## SECTION 1.2 EXERCISES

For Exercise 1.16, see page 11; for Exercise 1.17, see page 12; for Exercises 1.18 and 1.19, see page 14; for Exercise 1.20, see page 16; for Exercises 1.21 and 1.22, see page 16; for Exercise 1.23, see page 19; and for Exercise 1.24, see page 21.

### Question 1.25

1.25 Your Facebook app can generate a million dollars a month. A report on Facebook suggests that Facebook apps can generate large amounts of money, as much as \$1 million a month.9 The following table gives the numbers of Facebook users by country for the top 10 countries based on the number of users:10

FACEBK

(in millions)
Brazil 29.30
India 37.38
Mexico 29.80
Germany 21.46
France 23.19
Philippines 26.87
Indonesia 40.52
United Kingdom 30.39
United States 155.74
Turkey 30.63
1. (a) Use a bar graph to describe the numbers of users in these countries.

2. (b) Do you think that the United States is an outlier in this data set? Explain your answer.

3. (c) Describe the major features of your graph in a short paragraph.

### Question 1.26

1.26 Facebook use increases by country. Refer to the previous exercise. The report also gave the increases in the number of Facebook users for a one-month period for the same countries:

FACEBK

Country Increase in users
(in millions)
Brazil 2.47
India 1.75
Mexico 0.84
Germany 0.51
France 0.38
Philippines 0.38
Indonesia 0.37
United Kingdom 0.22
United States 0.65
Turkey 0.09

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1. (a) Use a bar graph to describe the increase in users in these countries.

2. (b) Describe the major features of your graph in a short paragraph.

3. (c) Do you think a stemplot would be a better graphical display for these data? Give reasons for your answer.

4. (d) Write a short paragraph about possible business opportunities suggested by the data you described in this exercise and the previous one.

### Question 1.27

1.27 The Titanic and class. On April 15, 1912, on her maiden voyage, the Titanic collided with an iceberg and sank. The ship was luxurious but did not have enough lifeboats for the 2224 passengers and crew. As a result of the collision, 1502 people died.11 The ship had three classes of passengers. The level of luxury and the price of the ticket varied with the class, with first class being the most luxurious. There were 323 passengers in first class, 277 in second class, and 709 in third class.12

TITANIC

1. (a) Make a bar graph of these data.

2. (b) Give a short summary of how the number of passengers varied with class.

3. (c) If you made a bar graph of the percent of passengers in each class, would the general features of the graph differ from the one you made in part (a)? Explain your answer.

### Question 1.28

1.28 Another look at the Titanic and class. Refer to the previous exercise.

TITANIC

1. (a) Make a pie chart to display the data.

2. (b) Compare the pie chart with the bar graph. Which do you prefer? Give reasons for your answer.

### Question 1.29

1.29 Who survived? Refer to the two previous exercises. The number of first-class passengers who survived was 200. For second and third class, the numbers were 119 and 181, respectively. Create a graphical summary that shows how the survival of passengers depended on class.

TITANIC

### Question 1.30

1.30 Potassium from potatoes. The 2015 Dietary Guidelines for Americans13 notes that the average potassium (K) intake for U.S. adults is about half of the recommended amount. A major source of potassium is potatoes. Nutrients in the diet can have different absorption depending on the source. One study looked at absorption of potassium from different sources. Participants ate a controlled diet for five days, and the amount of potassium absorbed was measured. Data for a diet that included 40 milliequivalents (mEq) of potassium were collected from 27 adult subjects.14

KPOT40

1. (a) Make a stemplot of the data.

2. (b) Describe the pattern of the distribution.

3. (c) Are there any outliers? If yes, describe them and explain why you have declared them to be outliers.

4. (d) Describe the shape, center, and spread of the distribution.

### Question 1.31

1.31 Potassium from a supplement. Refer to the previous exercise. Data were also recorded for 29 subjects who received a potassium salt supplement with 40 mEq of potassium. Answer the questions in the previous exercise for the supplemented subjects.

KSUP40

### Question 1.32

1.32 Energy consumption. The U.S. Energy Information Administration reports data summaries of various energy statistics. Let’s look at the total amount of energy consumed, in quadrillions of British thermal units (Btu), for each month in a recent year. Here are the data:15

ENERGY

Month Energy
Month Energy
January 9.58 July 8.23
February 8.46 August 8.21
March 8.56 September 7.64
April 7.56 October 7.78
May 7.66 November 8.19
June 7.79 December 8.82
1. (a) Look at the table and describe how the energy consumption varies from month to month.

2. (b) Make a time plot of the data and describe the patterns.

3. (c) Suppose you wanted to communicate information about the month-to-month variation in energy consumption. Which would be more effective, the table of the data or the graph? Give reasons for your answer.

### Question 1.33

1.33 Energy consumption in a different year. Refer to the previous exercise. Here are the data for the previous year:

ENERGY

Month Energy
Month Energy
January 8.99 July 8.27
February 8.02 August 8.17
March 8.38 September 7.64
April 7.52 October 7.72
May 7.62 November 8.14
June 7.72 December 9.08

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1. (a) Analyze these data using the questions in the previous exercise as a guide.

2. (b) Compare the patterns across the two years. Describe any similarities and differences.

### Question 1.34

1.34 Favorite colors. What is your favorite color? One survey produced the following summary of responses to that question: blue, 42%; green, 14%; purple, 14%; red, 8%; black, 7%; orange, 5%; yellow, 3%; brown, 3%; gray, 2%; and white, 2%.16 Make a bar graph of the percents and write a short summary of the major features of your graph.

FAVCOL

### Question 1.35

1.35 Least-favorite colors. Refer to the previous exercise. The same study also asked people about their least-favorite color. Here are the results: orange, 30%; brown, 23%; purple, 13%; yellow, 13%; gray, 12%; green, 4%; white, 4%; red, 1%; black, 0%; and blue, 0%. Make a bar graph of these percents and write a summary of the results.

LFAVCOL

### Question 1.36

1.36 Garbage. The formal name for garbage is “municipal solid waste.” In the United States, approximately 250 million tons of garbage are generated in a year. Following is a breakdown of the materials that made up American municipal solid waste in 2012:17

GARBAGE

Material Weight
(million tons)
Percent
of total
Food scraps 36.4 14.5
Glass 11.6 4.6
Metals 22.4 8.9
Paper, paperboard 68.6 27.4
Plastics 31.7 12.7
Rubber, leather 7.5 3.0
Textiles 14.3 5.7
Wood 15.8 6.3
Yard trimmings 34.0 13.5
Other 8.5 3.4
Total 250.9 100.0
1. (a) Add the weights. The sum is not exactly equal to the value of 250.9 million tons given in the table. Why?

2. (b) Make a bar graph of the percents. The graph gives a clearer picture of the main contributors to garbage if you order the bars from tallest to shortest.

3. (c) Also make a pie chart of the percents. Comparing the two graphs, notice that it is easier to see the small differences among “Food scraps,” “Plastics,” and “Yard trimmings” in the bar graph.

### Question 1.37

1.37 Vehicle colors. Vehicle colors differ among regions of the world. Here are data on the most popular colors for vehicles in North America:18

VCOLOR

Color (percent)
White 24
Black 19
Silver 16
Gray 15
Red 10
Blue 7
Brown 5
Other 4
1. (a) Describe these data with a bar graph.

2. (b) Describe these data with a pie chart.

3. (c) Which graphical summary do you prefer. Give reasons for your answer.

### Question 1.38

1.38 Sketch a skewed distribution. Sketch a histogram for a distribution that is skewed to the left. Suppose that you and your friends emptied your pockets of coins and recorded the year marked on each coin. The distribution of dates would be skewed to the left. Explain why.

### Question 1.39

1.39 Grades and self-concept. Table 1.3 presents data on 78 seventh-grade students in a rural midwestern school.19 The researcher was interested in the relationship between the students’ “self-concept” and their academic performance. The data we give here include each student’s grade point average (GPA), score on a standard IQ test, and gender, taken from school records. Gender is coded as F for female and M for male. The students are identified only by an observation number (OBS). The missing OBS numbers show that some students dropped out of the study. The final variable is each student’s score on the Piers-Harris Children’s Self-Concept Scale, a psychological test administered by the researcher.

SEVENGR

1. (a) How many variables does this data set contain? Which are categorical variables and which are quantitative variables?

2. (b) Make a stemplot of the distribution of GPA, after rounding to the nearest tenth of a point.

3. (c) Describe the shape, center, and spread of the GPA distribution. Identify any suspected outliers from the overall pattern.

4. (d) Make a back-to-back stemplot of the rounded GPAs for female and male students. Write a brief comparison of the two distributions.

### Question 1.40

1.40 Describe the IQ scores. Make a graph of the distribution of IQ scores for the seventh-grade students in Table 1.3. Describe the shape, center, and spread of the distribution, as well as any outliers. IQ scores are usually said to be centered at 100. Is the midpoint for these students close to 100, clearly above, or clearly below?

SEVENGR

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Table : TABLE 1.3 Educational Data for 78 Seventh-Grade Students
OBS GPA IQ Gender Self-
concept
OBS GPA IQ Gender Self-
concept
001 7.940 111 M 67 043 10.760 123 M 64
002 8.292 107 M 43 044 9.763 124 M 58
003 4.643 100 M 52 045 9.410 126 M 70
004 7.470 107 M 66 046 9.167 116 M 72
005 8.882 114 F 58 047 9.348 127 M 70
006 7.585 115 M 51 048 8.167 119 M 47
007 7.650 111 M 71 050 3.647 97 M 52
008 2.412 97 M 51 051 3.408 86 F 46
009 6.000 100 F 49 052 3.936 102 M 66
010 8.833 112 M 51 053 7.167 110 M 67
011 7.470 104 F 35 054 7.647 120 M 63
012 5.528 89 F 54 055 0.530 103 M 53
013 7.167 104 M 54 056 6.173 115 M 67
014 7.571 102 F 64 057 7.295 93 M 61
015 4.700 91 F 56 058 7.295 72 F 54
016 8.167 114 F 69 059 8.938 111 F 60
017 7.822 114 F 55 060 7.882 103 F 60
018 7.598 103 F 65 061 8.353 123 M 63
019 4.000 106 M 40 062 5.062 79 M 30
020 6.231 105 F 66 063 8.175 119 M 54
021 7.643 113 M 55 064 8.235 110 M 66
022 1.760 109 M 20 065 7.588 110 M 44
024 6.419 108 F 56 068 7.647 107 M 49
026 9.648 113 M 68 069 5.237 74 F 44
027 10.700 130 F 69 071 7.825 105 M 67
028 10.580 128 M 70 072 7.333 112 F 64
029 9.429 128 M 80 074 9.167 105 M 73
030 8.000 118 M 53 076 7.996 110 M 59
031 9.585 113 M 65 077 8.714 107 F 37
032 9.571 120 F 67 078 7.833 103 F 63
033 8.998 132 F 62 079 4.885 77 M 36
034 8.333 111 F 39 080 7.998 98 F 64
035 8.175 124 M 71 083 3.820 90 M 42
036 8.000 127 M 59 084 5.936 96 F 28
037 9.333 128 F 60 085 9.000 112 F 60
038 9.500 136 M 64 086 9.500 112 F 70
039 9.167 106 M 71 087 6.057 114 M 51
040 10.140 118 F 72 088 6.057 93 F 21
041 9.999 119 F 54 089 6.938 106 M 56

### Question 1.41

1.41 Describe the self-concept scores. Based on a suitable graph, briefly describe the distribution of self-concept scores for the students in Table 1.3. Be sure to identify any suspected outliers.

SEVENGR

27

### Question 1.42

1.42 The Boston Marathon. Women were allowed to enter the Boston Marathon in 1972. Here are the times (in minutes, rounded to the nearest minute) for the winning women from 1972 to 2015.

Make a graph that shows change over time. What overall pattern do you see? Have times stopped improving in recent years? If so, when did improvement end?

MARATH

Year Time Year Time Year Time Year Time
1972 190 1983 143 1994 142 2005 145
1973 186 1984 149 1995 145 2006 143
1974 167 1985 154 1996 147 2007 149
1975 162 1986 145 1997 146 2008 145
1976 167 1987 146 1998 143 2009 152
1977 168 1988 145 1999 143 2010 146
1978 165 1989 144 2000 146 2011 142
1979 155 1990 145 2001 144 2012 151
1980 154 1991 144 2002 141 2013 146
1981 147 1992 144 2003 145 2014 139
1982 150 1993 145 2004 144 2015 145