Chapter 1 Review
AP Statistics
Name:______________________________
Multiple Choice Practice.
1.
If the standard deviation of a set of observations is 0, you can conclude
(a)
(b)
(c)
(d)
(e)
That there is no relationship between the observations.
That the average value is 0.
That all observations are the same value.
That a mistake in arithmetic has been made.
None of the above.
2. A random sample of golf scores gives the following summary statistics: n = 20, 𝑥̅ = 84.5, 𝑠𝑥 = 11.5, min = 68, Q1 =
78, M = 86, Q3 = 91, max = 112. What can be said about the number of outliers?
(a)
(b)
(c)
(d)
(e)
0
1
2
At least 1
At least 2
3. When a set of data has suspect outliers, which of the following are preferred measures of central tendency and of
variability?
(a)
(b)
(c)
(d)
(e)
Mean and standard deviation
Mean and variance
Mean and range
Median and range
Median and interquartile range
4. In which of the following histograms is the mean less than the median?
(a)
(b)
(d)
(c)
(e)
5. For which of the following would it be inappropriate to display the data with a single pie chart?
(a)
(b)
(c)
(d)
(e)
The distribution of car colors for vehicles purchased in the last month.
The distribution of unemployment percentages for each of the 50 states.
The distribution of favorite sport for a sample of 30 middle school students.
The distribution of shoe type worn by shopper at a local mall.
The distribution of presidential candidate preference for voters in a state.
6. When comparing two distributions, it would be best to use relative frequency histograms (percents) rather than
frequency histograms (counts) when
(a)
(b)
(c)
(d)
(e)
The distributions have different shapes.
The distributions have different spreads.
The distributions have different centers.
The distributions have different numbers of observations.
At least one of the distributions has outliers.
7. The stemplot shows the number of home runs hit by each of the 30 Major League Baseball teams in 2011. Home run
totals above what value should be considered outliers?
09
10
11
12
13
14
15
16
17
18
19
20
21
22
15
3789
47
19
(a)
(b)
(c)
(d)
(e)
89
34445
239
223
356
1
3
0
2
173
210
222
229
257
8. Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive to
earthquakes with intensities between 4.0 and 9.0 on the Richter scale. Measurements of nine earthquakes gave the
following readings:
4.5
(a)
(b)
(c)
(d)
(e)
L
5.5
H
8.7
8.9
6.0
H
5.2
5.75
6.00
6.47
8.70
Cannot be determined
9. You record the year released, the rating, the length (in minutes), genre, and Box office sales for 7 movies. The
number and type of variables you have recorded is:
(a)
(b)
(c)
(d)
(e)
5 quantitative, 0 categorical.
6 quantitative, 0 categorical.
4 quantitative, 2 categorical.
3 quantitative, 2 categorical.
2 quantitative, 3 categorical.
Multiple Choice Answers: 1. C, 2. D, 3. E, 4. C, 5. B, 6. D, 7. E, 8. B, 9. D
Resistance
Which summary is best to use if we have a skewed distribution? Why?
Which summary is best to use if we have a symmetric distribution (free of outliers)? Why?
Free Response Practice - You will probably need your own paper to work through this section.
10. (R1.7 p. 77) Here are the survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a
medical experiment. Survival times, whether of machines under stress or cancer patients after treatment, usually have
distributions that are skewed to the right.
43
80
91
103
137
191
45
80
92
104
138
198
53
81
92
107
139
211
56
81
97
108
144
214
56
81
99
109
145
243
57
82
99
113
147
249
58
83
100
114
156
329
66
83
100
118
162
380
67
84
101
121
174
403
73
88
102
123
178
511
74
89
102
126
179
522
79
91
102
128
184
598
(a) Make a histogram of the data and describe its main features. Does it show the expected right skew?
(b) Now make a boxplot of the data. Be sure to check for outliers.
(c) Which measure of center and spread would you use to summarize the distribution – the mean and standard deviation
or the median and IQR? Justify your answer.
11. (2010B #1) As a part of the United States Department of Agriculture’s Super Dump cleanup efforts in the early 1990s,
various sites in the country were targeted for cleanup. Three of the targeted sites—River X, River Y, and River Z—had
become contaminated with pesticides because they were located near abandoned pesticide dump sites. Measurements of the
concentration of aldrin (a commonly used pesticide) were taken at twenty randomly selected locations in each river near the
dump sites.
The boxplots shown below display the five-number summaries for the concentrations, in parts per million (ppm) of aldrin, for
the twenty locations that were sampled in each of the three rivers.
(a) Compare the distributions of the concentration of aldrin
among the three rivers.
(b) The twenty concentrations of aldrin for River X are given
below.
3.4 4.0 5.6 3.7 8.0 5.5 5.3 4.2 4.3 7.3
8.6 5.1 8.7 4.6 7.5 5.3 8.2 4.7 4.8 4.6
Construct a stemplot that displays the concentrations of aldrin
for River X.
(c) Describe a characteristic of the distribution of aldrin concentrations in River X that can be seen in the stemplot but
cannot be seen in the boxplot.
12. (FR 65) A set of 91 scores has the following histogram:
(a) Draw a boxplot of the data in the
histogram.
(b) What feature does the histogram show that
is missed by the boxplot?
(c) What feature is more clearly distinguished
in the boxplot than in the histogram?
6
8
10
12
14
16
18
20
22
24
13. (2004 #1) A consumer advocate conducted a test of two popular gasoline additives, A and B. there are claims that the
use of either of these additives will increase gasoline mileage in cars. A random sample of 30 cars was selected. Each
car was filled with gasoline and the cars were run under the same driving conditions until the gas tanks were empty. The
distance traveled was recorded for each car.
Additive A was randomly assigned to 15 of the cars and additive B was randomly assigned to the other 15 cars. The gas
tank of each car was filled with gasoline and the assigned additive. The cars were again run under the same driving
conditions until the tanks were empty. The distance traveled was recorded and the difference in the distance with the
additivie minus the distance without the additive for each car was calculated.
The following table summarizes the calculated differences. Note that negative values indicate less distance was traveled
with the additive than without the additive.
Additive
A
B
Values Below Q1
-10, -8, -2
-5, -3, -3
Q1
1
-2
Median
3
1
Q3
4
25
Values above Q3
5, 7, 9
35, 37, 40
(a) Display parallel boxplots (showing outliers, if any) of the difference of the two additives.
(b) Two ways that the effective ness of a gasoline additive can be evaluated are by looking at either


The proportion of cars that have increased gas mileage when the additive is used in those cars
or
The mean increase in gas mileage when the additive is used in those cars.
i. Which additive, A or B, would you recommend if the goal is to increase gas mileage in the highest proportion of
cars? Explain your choice.
ii. Which additive, A or B, would you recommend if the goal is to have the highest mean increase in gas mileage?
Explain your choice.
14. (R1.4, p. 77) Is there a relationship between Facebook use and age among college students? The following two-way
table displays data for the 219 students who responded to the survey.
Facebook user?
Yes
No
Younger (18 – 22)
78
4
Age
Middle (23 – 27)
49
21
Older (28 and up)
21
46
(a) Find the marginal distribution for age.
(b) Find the conditional distribution for age among Facebook users. Now, find the conditional distribution for age
among non-Facebook users. Compare the distributions using a bar graph.
15. (#11, p. 21) Births are not evenly distributed across the days of the week. Here are the average numbers of babies born
each day of the week in the U.S. in a recent year:
Day
Births
Sunday
7374
(a) Present these data in a well-labeled bar graph. Would it also be
correct to make a pie chart?
Monday
11,704
Tuesday
13,169
(b) Suggest some possible reasons why there are fewer births on
Wednesday
13,038
weekends.
Thursday
13,013
Friday
12,664
Saturday
8459