business statistics, 4e, by ken black. © 2003 john wiley & sons. 2-1 business statistics, 4e by...
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Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-1
Business Statistics, 4eby Ken Black
Chapter 2
Charts & Graphs
Discrete Distributions
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-2
Learning Objectives
• 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
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-3
Ungrouped Versus Grouped Data
• Ungrouped data• have not been summarized in any way• are also called raw data
• Grouped data• have been organized into a frequency
distribution
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-4
Example of Ungrouped Data
42
30
53
50
52
30
55
49
61
74
26
58
40
40
28
36
30
33
31
37
32
37
30
32
23
32
58
43
30
29
34
50
47
31
35
26
64
46
40
43
57
30
49
40
25
50
52
32
60
54
Ages of a Sample of Managers from
Urban Child CareCenters in theUnited States
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-5
Frequency Distribution of Child Care Manager’s Ages
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-6
Data Range
42
30
53
50
52
30
55
49
61
74
26
58
40
40
28
36
30
33
31
37
32
37
30
32
23
32
58
43
30
29
34
50
47
31
35
26
64
46
40
43
57
30
49
40
25
50
52
32
60
54
Smallest
Largest
Range = Largest - Smallest
= 74 - 23
= 51
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-7
Number of Classes and Class Width
• The number of classes should be between 5 and 15.• Fewer than 5 classes cause excessive summarization.• More than 15 classes leave too much detail.
• Class Width• Divide the range by the number of classes for an
approximate class width• Round up to a convenient number
10 = Width Class
8.5 =6
51 = Width Class eApproximat
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-8
Class Midpoint
Class Midpoint = beginning class endpoint + ending class endpoint
2
= 30 + 40
2= 35
Class Midpoint = class beginning point + 1
2class width
= 30 + 1
210
= 35
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-9
Relative Frequency RelativeClass Interval Frequency Frequency
20-under 30 6 .12
30-under 40 18 .36
40-under 50 11 .22
50-under 60 11 .22
60-under 70 3 .06
70-under 80 1 .02
Total 50 1.00
6
50
18
50
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-10
Cumulative Frequency
CumulativeCumulativeClass IntervalClass Interval FrequencyFrequency FrequencyFrequency
20-under 3020-under 30 66 66
30-under 4030-under 40 1818 2424
40-under 5040-under 50 1111 3535
50-under 6050-under 60 1111 4646
60-under 7060-under 70 33 4949
70-under 8070-under 80 1 1 5050
TotalTotal 5050
18 + 611 + 24
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-11
Class Midpoints, Relative Frequencies, and Cumulative Frequencies
RelativeRelative CumulativeCumulativeClass IntervalClass Interval FrequencyFrequency MidpointMidpoint FrequencyFrequency FrequencyFrequency20-under 3020-under 30 66 2525 .12.12 6630-under 4030-under 40 1818 3535 .36.36 242440-under 5040-under 50 1111 4545 .22.22 353550-under 6050-under 60 1111 5555 .22.22 464660-under 7060-under 70 33 6565 .06.06 494970-under 8070-under 80 1 1 7575 .02 .02 5050 TotalTotal 5050 1.001.00
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-12
Cumulative Relative Frequencies
Cumulative Relative Cumulative RelativeClass Interval Frequency Frequency Frequency Frequency20-under 30 6 .12 6 .1230-under 40 18 .36 24 .4840-under 50 11 .22 35 .7050-under 60 11 .22 46 .9260-under 70 3 .06 49 .9870-under 80 1 .02 50 1.00 Total 50 1.00
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-13
Common Statistical Graphs
• Histogram -- vertical bar chart of frequencies• Frequency Polygon -- line graph of
frequencies• Ogive -- line graph of cumulative frequencies• Pie Chart -- proportional representation for
categories of a whole• Stem and Leaf Plot• Pareto Chart• Scatter Plot
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-14
Histogram
Class IntervalFrequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
010
20
0 10 20 30 40 50 60 70 80
Years
Fre
qu
ency
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-15
Histogram Construction
Class IntervalClass Interval FrequencyFrequency
20-under 3020-under 30 66
30-under 4030-under 40 1818
40-under 5040-under 50 1111
50-under 6050-under 60 1111
60-under 7060-under 70 33
70-under 8070-under 80 110
1020
0 10 20 30 40 50 60 70 80
Years
Fre
qu
ency
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-16
Frequency Polygon
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1 010
20
0 10 20 30 40 50 60 70 80
Years
Fre
qu
ency
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-17
Ogive
Cumulative
Class Interval Frequency
20-under 30 6
30-under 40 24
40-under 50 35
50-under 60 46
60-under 70 49
70-under 80 50
020
40
60
0 10 20 30 40 50 60 70 80
Years
Fre
qu
en
cy
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-18
Relative Frequency Ogive
Cumulative
Relative
Class Interval Frequency
20-under 30 .12
30-under 40 .48
40-under 50 .70
50-under 60 .92
60-under 70 .98
70-under 80 1.00
0.000.100.200.300.400.500.600.700.800.901.00
0 10 20 30 40 50 60 70 80
Years
Cu
mu
lati
ve
Re
lati
ve
Fre
qu
en
cy
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-19
Complaints by Amtrak Passengers
COMPLAINT NUMBER PROPORTION DEGREES
Stations, etc. 28,000 .40 144.0
TrainPerformance
14,700 .21 75.6
Equipment 10,500 .15 50.4
Personnel 9,800 .14 50.6
Schedules,etc.
7,000 .10 36.0
Total 70,000 1.00 360.0
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-20
Complaints by Amtrak Passengers
Stations, Etc.40%
Train Performance
21%
Equipment15%
Personnel14%
Schedules, Etc.10%
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-21
Second Quarter Truck Production in the U.S. (Hypothetical values)
2d QuarterTruck
ProductionCompany
A
B
C
D
ETotals
357,411
354,936
160,997
34,099
12,747920,190
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-22
39%39%
17%4%
1%
A B C D E
Second Quarter U.S. Truck Production
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-23
Pie Chart Calculations for Company A
2d QuarterTruck
ProductionProportion DegreesCompany
A
B
C
D
ETotals
357,411
354,936
160,997
34,099
12,747920,190
.388
.386
.175
.037
.0141.000
140
139
63
13
5360
357, 411
920,190 =
.388 360 =
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-24
Safety Examination Scores for Plant Trainees
86
76
23
77
81
79
68
77
92
59
68
75
83
49
91
47
72
82
74
70
56
60
88
75
97
39
78
94
55
67
83
89
67
91
81
Raw Data Stem
2
3
4
5
6
7
8
9
Leaf
3
9
7 9
5 6 9
0 7 7 8 8
0 2 4 5 5 6 7 7 8 9
1 1 2 3 3 6 8 9
1 1 2 4 7
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-25
Construction of Stem and Leaf Plot
86
76
23
77
81
79
68
77
92
59
68
75
83
49
91
47
72
82
74
70
56
60
88
75
97
39
78
94
55
67
83
89
67
91
81
Raw Data Stem
2
3
4
5
6
7
8
9
Leaf
3
9
7 9
5 6 9
0 7 7 8 8
0 2 4 5 5 6 7 7 8 9
1 1 2 3 3 6 8 9
1 1 2 4 7
Stem
Leaf
Stem
Leaf
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-26
Pareto Chart
0
10
20
30
40
50
60
70
80
90
100
PoorWiring
Short inCoil
DefectivePlug
Other
Fre
qu
ency
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2-27
Scatter Plot
Registered Vehicles (1000's)
Gasoline Sales (1000's of Gallons)
5 60
15 120
9 90
15 140
7 60
0
100
200
0 5 10 15 20Registered Vehicles
Gas
olin
e Sa
les