7.4: Review Questions
Line Graphs and Scatter Plots
Show all work necessary to answer each question.
Section A – All questions in this section are selected response.
- What term is used to describe a data set in which all points between 2 consecutive points are meaningful?
- discrete data
- continuous data
- random data
- fractional data
- What is the correlation of a scatter plot that has few points that are not bunched together?
- strong
- no correlation
- weak
- negative
- Which of the following calculations will create the line of best fit on the TI-83?
- quadratic regression
- cubic regression
- exponential regression
- linear regression \begin{align*}(ax + b)\end{align*}
- What type of variable is represented by the number of pets owned by families?
- qualitative
- quantitative
- independent
- continuous
- What term is used to define the connection between 2 data sets?
- relationship
- scatter plot
- correlation
- discrete
- What type of data, when plotted on a graph, does not have the points joined?
- discrete data
- continuous data
- random data
- independent data
- What name is given to a graph that shows change over time, with points that are joined but have no defined slope?
- linear graph
- broken-line graph
- scatter plot
- line of best fit
Section B – All questions in this section are long answer questions. Be sure to show all of the work necessary to arrive at the correct answer.
- Select the best descriptions for the following variables and indicate your selections by marking an ‘\begin{align*}x\end{align*}’ in the appropriate boxes.
Variable | Quantitative | Qualitative | Discrete | Continuous |
---|---|---|---|---|
Men’s favorite TV shows | ||||
Salaries of baseball players | ||||
Number of children in a family | ||||
Favorite color of cars | ||||
Number of hours worked weekly |
- Describe the correlation of each of the following graphs:
- Answer the questions below for the following broken-line graph, which shows the distance, over time, of a bus from the bus depot.
- What was the fastest speed of the bus?
- How many times did the bus stop on its trip? (Do not count the beginning and the end of the trip.)
- What was the initial distance of the bus from the bus depot?
- What was the total distance traveled by the bus?
- The following table represents the sales of Volkswagen Beetles in Iowa between 1994 and 2003:
Year | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 |
---|---|---|---|---|---|---|---|---|---|---|
Beetles Sold | 50 | 60 | 55 | 50 | 70 | 65 | 75 | 65 | 80 | 90 |
(a) Create a scatter plot and draw the line of best fit for the data. Hint: Let 0 = 1994, 1 = 1995, etc.
(b) Use the graph to predict the number of Beetles that will be sold in Iowa in the year 2007.
(c) Describe the correlation for the above graph.
- You are selling your motorcycle, and you decide to advertise it on the Internet on Walton’s Web Ads. He has 3 plans from which you may choose. The plans are shown on the following graph. Use the graph and explain when it is best to use each plan.
- The data below gives the fuel efficiency of cars with the same-sized engines when driven at various speeds. \begin{align*}& \text{Speed (m/h)} \qquad \qquad \qquad \ \quad 32 \quad 64 \quad 77 \quad 42 \quad 82 \quad 57 \quad 72\\
& \text{Fuel Efficiency (m/gal)} \qquad \quad 40 \quad 27 \quad 24 \quad 37 \quad 22 \quad 36 \quad 28\end{align*}
- Draw a scatter plot and a line of best fit. (You may use technology.)
- If a car were traveling at a speed of 47 m/h, estimate the fuel efficiency of the car.
- If a car has a fuel efficiency of 29 m/gal, estimate the speed of the car.
- For the following broken-line graph, write a story to accompany the graph, and provide a detailed description of the events that are occurring.
- Plot the following points on a scatter plot, with \begin{align*}m\end{align*} as the independent variable and \begin{align*}n\end{align*} as the dependent variable. Number both axes from 0 to 20. If a correlation exists between the values of \begin{align*}m\end{align*} and \begin{align*}n\end{align*}, describe the correlation (strong negative, weak positive, etc.).
- \begin{align*}m \quad 5 \quad 14 \quad 2 \quad 10 \quad 16 \quad 4 \quad 18 \quad 2 \quad 8 \quad 11\!\\ n \quad \ 6 \quad 13 \quad 4 \quad 10 \quad 15 \quad 7 \quad 16 \quad 5 \quad 8 \quad 12\end{align*}
- \begin{align*}m \quad 13 \quad 3 \quad 18 \quad 9 \quad 20 \quad 15 \quad 6 \quad 10 \quad 21 \quad 4\!\\ n \quad \ 7 \quad 14 \quad 9 \quad 16 \quad 7 \quad 13 \quad 10 \quad 13 \quad 3 \quad 19\end{align*}
Pie Charts, Bar Graphs, Histograms, and Stem-and-Leaf Plots
Section A – All questions in this section are selected response. Circle the correct answer.
- In the following stem-and-leaf plot that represents the ages of 23 people waiting in line at Tim Horton’s, how many people were older than 32?
- 4
- 12
- 14
- 11
The above histogram shows data collected during a recent fishing derby. The number of fish caught is being compared to the size of the fish caught. How many fish caught were between 20 cm and 29 cm in length?
(a) 3
(b) 11
(c) 25
(d) 6
- What name is given to a distribution that has 2 peaks of the same height?
- uniform
- unimodal
- bimodal
- discrete
- What is the midpoint of the bin [14.5-23.5)?
- 19
- 4.5
- 18.5
- 38
- The following stem-and-leaf plot shows the cholesterol levels of a random number of students. These values range from 2.3 to 8.9. What percentage of the students have levels between 5.0 and 7.1, inclusive?
- 6 %
- 20%
- 24%
- 28%
- What is the dependent variable in the following relationship? The time it takes to run the 100 yard dash and the fitness level of the runner.
- fitness level
- time
- length of the track
- age of the runner
- What name is given to the graph that uses lines to join the midpoints of the classes?
- bar graph
- stem-and-leaf
- histogram
- frequency polygon
- What is the mode of the following data set displayed in a stem-and-leaf plot?
- 32
- 41
- 7
- 23
How many of the above people have less than $800 in the bank?
(a) 2
(b) 4
(c) 3
(d) 6
- On a recent math test, 9 students out of the 25 who took the test scored above 85. What percentage of the students scored above 85?
- 0.36%
- 3.6%
- 360%
- 36%
Section B – All questions in this section are long-answer questions. Be sure to show all of the work necessary to arrive at the correct answer.
- Construct a stem-and-leaf plot for the following data values: \begin{align*}& 20 \quad 12 \quad 39 \quad 38 \quad 18 \quad 58 \quad 49 \quad 59 \quad 66 \quad 50\\ & 23 \quad 32 \quad 43 \quad 53 \quad 67 \quad 35 \quad 29 \quad 13 \quad 42 \quad 55\\ & 37 \quad 19 \quad 38 \quad 22 \quad 46 \quad 71 \quad 9 \quad \ 65 \quad 15 \quad 38\end{align*}
- The following pie chart represents the time spent doing various activities during one day. Using the pie chart, supply a possible activity that may be represented by each of the percentages shown in the chart.
- Just like Presidents of the United States, Canadian Prime Ministers must be sworn into office. The following data represents the ages of 22 Canadian Prime Ministers when they were sworn into office. Construct a stem-and-leaf plot to represent the ages, and list 4 facts that you know from the graph. \begin{align*}& 52 \quad 74 \quad 60 \quad 39 \quad 65 \quad 46 \quad 55 \quad 66 \quad 54 \quad 51 \quad 70 \quad 47 \quad 69 \quad 47 \quad 57 \quad 46\\ & 48 \quad 66 \quad 61 \quad 59 \quad 46 \quad 45\end{align*}
- A questionnaire on the makes of people's vehicles showed the following responses from 30 participants. Construct a frequency distribution and a bar graph to represent the data. (F = Ford, H = Honda, V = Volkswagen, M = Mazda) \begin{align*}& F \quad M \quad M \quad M \quad V \quad M \quad F \quad M \quad F \quad V \quad H \quad H \quad F \quad V \quad F\\ & H \quad H \quad F \quad M \quad M \quad V \quad H \quad M \quad V \quad V \quad F \quad V \quad H \quad M \quad F\end{align*}
- The following histogram displays the heights of students in a classroom: Use the information represented in the histogram to answer the following questions:
- How many students were in the class?
- How many students were over 60 inches in height?
- How many students had a height between 54 in and 62 in?
- Is the distribution unimodal or bimodal? How do you know?
- The following frequency polygon represents the weights of players who all participated in the same sport. Use the polygon to answer the following questions:
- How many players played the sport?
- What was the most common weight for the players?
- What sport do you think the players may have been playing?
- What do the weights of 55 kg and 105 kg represent?
- What 2 weights have no recorded players weighing those amounts?
- The following pie chart, which is incomplete, shows the extracurricular activities for 200 high school students: Use the pie chart to answer the following questions:
- What makes the above pie chart incomplete?
- How many students participated in sports?
- How many students do CMT?
- How many students participate in volunteer activities after school?
- Construct the pie chart so that it shows percentages and not degrees.
- The following data represents the results of a test taken by a group of students: \begin{align*}& 95 \quad 56 \quad 70 \quad 83 \quad 59 \quad 66 \quad 88 \quad 52 \quad 50 \quad 77 \quad 69 \quad 80\\ & 54 \quad 75 \quad 68 \quad 78 \quad 51 \quad 64 \quad 55 \quad 67 \quad 74 \quad 57 \quad 73 \quad 53\end{align*} Construct a frequency distribution table using a bin size of 10 and display the results in a properly labeled histogram.
- Using the data for question 8, use technology to construct the histogram.
- In a few sentences, explain the type of graph that you find most helpful for interpreting data.
Box-and-Whisker Plots
Section A – All questions in this section are selected response.
- Which of the following is not a part of the five-number summary?
- \begin{align*}Q_1\end{align*} and \begin{align*}Q_3\end{align*}
- the mean
- the median
- minimum and maximum values
- What percent of the data is contained in the box of a box-and-whisker plot?
- 25%
- 100%
- 50%
- 75%
- What name is given to the horizontal lines to the left and right of the box of a box-and-whisker plot?
- axis
- whisker
- range
- plane
- What term describes the distribution of a data set if the median of the data set is located to the left of the center of the box in a box-and-whisker plot?
- positively skewed
- negatively skewed
- approximately symmetric
- not skewed
- What 2 values of the five-number summary are connected with 2 horizontal lines on a box-and-whisker plot?
- Minimum value and the median
- Maximum value and the median
- Minimum and maximum values
- \begin{align*}Q_1\end{align*} and \begin{align*}Q_3\end{align*}
Section B - Show all work necessary to answer each question.
- For the following data sets, determine the five-number summaries:
- 74, 69, 83, 79, 60, 75, 67, 71
- 6, 9, 3, 12, 11, 9, 15, 5, 7
- For each of the following box-and-whisker plots, list the five-number summary and comment on the distribution of the data:
- The following data represents the number of coins that 12 randomly selected people had in their piggy banks: \begin{align*}35 \quad 58 \quad 29 \quad 44 \quad 104 \quad 39 \quad 72 \quad 34 \quad 50 \quad 41 \quad 64 \quad 54\end{align*} Construct a box-and-whisker plot for the above data.
- The following data represent the time (in minutes) that each of 20 people waited in line at a local book store to purchase the latest Harry Potter book: \begin{align*}& 15 \quad 8 \quad 5 \quad \ 10 \quad 14 \quad 17 \quad 21 \quad 23 \quad 6 \quad 19 \quad 31 \quad 34 \quad 30 \quad 31\\ & 3 \quad 22 \quad 17 \quad 25 \quad 5 \quad 16\end{align*} Construct a box-and-whisker plot for the above data. Are the data skewed in any direction?
- Firman’s Fitness Factory is a new gym that offers reasonably-priced family packages. The following table represents the number of family packages sold during the opening month: \begin{align*}& 24 \quad 21 \quad 31 \quad 28 \quad 29\\ & 27 \quad 22 \quad 27 \quad 30 \quad 32\\ & 26 \quad 35 \quad 24 \quad 22 \quad 34\\ & 30 \quad 28 \quad 24 \quad 32 \quad 27\\ & 32 \quad 28 \quad 27 \quad 32 \quad 23\\ & 20 \quad 32 \quad 28 \quad 32 \quad 34\end{align*} Construct a box-and-whisker plot for the data. Are the data symmetric or skewed?
- The following data represents the number of flat-screen televisions assembled at a local electronics company for a sample of 28 days: \begin{align*}& 48 \quad 55 \quad 51 \quad 44 \quad 59 \quad 49 \quad 47\\ & 45 \quad 51 \quad 56 \quad 50 \quad 57 \quad 53 \quad 55\\ & 47 \quad 49 \quad 51 \quad 54 \quad 56 \quad 54 \quad 47\\ & 50 \quad 53 \quad 52 \quad 55 \quad 51 \quad 59 \quad 48\end{align*} Using technology, construct a box-and-whisker plot for the data. What are the values for the five-number summary?
- Construct a box-and-whisker plot to represent the average number of sick days used by 9 employees of a large industrial plant. The numbers of sick days are as follows: \begin{align*}39 \quad 31 \quad 18 \quad 34 \quad 25 \quad 22 \quad 32 \quad 23 \quad 22\end{align*}
- Shown below is the number of new stage shows that appeared in Las Vegas for each of the past several years. Construct a box-and-whisker plot for the data and comment of the shape of the distribution. \begin{align*}31 \quad 29 \quad 34 \quad 30 \quad 38 \quad 40 \quad 36 \quad 38 \quad 32 \quad 39 \quad 35\end{align*}
- The following data represent the average snowfall (in centimeters) for 18 Canadian cities for the month of January. Construct a box-and-whisker plot to model the data. Is the data skewed? Justify your answer.
Name of City | Amount of Snow(cm) |
---|---|
Calgary | 123.4 |
Charlottetown | 74.5 |
Edmonton | 80.6 |
Fredericton | 73.8 |
Halifax | 64.0 |
Labrador City | 110.4 |
Moncton | 82.4 |
Montreal | 63.6 |
Ottawa | 48.9 |
Quebec City | 53.8 |
Regina | 35.9 |
Saskatoon | 25.4 |
St. John’s | 97.5 |
Sydney | 44.2 |
Toronto | 21.8 |
Vancouver | 12.8 |
Victoria | 8.3 |
Winnipeg | 76.2 |
- Using the procedure outlined in this chapter, check the following data sets for outliers:
- 25, 33, 55, 32, 17, 19, 15, 18, 21
- 149, 123, 126, 122, 129, 120