Student’s Solutions Manual and Study Guide: Chapter 2
Page 1
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.
2.
3.
4.
Construct a frequency distribution from a set of data
Construct different types of quantitative data graphs, including
histograms, frequency polygons, ogives, dot plots, and stem-and-leaf
plots, in order to interpret the data being graphed
Construct different types of qualitative data graphs, including pie charts,
bar graphs, and Pareto charts, in order to interpret the data being
graphed
Recognize basic trends in two-variable scatter plots of numerical data
CHAPTER OUTLINE
2.1
2.2
2.3
2.4
Frequency Distributions
Class Midpoint
Relative Frequency
Cumulative Frequency
Quantitative Data Graphs
Histograms
Frequency Polygons
Ogives
Dot Plots
Stem and Leaf Plots
Qualitative Data Graphs
Pie Charts
Bar Graphs
Pareto Charts
Graphical Depiction of Two-Variable Numerical Data: Scatter Plots
Student’s Solutions Manual and Study Guide: Chapter 2
Page 2
KEY TERMS
Bar Graph
Class Mark
Class Midpoint
Cumulative Frequency
Dot Plot
Frequency Distribution
Frequency Polygon
Grouped Data
Histogram
Ogive
Pareto Chart
Pie Chart
Range
Relative Frequency
Scatter Plot
Stem-and-Leaf Plot
Ungrouped Data
Student’s Solutions Manual and Study Guide: Chapter 2
Page 3
STUDY QUESTIONS
1. The following data represents the number of printer ribbons used annually in a company by
twenty-eight departments. 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 _______________.
9. The midpoint for the class 25-under 30 is ___________.
Student’s Solutions Manual and Study Guide: Chapter 2
Page 4
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. A graph that is especially useful for observing the overall shape of the distribution of
data points along with identifying data values or intervals for which there are
groupings and gaps in the data is called a ______________________.
15. 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
16. 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 __________________.
17. A two-dimensional plot of pairs of points often used to examine the relationship of two
numerical variables is called a _________________.
Student’s Solutions Manual and Study Guide: Chapter 2
Page 5
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. Dot Plot
6. Averaging the two class endpoints
15. 32
33
34
35
7. 21/151 = .1391
1 2 8 9
2 2 8 9
0 1 2 6 6
7
8. 131
16. Pareto Chart
9. 27.5
17. Scatter Plot
Student’s Solutions Manual and Study Guide: Chapter 2
Page 6
SOLUTIONS TO PROBLEMS IN CHAPTER 2
2.1
a)
One possible 5 class frequency distribution:
Class Interval
0 - under 20
20 - under 40
40 - under 60
60 - under 80
80 - under 100
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
7
15
12
12
4
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.
Student’s Solutions Manual and Study Guide: Chapter 2
Page 7
2.3
Class
Interval
Frequency
0-5
6
5 - 10
8
10 - 15
17
15 - 20
23
20 - 25
18
25 - 30
10
30 - 35
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.
Student’s Solutions Manual and Study Guide: Chapter 2
2.7
Histogram:
Frequency Polygon:
Page 8
Student’s Solutions Manual and Study Guide: Chapter 2
2.9
STEM
LEAF
21
22
23
24
25
26
27
2.11
Page 9
2
0
0
0
0
0
0
8
1
0
0
3
1
1
8
2
4
3
4
1
3
9
4
5
6
5
2
6
8
9
5
3
Firm
Caterpillar
Deere
Illinois Too Works
Eaton
American Standard
TOTAL
6
8
9
7
3
7
9
9
7
5
9 9
9 9 9
8 9
6
Proportion
Degrees
.372
.246
.144
.121
.117
1.000
134
89
52
44
42
361
Pie Chart:
Annual Sales
American Standard
12%
Eaton
12%
Caterpillar
37%
Illinois Tool Works
14%
Deere
25%
Student’s Solutions Manual and Study Guide: Chapter 2
Page 10
Bar Graph:
Chart of Revenue
30000
25000
Revenue
20000
15000
10000
5000
0
2.13
Caterpillar
Deere
Illinois Tool Works
Eaton
Equipment Companies
Brand
Pfizer
Johnson & Johnson
Merck
Bristol-Myers Squibb
Abbott Laboratories
Wyeth
TOTAL
Pie Chart:
Proportion
.289
.259
.125
.120
.112
.095
1.000
American Standard
Degrees
104
93
45
43
40
34
359
Student’s Solutions Manual and Study Guide: Chapter 2
Page 11
Pharmaceutical Sales
Wyeth
9%
Pfizer
29%
Abbott Lab.
11%
Bristol-Myers Squibb
12%
Merck
13%
Johnson & Johnson
26%
Bar Graph:
Chart of Sales
60000
50000
Sales
40000
30000
20000
10000
0
r
ize
f
P
on
ns
h
Jo
&
n
so
n
h
Jo
M
ck
er
s
er
b
ib
u
Sq
y
-M
l
to
is
Br
Phar. Co.
r
bo
a
tL
ot
b
Ab
ie
or
t
a
s
W
th
ye
Student’s Solutions Manual and Study Guide: Chapter 2
Page 12
2.15
3500
3000
Industrial Products
2500
2000
1500
1000
500
0
0
1000
2000
3000
4000
5000
6000
7000
Human Food
Generally, as the amount of fish caught for human consumption increases, the
amount used for industrial products tends to decrease.
2.17
Class Interval
Frequencies
16 - under 23
23 - under 30
30 - under 37
37 - under 44
44 - under 51
51 - under 58
TOTAL
6
9
4
4
4
3
30
Student’s Solutions Manual and Study Guide: Chapter 2
2.19
Page 13
Class Interval
Frequencies
50 - under 60
60 - under 70
70 - under 80
80 - under 90
90 - under 100
TOTAL
13
27
43
31
9
123
Histogram:
Student’s Solutions Manual and Study Guide: Chapter 2
Frequency Polygon:
Ogive:
Page 14
Student’s Solutions Manual and Study Guide: Chapter 2
2.21
STEM
LEAF
28
29
30
31
32
33
2.23
Page 15
4
0
1
1
4
5
6
4
6
2
4
9
8
8 9
4 6 7 7
6
Bar Graph:
Category
A
B
C
D
E
Frequency
7
12
14
5
19
20
Frequency
15
10
5
0
A
B
C
Category
D
E
Student’s Solutions Manual and Study Guide: Chapter 2
Page 16
2.25
16
14
12
Y
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
X
2.27
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
Cumulative
Frequency
8
14
19
31
46
53
Student’s Solutions Manual and Study Guide: Chapter 2
2.29
Page 17
Frequency Distribution:
Class Interval
10 - under 20
20 - under 30
30 - under 40
40 - under 50
50 - under 60
60 - under 70
70 - under 80
80 - under 90
Histogram:
Frequency
2
3
9
7
12
9
6
2
50
Student’s Solutions Manual and Study Guide: Chapter 2
Page 18
Frequency Polygon:
The normal distribution appears to peak near the center and diminish towards the
end intervals.
Student’s Solutions Manual and Study Guide: Chapter 2
2.31
Amount Spent
on Prenatal Care
$ 0 - under $100
$100 - under $200
$200 - under $300
$300 - under $400
$400 - under $500
$500 - under $600
Histogram:
Page 19
Frequency
3
6
12
19
11
6
57
Cumulative
Frequency
3
9
21
40
51
57
Student’s Solutions Manual and Study Guide: Chapter 2
Frequency Polygon:
Ogive:
Page 20
Student’s Solutions Manual and Study Guide: Chapter 2
2.33
Genre
R&B
Alternative
Rap
Country
Soundtrack
Metal
Classical
Latin
TOTAL
Page 21
Albums Sold
146.4
102.6
73.7
64.5
56.4
26.6
14.8
14.5
Proportion
.29
.21
.15
.13
.11
.05
.03
.03
1.00
Degrees
104
76
54
47
40
18
11
11
361
Pie Chart:
Classical
3%
Metal
5%
Soundtrack
11%
Latin
3%
R&B
29%
Country
13%
Rap
15%
Alternative
21%
Student’s Solutions Manual and Study Guide: Chapter 2
Page 22
Bar Chart:
160
140
Albums Sold
120
100
80
60
40
20
0
R&B
Alternative
Rap
Country Soundtrack
Genre
Metal
Classical
Latin
Student’s Solutions Manual and Study Guide: Chapter 2
Page 23
2.35
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
.366
.281
.114
.054
132
103
41
19
102,500,000
89,300,000
85,900,000
63,300,000
.051
.044
.043
.031
18
16
15
11
29,100,000
.014
5
0.998
360
TOTAL
Pie Chart:
Fab. Metals
4%
Food
4%
Petro. Elec.
3% 1%
Trans. Equip.
5%
Chem.
38%
Plas. & Rubber
5%
Paper
11%
Prim. Metals
29%
Student’s Solutions Manual and Study Guide: Chapter 2
Page 24
Bar Graph:
800000000
700000000
Release
600000000
500000000
400000000
300000000
200000000
100000000
0
em
Ch
s
al
ic
im
Pr
ar
y
al
et
M
s
r
pe
a
P
s
ti c
as
l
P
d
an
r
be
b
Ru
Tr
s.
an
m
ip
u
Eq
t
en
od
Fo
F
Industry
d
te
a
c
ri
ab
s
al
et
M
Pe
um
le
o
tr
.
ec
El
t
en
m
p
ui
Eq
Student’s Solutions Manual and Study Guide: Chapter 2
2.37
STEM
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
LEAF
12 16
04 28
20 40
12
53 54
30 34
22 34
63
48 49
66
21 54
38 66
31 78
56
69
37 50
31 32
19 23
Page 25
24 32 99 99
39 46 61 88
59
58
66 78
90
57 63 91
66
58 73
2.39 There is an especially heavy concentration of values between about 24 and 33.
There is somewhat of a gap between 18 and 24 but an especially large gap between
52 and 66. Sixty-six appears to be an outlier.
2.41 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.