Another graphical technique useful for doing an exploratory analysis of quantitative data is called the stem and leaf diagram. The stem and leaf diagram is similar to the histogram introduced in Section 2.1 in that it displays the distribution for the quantitative variable.
However, unlike the histogram, in which the individual values of the data are lost if the vari- able of interest is broken into classes, the stem and leaf diagram shows the individual data values.
o u tc o m e 5
Lewis and Clark College,
$5,410
Idaho State University,
$6,320 University of Idaho,
$7,143 Boise State University,
$5,900 FIGURE 2.10 Pie Chart: Per-
Student Funding for Universities
Club Head Material Shaft Material 22%
21%
Club Head Size 21%
Golf Ball 27%
Don’t Know Shaft Length 8%
1%
Golf Equipment Impact
TRY EXERCISE 2-27 (pg. 81)
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Chapter 2 79Boise State University
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
$7,000
$8,000
$5,900
$7,143
$6,320
$5,410
University of
Idaho Idaho State
University Lewis and Clark College FIGURE 2.11 Bar Chart:
Per-Student Funding for Universities
EXAMPLE 2-9
Stem and Leaf Diagrams
Walk-In Health Clinic The administrator for the Walk-In Health Clinic is interested in the number of patients who enter the clinic daily. One method for analyzing the data for a sample of 200 days is the stem and leaf diagram. The following data represent the number of patients on each of the 200 days:
113 112 63 127 110 129 142 115 192 94
165 121 105 140 85 93 105 140 93 126
183 118 67 104 162 110 76 109 91 132
88 96 132 80 144 112 57 139 123 124
172 149 198 114 88 111 133 117 138 134
53 147 108 109 153 89 159 99 130 93
161 118 115 117 128 98 125 184 134 132
117 127 166 72 122 109 124 92 82 69
110 128 151 67 142 177 135 121 143 89
160 115 138 79 104 76 89 110 44 140
117 103 59 109 145 117 162 108 141 139
148 175 107 117 87 87 150 152 80 168
88 127 131 85 143 101 137 111 128 147
110 81 111 149 154 90 150 117 101 116
153 176 112 147 87 177 190 66 62 154
143 122 176 153 97 106 86 62 146 98
134 135 127 118 109 143 146 152 140 95
102 137 158 69 122 135 136 129 91 136
135 86 131 154 132 59 136 85 142 137
155 190 120 154 102 109 97 157 144 149
The stem and leaf diagram is constructed using the following steps:
s t e p 1 Sort the data from low to high.
The lowest value is 44 patients and the highest value is 198 patients.
s t e p 2 Split the values into a stem and leaf.
Leaf = units place; Stem = all digits left of the units place
For example, for the value 113, the stem is 11 and the leaf is 3. We are keeping one digit for the leaf.
HOW TO DO IT (Example 2-9)
Constructing Stem and Leaf Diagrams
1. Sort the data from low to high.
2. Analyze the data for the vari- able of interest to determine how you wish to split the values into a stem and a leaf.
3. List all possible stems in a sin- gle column between the lowest and highest values in the data.
4. For each stem, list all leaves associated with the stem.
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Graphs, Charts, and Tables—Describing Your Datas t e p 3 List all possible stems from lowest to highest.
s t e p 4 Itemize the leaves from lowest to highest and place next to the appropriate stems.
4 4
5 3 7 9 9 6 2 2 3 6 7 7 9 9 7 2 6 6 9
8 0 0 1 2 5 5 5 6 6 7 7 7 8 8 8 9 9 9 9 0 1 1 2 3 3 3 4 5 6 7 7 8 8 9 10 1 1 2 2 3 4 4 5 5 6 7 8 8 9 9 9 9 9 9
11 0 0 0 0 0 1 1 1 2 2 2 3 4 5 5 5 6 7 7 7 7 7 7 7 8 8 8 12 0 1 1 2 2 2 3 4 4 5 6 7 7 7 7 8 8 8 9 9
13 0 1 1 2 2 2 2 3 4 4 4 5 5 5 5 6 6 6 7 7 7 8 8 9 9 14 0 0 0 0 1 2 2 2 3 3 3 3 4 4 5 6 6 7 7 7 8 9 9 9 15 0 0 1 2 2 3 3 3 4 4 4 4 5 7 8 9
16 0 1 2 2 5 6 8 17 2 5 6 6 7 7
18 3 4
19 0 0 2 8
The stem and leaf diagram shows that most days have between 80 and 160 patients, with the most frequent value in the 110- to 120-patient range.
TRY EXERCISE 2-24 (pg. 80)
Skill Development
2-23. The following data reflect the percentages of employees with different levels of education:
Education Level Percentage Less than high school graduate 18
High school graduate 34
Some college 14
College graduate 30
Graduate degree 4
Total = 100 a. Develop a pie chart to illustrate these data.
b. Develop a horizontal bar chart to illustrate these data.
2-24. Given the following data on the age of a group of people, construct a stem and leaf diagram:
1 2 3 3 4 5
10 10 10 17 19 26
26 27 28 30 31 33
33 33 36 43 48 49
49 49 50 51 53 58
2-25. A university has the following number of students at each grade level:
Freshman 3,450
Sophomore 3,190
Junior 2,780
Senior 1,980
Graduate 750
a. Construct a bar chart that effectively displays these data.
b. Construct a pie chart to display these data.
c. Referring to the graphs constructed in parts a and b, indicate which you would favor as the more effective way of presenting these data. Discuss.
2-26. Given the following sales data for product type and sales region, construct at least two different bar charts that display the data effectively:
Region
Product Type East West North South
XJ-6 Model 200 300 50 170
X-15-Y Model 100 200 20 100
Craftsman 80 400 60 200
Generic 100 150 40 50
2.2 EXERCISES
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Chapter 2 812-27. An annual report for Murphy Oil Corporation reports the following refinery yields, in barrels per day, by product category for the United States and the United Kingdom.
United States
Product Category Refinery Yields—
barrels per day
Gasoline 61,128
Kerosene 11,068
Diesel and Home Heating Oils 41,305
Residuals 18,082
Asphalt, LPG, and other 14,802
Fuel and Loss 834
United Kingdom
Product Category Refinery Yields—
barrels per day
Gasoline 20,889
Kerosene 11,374
Diesel and Home Heating Oils 25,995
Residuals 8,296
Asphalt, LPG, and other 14,799
Fuel and Loss 2,810
a. Construct a pie chart to display United States refinery yields by product per day. Display the refinery yields data for each product category as a percentage of total refinery yields for all product categories.
b. Construct a pie chart to display United Kingdom refinery yields by product per day. Display the refinery yields data for each product category as a percentage of total refinery yields for all product categories.
c. Construct a bar chart that effectively compares United States and United Kingdom refinery yields by product category.
2-28. An online platform, Worldometers, features live world statistics on population, economics, and other
categories. The following data is the population of five major European countries in 2006 and 2016:
European Country
Population (in Millions) Year 2006 Year 2016
Germany 81.8 82.3
Turkey 62.3 73.4
France 59.5 63.4
Italy 56.8 59.1
United Kingdom 58.1 60.9
Source: www.worldometers.info/population/
a. Construct a pie chart for the population of the five European countries in 2006. Display the data for each country as a percentage of the total population in the countries.
b. Construct a pie chart in percentage for the five major European countries’ population in year 2016.
c. Construct a bar chart that compares the five major European countries’ population between the two years. Give a brief report for your graph.
2-29. A survey was conducted using a sample of 100 youths to determine what their most favorable leisure activity is. The following are the results (in percentage) obtained from the youths:
Leisure Activity Participation Percentage
Bike riding 12%
Watching TV/videos 51%
Electronic/computer games 32%
Art and craft 5%
a. Construct a pie chart (in percentage) to graphically display the data.
b. Construct a bar chart to graphically display the data.
c. Determine the main purpose of using a pie chart and a bar chart.
2-30. The following shows the amount of sugar (in million tons) exported by White Santy for the past five months.
Months March April May June July
Exported sugar amount (million tons)
0.69 0.58 0.55 0.62 0.65
a. Construct a bar chart for the exported sugar amount.
b. Construct a pie chart for the exported sugar amount.
c. Referring to parts a and b, identify which of the charts best represents the amount of sugar exported by White Santy for the past five months. Explain.
Business Applications
2-31. The number of British emigrants (in thousands) to five select destinations are shown in the following table:
Destination Australia Spain USA New Zealand France British emigra-
tion amount
52 34 26 21 28
a. Construct a bar chart to display the British emigrations.
b. Determine the proportion for the destination with the most British emigrations.
2-32. The first few years after the turn of the century saw a rapid increase in housing values, followed by a rapid decline due in part to the sub-prime crisis. The following table indicates the increase in the number of homes valued at more than one million dollars before 2005:
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Graphs, Charts, and Tables—Describing Your DataYear Number of $1 Million Homes
2000 394,878
2001 495,600
2002 595,441
2003 714,467
2004 1,034,386
Develop a horizontal bar chart to represent these data in graphical form.
2-33. Aunty Soo’s fish ball noodle stall at a local food court is a popular place for college students to meet. Soo noted that the business did not do well in the previous week. She refers to the sales record and lists the net profits earned last week as follows:
Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Net
profit ($)
192 145 183 132 189 176 190
Develop a horizontal bar chart to represent Soo’s net profit in the previous week, adding appropriate labels.
Summarize your findings.
2-34. WTS Travels is preparing its summer packages, and the sales manager, Raman, is trying to determine packages that are more profitable for the year. He refers to the last year’s sales records, which show the profits earned by their two summer packages over three months.
March April May
Package A profit ($ 000) 38.3 41.4 39.7 Package B profit ($ 000) 41.8 42.2 40.6
Raman wants a comparison of the two packages and wants to know the total profit earned by each within the three months. Construct an appropriate graph for Raman.
Based on your graph, write a short report for him.
2-35. The 2014 Annual Report of the Procter & Gamble Company (see www.pginvestor.com) reported the following percentages for its five global business segments:
Global Segment Percent of Total Sales
Beauty 24%
Grooming 10%
Health Care 9%
Fabric Care and Home Care 32%
Baby Care and Family Care 25%
a. Construct a bar chart that displays this information by global business segment.
b. Construct a pie chart that displays each global business segment’s percentage of total global segment net sales.
2-36. A fast-food restaurant monitors its drive-thru service times electronically to ensure that its speed of service
is meeting the company’s goals. A sample of 28 drive- thru times was recently taken and is shown here:
Speed of Service (Time in Seconds)
83 138 145 147
130 79 156 156
90 85 68 93
178 76 73 119
92 146 88 103
116 134 162 71
181 110 105 74
a. Construct a stem and leaf diagram of the speed of service times.
b. What range of time might the restaurant say is the most frequent speed of service?
2-37. A random sample of 30 customer records for a
physician’s office showed the following times (in days) required to collect insurance payments:
Number of Days to Collect Payment
34 55 36 39 36
32 35 30 47 31
60 66 48 43 33
24 37 38 65 35
22 45 33 29 41
38 35 28 56 56
a. Construct a stem and leaf diagram of these data.
b. Within what range of days are most payments collected?
2-38. The following data represent the seat capacity for major airlines on an annual basis:
Airline Seat Capacity (in Billions) Airline
Capacity
United Delta Northwest U.S. Airways ATA
145 130 92 54 21
a. Construct a bar graph representing the seat capacity of the major airlines for the five airlines indicated.
b. Produce a pie chart exhibiting the percentage of the total seat capacity for the five major airlines.
2-39. A survey conducted at a state university that asked students what brand of digital music device they owned yielded the following data:
Corporation Apple Samsung LG Nokia HTC Percentage 74% 6.4% 3.9% 3.6% 2.6%
a. Generate a bar chart to display these data.
b. Generate a pie chart to display these data.
c. Which of the two displays more effectively presents the data? Explain your answer.
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Chapter 2 83Computer Software Exercises
2-40. Suppose that cars with high consumer satisfaction ratings have a tendency to stay on dealers’ lots a shorter period of time. As an example, suppose the Honda Ridgeline had stayed on dealers’ lots an average of 24 days. The file titled Honda contains 50 lengths of stay on dealers’ lots for Ridgeline trucks.
Construct a stem and leaf display for these data.
2-41. The manager for a credit union has selected a random sample of 300 of the credit union’s credit card customers. The data are in a file called Capital. The manager is interested in graphically displaying the percentage of card holders of each gender.
a. Determine the appropriate type of graph to use in this application.
b. Construct the graph and interpret it.
2-42. A health insurance company selected a random sample of hospitals from each of four categories of hospitals: university related, religious related, community owned, and privately owned. At issue is the hospital charges associated with outpatient gall bladder surgery. The data are in the file called Hospitals.
a. Compute the average charge for each hospital category.
b. Construct a bar chart showing the averages by hospital category.
c. Discuss why a pie chart would not in this case be an appropriate graphical tool.
2-43. Amazon.com has become one of the success stories of the Internet age. Its growth can be seen by examining its increasing sales volume (in $billions)
and the net income/loss during Amazon’s
operations. A file titled Amazon contains these data for its first 17 years (source: 2011 Amazon Annual Report).
a. Construct one bar graph illustrating the relationship between sales and income for each separate year of Amazon’s existence.
b. Describe the type of relationship that exists between the years in business and Amazon’s sales volume.
c. Amazon’s sales rose sharply. However, its net income yielded losses, which increased during the first few years. In which year did this situation reverse itself and show improvement in the net income balance sheet?
2-44. In your capacity as assistant to the administrator at Freedom Hospital, you have been asked to develop a graphical presentation that focuses on the insurance carried by the geriatric patients at the hospital. The data file Patients contains data for a sample of geriatric patients. In developing your presentation, please do the following:
a. Construct a pie chart that shows the percentage of patients with each health insurance payer.
b. Develop a bar chart that shows total charges for patients by insurance payer.
c. Develop a stem and leaf diagram for the length-of- stay variable.
d. Develop a bar chart that shows the number of males and females by insurance carrier.