same for both the standard level exams and the higher level exams. The following data represents the results of a survey conducted to determine how many hours a random sample of students studied for their final exams at each level: HL Exams1516161719105655810 81217SL Exams 106 6  7 9 12 2625720188 18\begin{align*}& \text{HL Exams} \qquad 15 \quad 16 \quad 16 \quad 17 \quad 19 \quad 10 \quad 5 \quad 6 \quad 5 \quad 5 \quad 8 \quad 10 \quad \ 8 \quad 12 \quad 17\\ & \text{SL Exams} \qquad \ 10 \quad 6 \quad \ 6 \quad \ \ 7 \quad \ 9 \ \quad 12 \quad \ 2 \quad 6 \quad 2 \quad 5 \quad 7 \quad 20 \quad 18 \quad 8 \quad \ 18\end{align*} Draw a box-and-whisker plot for both sets of data on the same number line. Use the double box-and-whisker plots to determine the five-number summary for both sets of data. Compare the times students prepare for each level of exam.
2. Students in the AP math class at BCU High School took their SATs for university entrance. The following scores were obtained for the math and verbal sections: \begin{align*}& \text{Math} \qquad \ \ 529 \quad 533 \quad 544 \quad 562 \quad 513 \quad 519 \quad 560 \quad 575 \quad 568 \quad 537 \quad 561 \quad 522 \quad 563 \quad 571\\ & \text{Verbal} \qquad \ 499 \quad 509 \quad 524 \quad 530 \quad 550 \quad 499 \quad 545 \quad 560 \quad 579 \quad 524 \quad 478 \quad 487 \quad 482 \quad 570\end{align*} Draw a box-and-whisker plot for both sets of data on the same number line. Use the double box-and-whisker plots to determine the five-number summary for both sets of data. Compare the data for the 2 sections of the SAT using the five-number summary data.
3. The following box-and-whisker plots were drawn to analyze the data collected in a survey of scores for the doubles performances in the figure skating competitions at 2 Winter Olympic games. The box-and-whisker plot on the top represents the scores obtained at the 2010 winter games in Whistler, BC. The box-and-whisker plot on the bottom represents the scores obtained at the 2006 winter games in Torino, Italy. Here is what the double box-and-whisker plots look like when created with a TI-84 calculator:
4. Use the double box-and-whisker plots to determine the five-number summary for both sets of data. Compare the scores obtained at each of the Winter Olympic games.

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