Review
Identify the Wʹs for the description of data.
1) A survey of bicycles parked outside college dormitories at a small university recorded the style (mountain bike, ten
speed, etc.), the brand, the color, and the age.
2) The State Athletic Association requires coaches to keep these records on all athletes: age, days absent, medical
history, emergency contact, and any allergies the athlete may have.
Name the variables in each description of data, then tell whether they are quantitative or categorical. For each
quantitative variable name its unit of measure.
3) When determining the batting average for a baseball player you must have data on the number of hits in the season,
and the number of at-bats in the season.
A) Number of hits, quantitative, hits; number of at-bats, quantitative, at-bats.
B) Number of hits, comparative; number of at-bats, quantitative, at-bats; players, categorical.
C) Number of hits, quantitative, hits; number of at-bats, comparative.
D) Number of hits, comparative; number of at-bats, quantitative, at-bats.
E) Number of hits, quantitative, games; number of at-bats, quantitative, at-bats; player, categorical.
Classify the variable as categorical or quantitative.
4) A personʹs height in feet
A) Quantitative
B) Categorical
5) A personʹs political affiliation
A) Categorical
B) Quantitative
6) The speed of a car in miles per hour
A) Categorical
B) Quantitative
Provide an appropriate response.
7) A magazine article reported on Springfield School Districtʹs magnet school programs. Of the 1470 qualified
applicants, 798 were accepted, 252 were wait-listed, and 420 were turned away for lack of space. Find the relative
frequency distribution of the decisions made, and write a sentence describing it.
A) 1470 students applied for admission to the magnet schools program. 54% were accepted, 17% were wait-listed,
and 29% were turned away.
B) 1470 students applied for admission to the magnet schools program. 54% were accepted, and 46% were turned
away.
C) 1470 students applied for admission to the magnet schools program. 54% were accepted, 32% were wait-listed,
and 29% were turned away.
D) 1470 students applied for admission to the magnet schools program. 54% were accepted, 32% were wait-listed,
and 53% were turned away.
E) 1470 students applied for admission to the magnet schools program. 71% were accepted, and 29% were turned
away.
Origin
Provide an appropriate response. Round to the nearest tenth of a percent if necessary.
8) A survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as
seen in the table.
Driver
Student
Staff
American
108
85
European
38
22
Asian
69
58
What percent of all the cars surveyed were foreign?
9) Just how accurate are the weather forecasts we hear every day? The table below compares the daily forecast with a
cityʹs actual weather for a year.
Actual Weather
Rain
No rain
Rain
26
52
No rain
9
278
On what percent of days was rain predicted?
Provide an appropriate response.
10) A magazine article reported on Springfield School Districtʹs magnet school programs. Of the 1607 qualified
applicants, 514 were Black or Hispanic, 262 were Asian, and 831 were White. Summarize the relative frequency
distribution of ethnicity with a sentence or two in the proper context.
A) Of the 1607 students who applied for admission to the magnet schools program, 32% were Black or Hispanic, 16%
were Asian, and 52% were White.
B) Of the 1607 students accepted in the magnet schools program, 32% were Black or Hispanic, 16% were Asian, and
52% were White.
C) Of the 1607 students who applied for admission to the magnet schools program, 16% were Black, 16% were
Hispanic, 16% were Asian, and 52% were White.
D) Of the 1607 students who applied for admission to the magnet schools program, 62% were Black or Hispanic, 32%
were Asian, and 52% were White.
E) Of the 1607 students who applied for admission to the magnet schools program, 3% were Black or Hispanic, 2%
were Asian, and 5% were White.
11) The Centers for Disease Control lists causes of death for individual states in 2002. The mortality data for one state is
given.
Cause of Death
Percent
Heart Disease
28.1
Cancer
23.1
Circulatory diseases and stroke
7.4
Respiratory diseases
5.2
Accidents
4.7
Is it reasonable to conclude that, in this state, cancer or respiratory diseases were the cause of approximately 28% of
deaths in 2002?
12) The Centers for Disease Control lists causes of death for individual states in 2002. The mortality data for one state is
given.
Cause of Death
Percent
Heart Disease
29.6
Cancer
22.3
Circulatory diseases and stroke
8.1
Respiratory diseases
6.3
Accidents
4.4
In this state, what percent of deaths were from causes not listed here?
13) A local park district is planning to build a recreation center. The park district conducted a poll to find out the types of
physical activities the local population would be interested in. The poll was based on telephone responses from 1013
randomly selected adults. The table shows the percentages of people who expressed interest in various activities.
Activity
Percent
Running/Walking
56
Weight Training
47
Biking
39
Aerobics
24
Swimming
16
Is it reasonable to conclude that 63% expressed interest in either biking or aerobics?
Create the requested display for the data.
14) The focus of a recent survey was was on teenagersʹ familiarity with and use of modern technology. The teenagers
were asked if they used each of the following technologies on a daily basis and if the technology was critically
important to own. For each question, the percentage of those responding ʺYesʺ is given. Subtracting the ʺUse dailyʺ
percentage from the ʺCritically important to ownʺ percentage gives the ʺImportance Gap.ʺ Here are the results:
Use daily Critically important to own Importance gap
Computer
47%
79%
32
Telephone
54%
71%
17
DVD
38%
51%
13
Calculator
72%
78%
6
Stereo/audio
90%
72%
-18
Video games
48%
21%
-27
Create a bar chart for the ʺImportance Gapʺ.
18) Using the table in problem #17, which of the following displays is the most appropriate for these data?
I
II
III
A) II
B) III
C) I
D) All of these displays are equally appropriate.
E) None of these displays are appropriate.
16) The weights, in pounds, of the members of the varsity football team are listed below. Create a stem -and-leaf display
of the data. Do not use split stems.
144
152
142
151
160
152
131
164
141
153
140
149
144
135
156
147
133
172
159
135
159
148
171
163
Sex
Provide an appropriate response. Round to the nearest tenth of a percent if necessary.
17) Students in a political science course were asked to describe their politics as ʺLiberalʺ, ʺModerateʺ, or ʺConservative.ʺ
Here are the results:
Politics
Liberal
Moderate Conservative
Total
Female
43
36
6
85
Male
52
55
18
125
Total
95
91
24
210
What percent of the females in the class consider themselves to be ʺLiberalʺ?
Forecast
18) Just how accurate are the weather forecasts we hear every day? The table below compares the daily forecast with a
cityʹs actual weather for a year.
Actual Weather
Rain
No Rain
Rain
27
59
No Rain
10
269
What percent of the time was the forecast correct?
A) 18.9%
B) 76.4%
C) 7.4%
D) 73.7%
E) 81.1%
Sex
Provide an appropriate response. Round to the nearest tenth of a percent if necessary.
19) Students in a political science course were asked to describe their politics as ʺLiberalʺ, ʺModerateʺ, or ʺConservative.ʺ
Here are the results:
Politics
Liberal
Moderate Conservative
Total
Female
37
27
14
78
Male
44
39
23
106
Total
81
66
37
184
What percent of all students in the class are males who consider themselves to be ʺLiberalʺ?
A) 54.3%
B) 20.1%
C) 23.9%
D) 41.5%
E) 44%
Sex
20) Students in a political science course were asked to describe their politics as ʺLiberalʺ, ʺModerateʺ, or ʺConservative.ʺ
Here are the results:
Politics
Liberal
Moderate Conservative
Total
Female
45
37
12
94
Male
36
39
21
96
Total
81
76
33
190
What percent of all ʺModeratesʺ in the class are male?
Ethnicity
21) A magazine article reported on Springfield School Districtʹs magnet school programs. The article examined the
impact of an applicantʹs ethnicity on the likelihood of admission. The data are summarized in the table below.
Admission Decision
Accepted Wait-listed Turned away Total
Black/Hispanic
455
0
30
485
Asian
106
45
145
296
White
324
245
351
920
Total
885
290
526
1701
What percent of all applicants were Black or Hispanic?
Would you expect the distribution of this variable to be uniform, unimodal, or bimodal? Symmetric or skewed?
Explain why.
22) Number of times each face of a fair five-sided die shows in 50 tosses.
A) The distribution would likely be uniform, with around 50 occurrences of each side.
B) The distribution would likely be uniform, with around 10 occurrences of each side.
C) The distribution would likely be unimodal and skewed right. The average of the numbers on the face of the die
would be around 3, with more tosses greater than 3.
D) The distribution would likely be unimodal and symmetric. The average of the numbers on the face of the die
would be around 3, with a some tosses greater than 3 and some less than 3.
E) The distribution would likely be unimodal and skewed left. The average of the numbers on the face of the die
would be around 3, with more tosses less than 3.
23) Ages of high school students.
A) The distribution would likely be unimodal and slightly skewed to the right. The average age of the high school
students would be about the same. The distribution would be slightly skewed to the right, since there are more seniors.
B) The distribution would likely be bimodal and slightly skewed to the right. The average age of the freshman and
sophomores would be at one mode, and the average age of the juniors and seniors would be at the other mode. The
distribution would be slightly skewed to the right, since there are more seniors.
C) The distribution would likely be unimodal and slightly skewed to the left. The average age of the high school
students would be about the same. The distribution would be slightly skewed to the left, since there are more
freshmen.
D) The distribution would likely be unimodal and symmetric. The average age of the high school students would be
about the same, with some students that are older and some that are younger than the average age.
E) The distribution would likely be uniform. Freshmen tend to be about 14 years old; sophomores, 15; juniors, 16; and
seniors, 17. Since there is about an equal number of students in each class, the distribution is uniform.
Describe the distribution (shape, center, spread, unusual features).
24) Atlanta area animal shelters euthanize more animals per year than most other major city shelters. The following stemand-leaf display shows the number of homeless cats and dogs that had to be euthanized each year in the Atlanta area
for the period 1985-2004. Use both the stemplot and timeplot to describe the distribution.
Euthanized Animal Totals
81 0 0 1 3 3 8
82 1 1 5 7
83
84 6
85
86
87 0 5 7
88 4 4 4 9
89 3
90 0
Key:
87 5 = 87,500 cats and dogs euthanized
Compare the distributions (shape, center, spread, unusual features).
25) The back-to-back dotplot shows the number of fatalities per year caused by tornadoes in a certain state for two
periods: 1950-1974 and 1975-1999. In addition to comparing these distributions, state a reason explaining any
differences.
A fitness instructor measured the heart rates of the participants in a
yoga class at the conclusion of the class. The data is summarized in
the histogram below. There were fifteen people who participated in
the class between the ages of 25 and 45. Use the histogram to
answer the question.
26) How many participants had a heart rate between 120 and 130
bpm?
A) 3 B) 5 C) 2 D) 4
27) What percentage of the participants had a heart rate greater than
130 bpm?
A) 33% B) 13% C) 53% D) 27%
Describe the distribution (shape, center, spread, unusual features).
28) A student at a local university took a total of 20 exams during freshman year. The
student recorded the exam scores as percentages and created the following stemand-leaf display. The lower stem contains leaves with the digits 0-4 and the upper
stem contains leaves with digits 5-9. In addition to describing the distribution,
give a reason to account for the shape of this distribution.
Exam Grades
9 666666789
9 0122
8 5678
8
7 9
7
6
6 24
5
Key: 9 | 1 = 91%
29) A dotplot of the number of tornadoes each year in a certain county from
1948 to 2004 is given. Each dot represents a year in which there were that
many tornadoes.
Create the requested display for the data.
30) In a college health course, 49 students participated in a physical fitness assessment. One measure used in the
assessment was body fat. The body fat percentages for the 48 students is broken into two groups, men and women.
Create a back-to-back stem-and-leaf display of the data. Use split stems. Let the lower leaf represent digits 0-4 and the
upper leaf represent 5-9.
Menʹs Body Fat (%)
20 15 12 7
16
21 19 19 18 23
9
14 8
21 14 16 17 13 8
19 14 16 20 12 14
Womenʹs Body Fat (%)
33 28 25 26 30 15 28 20 29 27 18 18 35 16 21 25 24 19 11 25
27 27 21 30
Compare the distributions (shape, center, spread, unusual features).
31) The histograms show the cost of living, in dollars, for 32 U.S. cities. The histogram on the left shows the cost of
living for the 32 cities using bins $10 wide, and the histogram on the right displays the same data using bins that are
$6 wide.
Histogram
Collection 1
16
Histogram
Collection 1
12
14
10
12
8
10
8
6
6
4
4
2
2
80
90
100
110
120
Cost_of_Living
130
140
90
100
110
120
Cost_of_Living
130
140
32) The histograms below show the distribution of quiz scores on a ten point math quiz with and without a fifteen minute
review before the quiz. Describe the different shapes of the distributions. Does it appear that the fifteen minute review
resulted in improved quiz scores? Explain the evidence that supports your conclusion.
Without 15 minutes review before quiz
With 15 minutes review before quiz
9
10
8
8
7
6
6
5
4
4
3
2
2
1
4
5
6
7
8
Quiz_Scores_out_of_10_points
9
10
Answer Key
1) Who: Bicycles parked at college dormitories.; Cases:
Each bicycle is a case; What: Style, brand, color, and
age of bicycle; When: Not specified; Where: A small
university; Why: Not specified; How: A survey was
taken outside college dormitories.
4
5
6
7
8
Quiz_Scores_out_of_10_points
9
10
2) Who: Athletes; Cases: Each athlete is an individual
case; What: Age, days absent, medical history,
emergency contact, and allergy history; When:
Current; Where: Not specified; Why: State
requirement; How: Information is collected and
stored as athletic records.
3) A
4) A
5) A
6) B
7) A
8) 49.2%
9) 21.4%
10) A
11) Yes, because these categories do not overlap.
12) 29.3%
13) No, because these categories overlap.
14)
15) B
16)
13 1 3 5 5
14 0 1 2 4 4 7 8 9
15 1 2 2 3 6 9 9
16 0 3 4
17 1 2
Key: 14 | 2 = 142 pounds
17) 50.6%
18) E
19) C
20) 51.3%
21) 28.5%
22) B
23) E
24) The distribution of the number of cats and dogs that
were euthanized is bimodal. The upper cluster is
between 87,000 and 90,000 euthanized, with a center
at around 88,400. The lower cluster is between
81,000 and 82,000 euthanized, with a center at
around 81,000. The timeplot shows that the number
of animals euthanized has increased over the period
1985-2004, with a significant increase between 1994
and 1996.
25) The distribution of the number of fatalities per year
for the period 1950-1974 is unimodal and
approximately symmetric. The center of the
distribution is about 2 fatalities per year. The
number of fatalities per year ranges from 0 to 5
deaths. For the period 1975-1999, the distribution of
the number of fatalities per year is also unimodal,
but skewed to the right. A typical number of
fatalities for this distribution is 0 fatalities, with a
range of 0 to 5 deaths. Before 1975, there were more
fatalities as a result of tornadoes. Higher
construction standards, better warning systems, or
medical advancements could all account for this
difference.
26) A
27) C
28) The distribution of exam scores is skewed to the left.
Typically, the student scored 96% on exams, and the
exam scores are tightly clustered in the 90s. Two
exam scores are outliers, when the student scored
below 65%. It is possible that the student had a
difficult time with one of his or her courses in that
year. Regardless of the possible reasons, these two
scores were unusual compared to the studentʹs other
exam scores.
29) The distribution of the number of tornadoes per year
is unimodal and skewed to the left, with a center
around 5 tornadoes per year. The number of
tornadoes per year ranges from 0 to 7.
30)
Menʹs Body Fat
Womenʹs Body Fat
(%)
(%)
9887 0
4444322 1 1
999876665 1 56889
31100 2 0114
2 5556777889
3 003
3 5
Key: 1 | 5 = 15% body fat
31) The distribution in the left histogram of the cost of
living in the 32 U.S. cities is unimodal and skewed
to the right. The distribution is centered around
$100, and spread out, with values ranging from $80
to $140. The distribution in the right histogram
appears bimodal, with many cities costing just under
$104 and another smaller cluster around $119.
There also appears to be an outlier in the right
histogram at $134 that was not apparent in the
histogram on the left.
32) Without the 15 minute review the distribution of
quiz scores is roughly symmetrical with a typical
score of 6 out of 10. With the 15 minute review the
distribution of quiz scores is left-skewed with a
typical score of 8 out of 10. The 15 minute review
worked. Without the review roughly 23% scored
higher than 8 out of 10, but after the review roughly
70% scored higher than 8 out of 10.