Chapter 2
Charts and Graphs
LEARNING OBJECTIVES
The overall objective of chapter 2 is for you to master several techniques for
summarizing and depicting data, thereby enabling you to:
1.
Recognize the difference between grouped and ungrouped data.
2.
Construct a frequency distribution.
3.
Construct a histogram, a frequency polygon, an ogive, a pie chart, a stem and leaf
plot, a Pareto chart, and a scatter plot.
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Student’s Solutions Manual and Study Guide
CHAPTER OUTLINE
2.1
Frequency Distributions
Class Midpoint
Relative Frequency
Cumulative Frequency
2.2
Graphic Depiction of Data
Histograms
Frequency Polygons
Ogives
Pie Charts
Stem and Leaf Plots
Pareto Charts
2.3
Graphical Depiction of Two-Variable Numerical Data: Scatter Plots
KEY TERMS
Class Mark
Class Midpoint
Cumulative Frequency
Frequency Distribution
Frequency Polygon
Grouped Data
Histogram
Ogive
Pareto Chart
Pie Chart
Range
Relative Frequency
Scatter Plot
Stem and Leaf Plot
Ungrouped Data
Chapter 2: Charts and Graphs 9
STUDY QUESTIONS
1. The following data represents the number of printer ribbons used in a company by each of 28
departments annually. This is an example of ______________ data.
8 4 5 10 6 5 4 6 3 4 4 6 1 12
2 11 2 5 3 2 6 7 6 12 7 1 8 9
2. Below is a frequency distribution of ages of managers with a large retail firm. This is an
example of _______________ data.
Age
20-29
30-39
40-49
50-59
over 60
f
11
32
57
43
18
3. For best results, a frequency distribution should have between _______________ and
_______________ classes.
4. The difference between the largest and smallest numbers is called the _______________.
5. Consider the values below. In constructing a frequency distribution, the beginning point
of the lowest class should be at least as small as _______________ and the endpoint of the
highest class should be at least as large as _______________.
27 21 8 10 9 16 11 12 21 11 29 19 17 22 28 28 29 19 18 26 17 34 19 16 20
6. The class midpoint can be determined by _______________.
7-9 Examine the frequency distribution below:
class
5 - under 10
10 - under 15
15 - under 20
20 - under 25
25 - under 30
30 - under 35
frequency
56
43
21
11
12
8
7. The relative frequency for the class 15 - under 20 is _______________.
8. The cumulative frequency for the class 20 - under 25 is _______________.
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Student’s Solutions Manual and Study Guide
9. The midpoint for the class 25 - under 30 is ___________.
10. The graphical depiction that is a type of vertical bar chart and is used to depict a frequency
distribution is a _______________.
11. The graphical depiction that utilizes cumulative frequencies is a _______________.
12. The graph shown below is an example of a _______________.
13. Consider the categories below and their relative amounts:
Category
A
B
C
D
E
Amount
112
319
57
148
202
If you were to construct a Pie Chart to depict these categories, then you would allot
_______________ degrees to category D.
14. Given the values below, construct a stem and leaf plot using two digits for the stem.
346 340 322 339 342 332 338
357 328 329 346 341 321 332
15. A vertical bar chart that displays the most common types of defects that occur with a product,
ranked in order from left to right, is called a __________________.
16. A two-dimensional plot of pairs of points often used to examine the relationship of two
numerical variables is called a _________________.
Chapter 2: Charts and Graphs 13
ANSWERS TO STUDY QUESTIONS
1. Raw or Ungrouped
10. Histogram
2. Grouped
11. Ogive
3. 5, 15
12. Frequency Polygon
4. Range
13. 148/838 of 360o = 63.6o
5. 8, 34
14. 32
33
34
35
6. Averaging the two class endpoints
1 2 8 9
2 2 8 9
0 1 2 6 6
7
7. 21/151 = .1391
15. Pareto Chart
8. 131
16. Scatter Plot
9. 27.5
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Student’s Solutions Manual and Study Guide
SOLUTIONS TO ODD-NUMBERED PROBLEMS IN CHAPTER 2
2.1
a)
One possible 5 class frequency distribution:
Class Interval
10 - under 25
25 - under 40
40 - under 55
55 - under 70
70 - under 85
b)
One possible 10 class frequency distribution:
Class Interval
10 - under 18
18 - under 26
26 - under 34
34 - under 42
42 - under 50
50 - under 58
58 - under 66
66 - under 74
74 - under 82
82 - under 90
c)
Frequency
9
13
11
9
8
50
Frequency
7
3
5
9
7
3
6
4
4
2
The ten class frequency distribution gives a more detailed breakdown of
temperatures, pointing out the smaller frequencies for the higher temperature
intervals. The five class distribution collapses the intervals into broader
classes making it appear that there are nearly equal frequencies in each class.
Chapter 2: Charts and Graphs 15
2.3
Class
Interval
0-5
5 - 10
10 - 15
15 - 20
20 - 25
25 - 30
30 - 35
Frequency
6
8
17
23
18
10
4
TOTAL 86
Class
Midpoint
2.5
7.5
12.5
17.5
22.5
27.5
32.5
Relative
Frequency
6/86 = .0698
.0930
.1977
.2674
.2093
.1163
.0465
1.0000
Cumulative
Frequency
6
14
31
54
72
82
86
The relative frequency tells us that it is most probable that a customer is in the
15 - 20 category (.2674). Over two thirds (.6744) of the customers are between 10
and 25 years of age.
2.5 Some examples of cumulative frequencies in business:
sales for the fiscal year,
costs for the fiscal year,
spending for the fiscal year,
inventory build-up,
accumulation of workers during a hiring buildup,
production output over a time period.
2.7 Histogram
Student’s Solutions Manual and Study Guide
16
Frequency Polygon
2.9
STEM
21
22
23
24
25
26
27
2. 11
LEAF
2, 8, 8, 9
0, 1, 2, 4, 6, 6, 7, 9, 9
0, 0, 4, 5, 8, 8, 9, 9, 9, 9
0, 0, 3, 6, 9, 9, 9
0, 3, 4, 5, 5, 7, 7, 8, 9
0, 1, 1, 2, 3, 3, 5, 6
0, 1,
Company
Delta
United
American
US Airways
Southwest
TOTAL
Proportion
Degrees
.27
.22
.21
.15
.15
97
79
76
54
54
1.00
360
Chapter 2: Charts and Graphs 17
2.13
STEM
1
2
3
4
5
6
7
8
LEAF
3, 6, 7, 7, 7, 9, 9, 9
0, 3, 3, 5, 7, 8, 9, 9
2, 3, 4, 5, 7, 8, 8
1, 4, 5, 6, 6, 7, 7, 8, 8, 9
0, 1, 2, 2, 7, 8, 9
0, 1, 4, 5, 6, 7, 9
0, 7
0
The stem and leaf plot shows that the number of passengers per flight was
relatively evenly distributed between the high teens through the sixties. Rarely
was there a flight with at least 70 passengers. The category of 40's contained the
most flights (10).
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Student’s Solutions Manual and Study Guide
2.15
3500
3000
Industrial Products
2500
2000
1500
1000
500
0
0
1000
2000
3000
4000
Human Food
2.17
Class Interval
Frequencies
16 - under 23
23 - under 30
30 - under 37
37 - under 44
44 - under 51
51 - under 58
6
9
4
4
4
3
TOTAL
30
5000
6000
7000
Chapter 2: Charts and Graphs 19
2.19
Class Interval
Frequencies
50 - under 60
60 - under 70
70 - under 80
80 - under 90
90 - under 100
13
27
43
31
9
TOTAL
Histogram
Frequency Polygon
123
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Student’s Solutions Manual and Study Guide
Ogive
2.21
STEM
LEAF
28
29
30
31
32
33
4, 6, 9
0, 4, 8
1, 6, 8, 9
1, 2, 4, 6, 7, 7
4, 4, 6
5
2.23
16
14
12
Y
10
8
6
4
2
0
0
2
4
6
8
10
X
12
14
16
18
Chapter 2: Charts and Graphs 21
2.25
Class
Interval
20 – 25
25 – 30
30 – 35
35 – 40
40 – 45
45 – 50
TOTAL
Frequency
8
6
5
12
15
7
53
Class
Midpoint
22.5
27.5
32.5
37.5
42.5
47.5
Relative
Frequency
8/53 = .1509
.1132
.0943
.2264
.2830
.1321
.9999
2.27
a) Histogram and a Frequency Polygon for 2.25
Class
Interval
20 - 25
25 - 30
30 - 35
35 - 40
40 - 45
45 - 50
TOTAL
Histogram
Frequency
8
6
5
12
15
7
53
Cumulative
Frequency
8
14
19
31
46
53
Cumulative
Frequency
8
14
19
3
46
53
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Student’s Solutions Manual and Study Guide
Frequency Polygon
b) Ogive
Chapter 2: Charts and Graphs 23
2.29
Amount Spent
on Prenatal Care
$ 0 - under $100
$100 - under $200
$200 - under $300
$300 - under $400
$400 - under $500
$500 - under $600
Histogram
Frequency
3
6
12
19
11
6
57
Cumulative
Frequency
3
9
21
40
51
57
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Student’s Solutions Manual and Study Guide
Frequency Polygon
Ogive
Chapter 2: Charts and Graphs 25
2.31 Genre
R&B
Alternative
Rap
Country
Soundtrack
Metal
Classical
Latin
TOTAL
Pie Chart
Albums Sold
Proportion
Degrees
146.4
102.6
73.7
64.5
56.4
26.6
14.8
14.5
.29
.21
.15
.13
.11
.05
.03
.03
104
76
54
47
40
18
11
11
1.00
361
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Student’s Solutions Manual and Study Guide
2.33
Industry
Total Release
Proportion
Degrees
Chemicals
Primary metals
Paper
Plastics & Rubber
Transportation
Equipment
Food
Fabricated Metals
Petroleum
Electrical
Equipment
737,100,000
566,400,000
229,900,000
109,700,000
.37
.28
.11
.05
133
101
40
18
102,500,000
89,300,000
85,900,000
63,300,000
.05
.04
.04
.03
18
14
14
11
29,100,000
.01
4
0.98
353
TOTAL
Pie Chart
Elec. Equip.
Petroleum
1%
Fab. Metals
3%
4%
Food
4%
Transportation Equipment
5%
Chemicals
38%
Plas. & Rubber
5%
Paper
11%
Primary Metals
29%
Chapter 2: Charts and Graphs 27
2.35
STEM
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
LEAF
12, 16, 24, 32, 99, 99
04, 28, 39, 46, 61, 88
20, 40, 59
12
53, 54
30, 34, 58
22, 34, 66, 78
63
48, 49, 90
66
21, 54, 57, 63, 91
38, 66, 66
31, 78
56
69
37, 50
31, 32, 58, 73
19, 23
2.37 The distribution of household income is bell-shaped with an average of about
$90,000 and a range of from $ 30,000 to $ 140,000.
2.39 The fewest number of audits is 12 and the most is 42. More companies (8)
performed 27 audits than any other number. Thirty-five companies performed
between 12 and 19 audits. Only 7 companies performed 40 or more audits.