3
wrangler/Shutterstock.com
Graphical Descriptive
Techniques II
Chapter Outline
3-1 Graphical Techniques to Describe a Set of Interval Data
3-2 Describing Time-Series Data
What Is Happening to the Price of Gasoline?
In the past two decades, the price of gasoline has been on a roller coaster. In 1995, the
Comstock Images/Getty Images
DATA average retail price of unleaded regular gasoline in the United States was
Xm03-00
about $1.20. Over the next 13 years, the average price rose to over $4.00.
It then fell precipitously to less than $1.80 in early 2016. (One U.S. gallon
equals 3.79 liters.) While the lower price is appreciated by all drivers, the rapidly chang-
ing price is somewhat bewildering to motorists. When the price was rising we understood
there were several reasons. First, oil is a finite resource; the world will eventually run out. On page 70, you will
find our answer.
In 2016, the world was consuming more than 100 million barrels per day—more than
36 billion barrels per year. The total proven world reserves of oil are 1,689,078,618,100
45
93453_ch03_hr_045-085.indd 45 1/31/17 8:25 PM
, 3-1 Graphical Techniques to Describe a Set of Interval Data
barrels. At today’s consumption levels, the proven reserves will be exhausted in 47 years. (It should be noted, how-
ever, that in 2009, the proven reserves of oil amounted to 1,349.4 billion barrels and in 2012 the proven reserves
were 1,481.5 billion barrels, indicating that new oil discoveries are offsetting increasing usage.) Second, China’s
and India’s industries are rapidly increasing and require ever-increasing amounts of oil. Third, over the last 20 years,
hurricanes have threatened the oil rigs in the Gulf of Mexico. In 1995, the price of oil (West Texas intermediate
crude) was under $20 per barrel (one barrel equals 42 U.S. gallons). In 2008, the price rose to over $130, and in
early 2016 the price fluctuated between $30 and $40. To help understand the gasoline/oil price relationship, we
determined the monthly average price of gasoline and the price of a barrel of West Texas intermediate crude for the
period 1995 to 2016. Use a graphical technique to describe the relationship. See page 70 for our solution.
C
Introduction hapter 2 introduced graphical techniques used to summarize and present nomi-
nal data. In this chapter, we do the same for interval data. Section 3-1 presents
techniques to describe a set of interval data, Section 3-2 introduces time series
and the method used to present time-series data, and Section 3-3 describes the tech-
nique we use to describe the relationship between two interval variables. We complete
this chapter with a discussion of how to properly use graphical methods in Section 3-4.
3-1 Graphical Techniques to Describe a Set of Interval Data
In this section we introduce the histogram, which is a powerful graphical technique used to
summarize a set of interval data. As you will see the histogram is also used to help explain
an important aspect of probability (see Chapter 8).
Example 3.1
DATA Xm03-01 Ages of Online PC Gamers
The value market of video games increases year by year and in 2019 it is expected
to reach 33.6 billion US dollars, with Asia Pacific being the largest gaming market. In
2018 there were more than 2.5 billion video gamers from all over the world with 35%
of them between ages of 21 to 35 years. As part of a larger study, a gaming
company, which recently released a new online PC game, wanted to acquire
information about the age of the gamers of its new online game. The company’s
marketing manager selected a random sample of 200 subscribers and recorded the
age of gamers. The results are shown here. What information can be extracted from
these data?
93453_ch03_hr_045-085.indd 46 1/31/17 8:25 PM
,10 15 18 15 13 23 18 31 20 23
53 14 22 21 14 16 24 15 19 13
16 18 14 22 11 18 24 25 18 18
15 20 14 26 22 14 18 49 23 27
14 17 24 30 10 25 26 14 22 40
53 30 28 28 32 23 15 19 35 49
20 28 19 21 10 9 14 41 14 24
33 22 22 12 44 25 20 17 21 30
15 16 15 16 30 44 39 28 22 20
40 19 13 9 26 17 32 20 51 22
15 25 15 10 13 25 51 22 16 23
13 28 15 24 20 30 23 49 45 50
15 15 16 22 31 8 16 21 20 36
22 52 16 18 23 27 27 17 46 30
, 25 10 10 20 19 33 22 22 16 12
26 21 11 21 19 49 21 18 31 21
17 16 17 16 29 42 25 38 22 21
16 9 25 14 25 21 18 16 46 32
15 25 23 48 12 16 45 16 27 22
33 14 20 31 26 42 14 25 27 17
Solution:
Little information can be developed just by casually reading through the 200
observations. If we examine the data more carefully, we may discover that the
youngest online PC player in this sample is 8 and the oldest is 53. To gain useful
information, we need to know how the ages are distributed between 0 and 60. Are
there many young players with few old ones? Are the ages somewhat similar or do
they vary considerably? To help answer these questions and others like them, we
will construct a frequency distribution from which a histogram can be drawn. In the
previous chapter, a frequency distribution was created by counting the number of
times each category of the nominal variable occurred. We create a frequency
distribution for interval data by counting the number of observations that fall into
each of a series of intervals, called classes that cover the complete range of
observations. We discuss how to decide the number of classes and the upper and
lower limits of the intervals later. We have chosen nine classes defined in such a
way that each observation falls into one and only one class. These classes are
defined as follows:
wrangler/Shutterstock.com
Graphical Descriptive
Techniques II
Chapter Outline
3-1 Graphical Techniques to Describe a Set of Interval Data
3-2 Describing Time-Series Data
What Is Happening to the Price of Gasoline?
In the past two decades, the price of gasoline has been on a roller coaster. In 1995, the
Comstock Images/Getty Images
DATA average retail price of unleaded regular gasoline in the United States was
Xm03-00
about $1.20. Over the next 13 years, the average price rose to over $4.00.
It then fell precipitously to less than $1.80 in early 2016. (One U.S. gallon
equals 3.79 liters.) While the lower price is appreciated by all drivers, the rapidly chang-
ing price is somewhat bewildering to motorists. When the price was rising we understood
there were several reasons. First, oil is a finite resource; the world will eventually run out. On page 70, you will
find our answer.
In 2016, the world was consuming more than 100 million barrels per day—more than
36 billion barrels per year. The total proven world reserves of oil are 1,689,078,618,100
45
93453_ch03_hr_045-085.indd 45 1/31/17 8:25 PM
, 3-1 Graphical Techniques to Describe a Set of Interval Data
barrels. At today’s consumption levels, the proven reserves will be exhausted in 47 years. (It should be noted, how-
ever, that in 2009, the proven reserves of oil amounted to 1,349.4 billion barrels and in 2012 the proven reserves
were 1,481.5 billion barrels, indicating that new oil discoveries are offsetting increasing usage.) Second, China’s
and India’s industries are rapidly increasing and require ever-increasing amounts of oil. Third, over the last 20 years,
hurricanes have threatened the oil rigs in the Gulf of Mexico. In 1995, the price of oil (West Texas intermediate
crude) was under $20 per barrel (one barrel equals 42 U.S. gallons). In 2008, the price rose to over $130, and in
early 2016 the price fluctuated between $30 and $40. To help understand the gasoline/oil price relationship, we
determined the monthly average price of gasoline and the price of a barrel of West Texas intermediate crude for the
period 1995 to 2016. Use a graphical technique to describe the relationship. See page 70 for our solution.
C
Introduction hapter 2 introduced graphical techniques used to summarize and present nomi-
nal data. In this chapter, we do the same for interval data. Section 3-1 presents
techniques to describe a set of interval data, Section 3-2 introduces time series
and the method used to present time-series data, and Section 3-3 describes the tech-
nique we use to describe the relationship between two interval variables. We complete
this chapter with a discussion of how to properly use graphical methods in Section 3-4.
3-1 Graphical Techniques to Describe a Set of Interval Data
In this section we introduce the histogram, which is a powerful graphical technique used to
summarize a set of interval data. As you will see the histogram is also used to help explain
an important aspect of probability (see Chapter 8).
Example 3.1
DATA Xm03-01 Ages of Online PC Gamers
The value market of video games increases year by year and in 2019 it is expected
to reach 33.6 billion US dollars, with Asia Pacific being the largest gaming market. In
2018 there were more than 2.5 billion video gamers from all over the world with 35%
of them between ages of 21 to 35 years. As part of a larger study, a gaming
company, which recently released a new online PC game, wanted to acquire
information about the age of the gamers of its new online game. The company’s
marketing manager selected a random sample of 200 subscribers and recorded the
age of gamers. The results are shown here. What information can be extracted from
these data?
93453_ch03_hr_045-085.indd 46 1/31/17 8:25 PM
,10 15 18 15 13 23 18 31 20 23
53 14 22 21 14 16 24 15 19 13
16 18 14 22 11 18 24 25 18 18
15 20 14 26 22 14 18 49 23 27
14 17 24 30 10 25 26 14 22 40
53 30 28 28 32 23 15 19 35 49
20 28 19 21 10 9 14 41 14 24
33 22 22 12 44 25 20 17 21 30
15 16 15 16 30 44 39 28 22 20
40 19 13 9 26 17 32 20 51 22
15 25 15 10 13 25 51 22 16 23
13 28 15 24 20 30 23 49 45 50
15 15 16 22 31 8 16 21 20 36
22 52 16 18 23 27 27 17 46 30
, 25 10 10 20 19 33 22 22 16 12
26 21 11 21 19 49 21 18 31 21
17 16 17 16 29 42 25 38 22 21
16 9 25 14 25 21 18 16 46 32
15 25 23 48 12 16 45 16 27 22
33 14 20 31 26 42 14 25 27 17
Solution:
Little information can be developed just by casually reading through the 200
observations. If we examine the data more carefully, we may discover that the
youngest online PC player in this sample is 8 and the oldest is 53. To gain useful
information, we need to know how the ages are distributed between 0 and 60. Are
there many young players with few old ones? Are the ages somewhat similar or do
they vary considerably? To help answer these questions and others like them, we
will construct a frequency distribution from which a histogram can be drawn. In the
previous chapter, a frequency distribution was created by counting the number of
times each category of the nominal variable occurred. We create a frequency
distribution for interval data by counting the number of observations that fall into
each of a series of intervals, called classes that cover the complete range of
observations. We discuss how to decide the number of classes and the upper and
lower limits of the intervals later. We have chosen nine classes defined in such a
way that each observation falls into one and only one class. These classes are
defined as follows:
