11.10: Practice and Exploration
- Page ID
- 64758
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. In a survey of 75 graduates of a job training program, 20 of the graduates found jobs, 15 did not find jobs and were still looking for employment, 22 elected to pursue further education opportunities, and 18 did not find jobs and stopped looking for employment. Construct a bar graph of this frequency distribution.
2. Bart purchases a large bag of marbles. Each marble is either red (R), green (G), blue (B), white (W), or clear (C). One by one Bart pulls each marble from the bag until he has counted 57 marbles. The colors of the marbles are given in the table below. Construct a frequency distribution for the data and then construct a bar chart of the frequencies. What conclusions can you make from the bar chart?
|
R |
C |
B |
G |
C |
R |
B |
R |
R |
C |
|
G |
W |
W |
G |
G |
C |
R |
G |
R |
W |
|
R |
C |
B |
G |
R |
W |
G |
B |
W |
R |
|
R |
B |
C |
R |
B |
C |
C |
R |
C |
R |
|
C |
C |
W |
G |
G |
W |
R |
R |
R |
W |
|
B |
G |
R |
C |
B |
W |
C |
|
|
|
3. Suppose Lisa has surveyed her classmates as to where they would like to go for the next school field trip. To present the results, she has produced a pie chart showing the percentage of each response. See Figure 11.22. The possible field trip locations are the Springfield Historical Society, the Springfield Tar Pits, the Springfield Knowledgeum, the Springfield Nuclear Power Plant, and Olde Springfield Towne. Looking at Figure 11.22, which two locations had the most votes? Which location had the least votes?
4. The online automotive research group iSeeCars.com published a study that considered the colors of automobiles sold between January 2023 and April 2024 (iSeeCars 2025). Figure 11.23 shows a sequence of pie charts of the color preferences for trucks, sport utility vehicles, passenger cars, and sports cars. Based on these pie charts, do you see any differences between the color preferences based on the type of automobile?
5. The data given below correspond to the population of the town of West in Texas based on the U.S. Decennial Census from 1900 to 2020. Produce a line plot of the data and comment on any major trends that are observed.
|
Year |
Population |
|
1900 |
851 |
|
1910 |
1645 |
|
1920 |
1629 |
|
1930 |
1807 |
|
1940 |
1979 |
|
1950 |
2130 |
|
1960 |
2352 |
|
1970 |
2406 |
|
1980 |
2485 |
|
1990 |
2515 |
|
2000 |
2692 |
|
2010 |
2807 |
|
2020 |
2531 |
6. Suppose that the owner of a performing arts theater is interested in whether there is a trend in the sales of popcorn and drinks during an event. The owner keeps track of sales of both items during a selected concert during 10-minute intervals starting at 7:00 p.m. when the doors open and 10:00 p.m. when sales are concluded for the event. The data are given in the table below. Produce a single line plot of the data and comment on any major trends that are observed.
|
Time |
Popcorn |
Drinks |
|
7:00 |
7 |
3 |
|
7:10 |
3 |
3 |
|
7:20 |
8 |
9 |
|
7:30 |
8 |
16 |
|
7:40 |
5 |
15 |
|
7:50 |
4 |
14 |
|
8:00 |
1 |
12 |
|
8:10 |
4 |
3 |
|
8:20 |
1 |
11 |
|
8:30 |
3 |
4 |
|
8:40 |
5 |
5 |
|
8:50 |
8 |
11 |
|
9:00 |
5 |
8 |
|
9:10 |
1 |
5 |
|
9:20 |
1 |
11 |
|
9:30 |
8 |
10 |
|
9:40 |
5 |
10 |
|
9:50 |
7 |
11 |
|
10:00 |
2 |
5 |
- The data given in the table below correspond to the mileage and asking price for 20 used cars of a similar type. The mileage is reported in thousands of miles, and the price is reported in thousands of dollars. Create a scatterplot of the data using the mileage on the horizontal axis and the price on the vertical axis. Comment on any trends that you observe. If you do not see much of a trend, can you think of some reasons why?
|
Mileage |
Price |
|
9 |
33 |
|
8 |
37 |
|
2 |
29 |
|
20 |
18 |
|
30 |
18 |
|
32 |
19 |
|
4 |
27 |
|
40 |
19 |
|
36 |
20 |
|
9 |
32 |
|
31 |
21 |
|
9 |
33 |
|
19 |
24 |
|
13 |
24 |
|
31 |
21 |
|
12 |
24 |
|
20 |
24 |
|
22 |
25 |
|
21 |
25 |
|
22 |
25 |
- The data in the table below show the age and race time of 25 participants in an annual 5k run. The age is reported in years, and the time is reported in minutes. Create a scatterplot of the data using the mileage on the horizontal axis and the price on the vertical axis. Comment on any trends that you observe. If you do not see much of a trend, can you think of some reasons why?
|
Age |
Time |
|
32 |
20 |
|
23 |
19 |
|
52 |
23 |
|
38 |
21 |
|
40 |
22 |
|
43 |
23 |
|
54 |
25 |
|
32 |
23 |
|
13 |
21 |
|
45 |
25 |
|
51 |
26 |
|
26 |
24 |
|
30 |
26 |
|
24 |
24 |
|
47 |
29 |
|
42 |
28 |
|
57 |
29 |
|
45 |
30 |
|
47 |
29 |
|
36 |
30 |
|
50 |
33 |
|
54 |
32 |
|
50 |
34 |
|
23 |
32 |
|
59 |
34 |