8.2.0: Exercises
- Page ID
- 171738
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The table below shows the answers to the question, “Which social media platform, if any, do you use most frequently?”
| None | Snapchat | Snapchat | |||
| Snapchat | None | Snapchat | |||
| None | Snapchat | ||||
| Snapchat | Snapchat | ||||
| None |
Make a bar chart to visualize these responses.
Make a pie chart to visualize these responses.
A sample of students at a large university were asked whether they were full-time students living on campus (Full-Time Residential, FTR), full-time students who commuted (FTC), or part-time students (PT). The raw data are in the table below:
| FTR | FTR | FTC | PT | FTR | PT | FTR | FTC |
| FTR | FTC | FTC | FTR | FTR | PT | FTC | FTC |
| FTC | PT | FTC | FTC | PT | FTR | FTC | PT |
| FTC | PT | FTR | PT | FTC | FTC | FTR | PT |
Make a bar chart to visualize these responses.
Make a pie chart to visualize these responses.
Students in a statistics class were asked how many countries (besides their home countries) they had visited; the table below gives the raw responses:
| 0 | 2 | 1 | 1 | 3 | 2 | 0 | 2 | 0 | 1 |
| 0 | 2 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 2 | 1 | 1 | 0 | 1 | 1 | 0 |
Create a bar graph visualizing these data (treating the responses as categorical).
Create a pie chart visualizing these data.
The purchasing department for a chain of bookstores wants to make sure they’re buying the right types of books to put on the shelves, so they take a sample of 20 books that customers bought in the last five days and record the genres:
| Nonfiction | Young Adult | Romance | Cooking | Young Adult |
| Young Adult | Thriller | Young Adult | Nonfiction | True Crime |
| Romance | Nonfiction | Thriller | True Crime | Romance |
| True Crime | Thriller | Romance | Young Adult | Young Adult |
Create a bar graph to visualize these data.
Create a pie chart to visualize these data.
An elementary school class is administered a standardized test for which scores range from 0 to 100, as shown below:
| 60 | 54 | 71 | 80 | 63 |
| 72 | 70 | 88 | 88 | 67 |
| 74 | 79 | 50 | 99 | 64 |
| 98 | 55 | 64 | 86 | 92 |
| 72 | 65 | 88 | 80 | 65 |
Make a stem-and-leaf plot to visualize these results.
Make a histogram to visualize these results. Use bins of width 10.
The following table gives the final results for the 2021 National Women’s Soccer League season. The columns are standings points (PTS; teams earn three points for a win and one point for a tie), wins (W), losses (L), ties (T), goals scored by that team (GF), and goals scored against that team (GA).
| Team | PTS | W | L | T | GF | GA |
|---|---|---|---|---|---|---|
| Portland Thorns FC | 44 | 13 | 6 | 5 | 33 | 17 |
| OL Reign | 42 | 13 | 8 | 3 | 37 | 24 |
| Washington Spirit | 39 | 11 | 7 | 6 | 29 | 26 |
| Chicago Red Stars | 38 | 11 | 8 | 5 | 28 | 28 |
| NJ/NY Gotham FC | 35 | 8 | 5 | 11 | 29 | 21 |
| North Carolina Courage | 33 | 9 | 9 | 6 | 28 | 23 |
| Houston Dash | 32 | 9 | 10 | 5 | 31 | 31 |
| Orlando Pride | 28 | 7 | 10 | 7 | 27 | 32 |
| Racing Louisville FC | 22 | 5 | 12 | 7 | 21 | 40 |
| Kansas City Current | 16 | 3 | 14 | 7 | 15 | 36 |
Make a stem-and-leaf plot for PTS.
Make a histogram for PTS, using bins of width 5.
Make a histogram for GF, using bins of width 5.
Make a histogram for GA, using bins of width 5.
For the following exercises, use the "CUNY" dataset–which gives the location (borough) of each college in the City University of New York (CUNY) system, the highest degree offered, and the proportions of total degrees awarded in a partial list of disciplines–to identify the right visualization to address each question. Then, create those visualizations.
What is the highest degree offered in colleges across the CUNY system?
What is the distribution of the proportion of degrees awarded in Information Science across the CUNY system?
In which boroughs are the CUNY colleges located?
What are the proportions of degrees awarded across the listed humanities fields (Foreign Language, English, Humanities, Philosophy & Religion, History) at City College?
What proportions of degrees are awarded in Social Service at the different institutions located in Manhattan?
For the following exercises, use the data found in the "Receivers" dataset on the top 25 receivers (by number of receptions; data collected from pro-football-reference.com) in the NFL during the 2020 season.
Make a stem-and-leaf plot for the longest receptions (“Long”).
Make a stem-and-leaf plot for receptions.
Make a histogram for yards.
Make a histogram for yards per reception (“Yds/Rec”).
Make a histogram for the longest receptions (“Long”).
Make a histogram for receptions.
Make a histogram for age.
Describe the distribution of age as left-skewed, symmetric, or right-skewed.
Describe the distribution of receptions as left-skewed, symmetric, or right-skewed.
Describe the distribution of yards as left-skewed, symmetric, or right-skewed.
Describe the distribution of touchdowns (“TD”) as left-skewed, symmetric, or right-skewed.
Describe the distribution of longest receptions as left-skewed, symmetric, or right-skewed.