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.
Recognize the difference between grouped and ungrouped data.
Construct a frequency distribution.
Construct a histogram, a frequency polygon, an ogive, a pie chart, a stem and leaf plot, a Pareto
chart, and a scatter plot.
CHAPTER OUTLINE
2.1
Frequency Distributions
Class Midpoint
Relative Frequency
Cumulative Frequency
2.2
Graphic Depiction of Data
Histograms
Using Histograms to Get an Initial Overview of the Data
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
7
8
Solutions Manual and Study Guide
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 _______________.
For questions 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 ___________.
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 _______________.
Chapter 2: Charts and Graphs 9
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 _________________.
10
Solutions Manual and Study Guide
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
Chapter 2: Charts and Graphs 11
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.
12
Solutions Manual and Study Guide
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
20
18
16
Frequency
14
12
10
8
6
4
2
0
15
25
35
45
Class Midpoints
55
65
75
Chapter 2: Charts and Graphs 13
Frequency Polygon
20
18
16
Frequency
14
12
10
8
6
4
2
0
15
25
35
45
55
65
Class Midpoints
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
75
14
Solutions Manual and Study Guide
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).
Chapter 2: Charts and Graphs 15
2.15
3500
Industrial Products
3000
2500
2000
1500
1000
500
0
0
1000
2000
3000
4000
Human Food
2.17
Class Interval
16 - under 23
23 - under 30
30 - under 37
37 - under 44
44 - under 51
51 - under 58
TOTAL
Frequencies
6
9
4
4
4
3
30
5000
6000
7000
16
Solutions Manual and Study Guide
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
123
Histogram
50
45
40
Frequency
35
30
25
20
15
10
5
0
55
65
75
85
95
Class Midpoints
Frequency Polygon
50
45
40
Frequency
35
30
25
20
15
10
5
0
55
65
75
Class Midpoints
85
95
Chapter 2: Charts and Graphs 17
Ogive
Cumulative Frequencies
140
120
100
80
60
40
20
0
50
60
70
80
90
100
Class Endpoints
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
5
10
X
15
20
18
Solutions Manual and Study Guide
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
Cumulative
Frequency
8
14
19
3
46
53
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
Cumulative
Frequency
8
14
19
31
46
53
Frequency
8
6
5
12
15
7
53
Histogram
16
14
Frequency
12
10
8
6
4
2
0
22.5
27.5
32.5
37.5
Class Midpoints
42.5
47.5
Chapter 2: Charts and Graphs 19
Frequency Polygon
16
14
Frequency
12
10
8
6
4
2
0
22.5
27.5
32.5
37.5
42.5
47.5
Class Midpoints
b) Ogive
Cumulative Frequencies
60
50
40
30
20
10
0
20
25
30
35
Class Endpoints
40
45
50
20
Solutions Manual and Study Guide
2.29
Amount Spent
on Prenatal Care
Frequency
$ 0 - under $100
$100 - under $200
$200 - under $300
$300 - under $400
$400 - under $500
$500 - under $600
3
6
12
19
11
6
57
Cumulative
Frequency
3
9
21
40
51
57
Histogram
20
18
16
Frequency
14
12
10
8
6
4
2
0
50
150
250
350
Class Midpoints
450
550
Chapter 2: Charts and Graphs 21
Frequency Polygon
20
18
16
Frequency
14
12
10
8
6
4
2
0
50
150
250
350
450
550
Class Midpoints
Ogive
Cumulative Frequency
60
50
40
30
20
10
0
0
100
200
300
Class Endpoints
400
500
600
22
Solutions Manual and Study Guide
2.31
Genre
Albums Sold
R&B
Alternative
Rap
Country
Soundtrack
Metal
Classical
Latin
Proportion
146.4
102.6
73.7
64.5
56.4
26.6
14.8
14.5
TOTAL
.29
.21
.15
.13
.11
.05
.03
.03
104
76
54
47
40
18
11
11
1.00
361
Pie Chart
Top Music Genres
Latin
3%
Classical
3%
Metal
5%
Soundtrack
11%
R&B
29%
Country
13%
Rap
15%
Degrees
Alternative
21%
Chapter 2: Charts and Graphs 23
2.33
Industry
Total Release
Proportion
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
Chemicals
Primary metals
Paper
Plastics & Rubber
Transportation
Equipment
Food
Fabricated Metals
Petroleum
Electrical
Equipment
TOTAL
Pie Chart
Food
4%
Fab. Metals
4%
Petroleum
3%
Elec. Equip.
1%
Transportation
Equipment
5%
Chemicals
38%
Plas. & Rubber
5%
Paper
11%
Primary Metals
29%
Degrees
24
Solutions Manual and Study Guide
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.