4.12: Graphing Distributions (Exercises)
- Page ID
- 19047
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)General Questions
Q1
Name some ways to graph quantitative variables and some ways to graph qualitative variables. (relevant section & relevant section)
Q2
Based on the frequency polygon displayed below, the most common test grade was around what score? Explain. (relevant section)
Q3
An experiment compared the ability of three groups of participants to remember briefly-presented chess positions. The data are shown below. The numbers represent the total number of pieces correctly remembered from three chess positions. Create side-by-side box plots for these three groups. What can you say about the differences between these groups from the box plots? (relevant section)
|
Non-players |
Beginners |
Tournament players |
|
22.1 |
32.5 |
40.1 |
|
22.3 |
37.1 |
45.6 |
|
26.2 |
39.1 |
51.2 |
|
29.6 |
40.5 |
56.4 |
|
31.7 |
45.5 |
58.1 |
|
33.5 |
51.3 |
71.1 |
|
38.9 |
52.6 |
74.9 |
|
39.7 |
55.7 |
75.9 |
|
43.2 |
55.9 |
80.3 |
|
43.2 |
57.7 |
85.3 |
Q4
You have to decide between displaying your data with a histogram or with a stem and leaf display. What factor(s) would affect your choice? (relevant section & relevant section)
Q5
In a box plot, what percent of the scores are between the lower and upper hinges? (relevant section)
Q6
A student has decided to display the results of his project on the number of hours people in various countries slept per night. He compared the sleeping patterns of people from the US, Brazil, France, Turkey, China, Egypt, Canada, Norway, and Spain. He was planning on using a line graph to display this data. Is a line graph appropriate? What might be a better choice for a graph? (relevant section & relevant section)
Q7
For the data from the \(1977\) \(\text{Stat. and Biom. 200 }\) class for eye color, construct: (relevant section)
- pie graph
- horizontal bar graph
- vertical bar graph
- a frequency table with the relative frequency of each eye color
Eye Color
Number of students
Brown
11
Blue
10
Green
4
Gray
1
(Question submitted by J. Warren, UNH)
Q8
A graph appears below showing the number of adults and children who prefer each type of soda. There were \(130\) adults and kids surveyed. Discuss some ways in which the graph below could be improved. (relevant section)
Q9
Which of the box plots below has a large positive skew? Which has a large negative skew? (relevant section & relevant section)
Questions from Case Studies
The following questions are from the Angry Moods (AM) case study.
Q10
(AM#6) Is there a difference in how much males and females use aggressive behavior to improve an angry mood? For the "Anger-Out" scores:
- Create parallel box plots. (relevant section)
- Create a back to back stem and leaf displays (You may have trouble finding a computer to do this so you may have to do it by hand.) (relevant section)
Q11
(AM#9) Create parallel box plots for the Anger-In scores by sports participation. (relevant section)
Q12
(AM#11) Plot a histogram of the distribution of the Control-Out scores. (relevant section)
Q13
(AM#14) Create a bar graph comparing the mean Control-In score for the athletes and the non-athletes. What would be a better way to display this data? (relevant section)
Q14
(AM#18) Plot parallel box plots of the Anger Expression Index by sports participation. Does it look like there are any outliers? Which group reported expressing more anger? (relevant section)
The following questions are from the Flatulence (F) case study.
Q15
(F#1) Plot a histogram of the variable "per day." (relevant section)
Q16
(F#7) Create parallel box plots of "how long" as a function gender. Why is the \(25^{th}\) percentile not showing? What can you say about the results? (relevant section)
Q17
(F#9) Create a stem and leaf plot of the variable "how long" What can you say about the shape of the distribution? (relevant section.1)
The following questions are from the Physicians' Reactions (PR) case study.
Q18
(PR#1) Create box plots comparing the time expected to be spent with the average-weight and overweight patients. (relevant section)
Q19
(PR#4) Plot histograms of the time spent with the average-weight and overweight patients. (relevant section)
Q20
(PR#5) To which group does the patient with the highest expected time belong?
The following questions are from the Smiles and Leniency (SL) case study
Q21
(SL#1) Create parallel box plots for the four conditions. (relevant section)
Q22
(SL#3) Create back to back stem and leaf displays for the false smile and neutral conditions. (It may be hard to find a computer program to do this for you, so be prepared to do it by hand). (relevant section)
The following questions are from the ADHD Treatment (AT) case study.
Q23
(AT#3) Create a line graph of the data. Do certain dosages appear to be more effective than others? (relevant section)
Q24
(AT#5) Create a stem and leaf plot of the number of correct responses of the participants after taking the placebo (\(d0\) variable). What can you say about the shape of the distribution? (relevant section)
Q25
Create box plots for the four conditions. You may have to rearrange the data to get a computer program to create the box plots.
The following question is from the SAT and College GPA case study.
Q26
Create histograms and stem and leaf displays of both high-school grade point average and university grade point average. In what way(s) do the distributions differ?
Q27
The \(\text{April 10th}\) issue of the Journal of the American Medical Association reports a study on the effects of anti-depressants. The study involved \(340\) subjects who were being treated for major depression. The subjects were randomly assigned to receive one of three treatments: St. John's wort (an herb), Zoloft (Pfizer's cousin of Lilly's Prozac) or placebo for an \(8\)-week period. The following are the mean scores (approximately) for the three groups of subjects over the eight-week experiment. The first column is the baseline. Lower scores mean less depression. Create a graph to display these means.
| Placebo | 22.5 | 19.1 | 17.9 | 17.1 | 16.2 | 15.1 | 12.1 | 12.3 |
| Wort | 23.0 | 20.2 | 18.2 | 18.0 | 16.5 | 16.1 | 14.2 | 13.0 |
| Zoloft | 22.4 | 19.2 | 16.6 | 15.5 | 14.2 | 13.1 | 11.8 | 10.5 |
The following questions are from 
. Visit the site
Q28
For the graph below, of heights of singers in a large chorus, please write a complete description of the histogram. Be sure to comment on all the important features.
Q29
Pretend you are constructing a histogram for describing the distribution of salaries for individuals who are \(40\) years or older, but are not yet retired.
- What is on the \(Y\)-axis? Explain.
- What is on the \(X\)-axis?
- What would be the probable shape of the salary distribution? Explain why.
Select Answers
S2
\(85\)