Upload
rushabh-vora
View
318
Download
3
Embed Size (px)
Citation preview
8/3/2019 Ken Black QA ch02
1/28
Business Statistics, 5th ed.
by Ken Black
Chapter 2
Charts& Graphs
Discrete Distributions
PowerPoint presentations prepared by Lloyd Jaisingh,Morehead State University
8/3/2019 Ken Black QA ch02
2/28
Learning Objectives
Recognize the difference betweengrouped and ungrouped data
Construct a frequency distribution Construct a histogram, a frequency
polygon, an ogive, a pie chart, a stemand leaf plot, a Pareto chart, and a
scatter plot
8/3/2019 Ken Black QA ch02
3/28
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 frequencydistribution
8/3/2019 Ken Black QA ch02
4/28
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 the
United States
8/3/2019 Ken Black QA ch02
5/28
Frequency Distribution of
Child Care Managers 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
8/3/2019 Ken Black QA ch02
6/28
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
Note:One can order
the data valuesfrom smallest to
largest to help find
the range.
8/3/2019 Ken Black QA ch02
7/28
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
So if the number of classes is 6, then
10=WidthClass
8.5=6
51
=WidthClasseApproximat
8/3/2019 Ken Black QA ch02
8/28
Class Midpoint
Class Midpoint =beginning class endpoint + ending class endpoint
2
= 30 + 402
= 35
Class Midpoint = class beginning point +1
2class width
= 30 +1
210
= 35
The midpoint of each class interval is called the class midpoint
or the class mark.
8/3/2019 Ken Black QA ch02
9/28
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
The relative frequency is the proportion of the total frequency
that is any given class interval in a frequency distribution.
8/3/2019 Ken Black QA ch02
10/28
Cumulative Frequency
CumulativeClass Interval Frequency Frequency
20-under 30 6 630-under 40 18 24
40-under 50 11 35
50-under 60 11 46
60-under 70 3 49
70-under 80 1 50
Total 50
18 + 6
11 + 24
The cumulative frequency is a running total of frequenciesthrough the classes of a frequency distribution.
8/3/2019 Ken Black QA ch02
11/28
Class Midpoints, Relative Frequencies,
and Cumulative Frequencies
Relative CumulativeClass Interval Frequency Midpoint Frequency Frequency
20-under 30 6 25 .12 630-under 40 18 35 .36 24
40-under 50 11 45 .22 35
50-under 60 11 55 .22 46
60-under 70 3 65 .06 49
70-under 80 1 75 .02 50
Total 50 1.00
8/3/2019 Ken Black QA ch02
12/28
Cumulative Relative Frequencies
Cumulative
Relative Cumulative Relative
Class Interval Frequency Frequency Frequency Frequency
20-under 30 6 .12 6 .12
30-under 40 18 .36 24 .48
40-under 50 11 .22 35 .70
50-under 60 11 .22 46 .92
60-under 70 3 .06 49 .9870-under 80 1 .02 50 1.00
Total 50 1.00
The cumulative relative frequency is a running total of
the relative frequencies through the classes of afrequency distribution.
8/3/2019 Ken Black QA ch02
13/28
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 forcategories of a whole
Stem and Leaf Plot
Pareto Chart
Scatter Plot
8/3/2019 Ken Black QA ch02
14/28
Histogram
Class Interval Frequency
20-under 30 6
30-under 40 1840-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
80706050403020
20
15
10
5
0
Years
Frequency
10
20
1
3
1111
18
6
8/3/2019 Ken Black QA ch02
15/28
Histogram Construction
Class Interval Frequency
20-under 30 6
30-under 40 1840-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
80706050403020
20
15
10
5
0
Years
Frequency
10
20
1
3
1111
18
6
8/3/2019 Ken Black QA ch02
16/28
Frequency Polygon
Class Interval Frequency
20-under 30 6
30-under 40 1840-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1908070605040302010
20
15
10
5
0
Years
Frequency
8/3/2019 Ken Black QA ch02
17/28
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
80706050403020
50
40
30
20
10
0
Years
Frequency
8/3/2019 Ken Black QA ch02
18/28
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 1.009080706050403020100
1.0
0.8
0.6
0.4
0.2
0.0
Years
CumulativeRelativeFrequency
8/3/2019 Ken Black QA ch02
19/28
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
8/3/2019 Ken Black QA ch02
20/28
Complaints by Amtrak Passengers
Stations, Etc.
40%Train
Performance
21%
Equipment15%
Personnel
14%
Schedules,
Etc.
10%
8/3/2019 Ken Black QA ch02
21/28
Second QuarterTruck
Production in
the U.S.
(Hypothetical
values)
2d Quarter
TruckProductionCompany
A
B
C
D
E
Totals
357,411
354,936
160,997
34,099
12,747
920,190
8/3/2019 Ken Black QA ch02
22/28
39%
39%
17%
4%1%
A B C D E
Second Quarter
U.S. Truck Production
8/3/2019 Ken Black QA ch02
23/28
Pie Chart Calculations for Company A
2d QuarterTruck
ProductionProportion DegreesCompany
A
B
C
D
E
Totals
357,411
354,936
160,997
34,099
12,747
920,190
.388
.386
.175
.037
.014
1.000
140
139
63
13
5
360
357,411
920,190=
.388 360 =
8/3/2019 Ken Black QA ch02
24/28
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
8/3/2019 Ken Black QA ch02
25/28
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
78
9
Leaf
3
9
7 9
5 6 9
0 7 7 8 8
0 2 4 5 5 6 7 7 8 91 1 2 3 3 6 8 9
1 1 2 4 7
Stem
Leaf
Stem
Leaf
8/3/2019 Ken Black QA ch02
26/28
Pareto Chart
Count
Percent
Type of DefectCount
5.0
Cum % 40.0 70.0 95.0 100.0
40 30 25 5
Percent 40.0 30.0 25.0
OtherDefective PlugShort in the CoilPoor wiring
100
80
60
40
20
0
100
80
60
40
20
0
8/3/2019 Ken Black QA ch02
27/28
Scatter Plot
Registered Vehicles (1000s)
GasolineSa
les(1000sofgallo
1614121086420
140
120
100
80
60
40
20
0
8/3/2019 Ken Black QA ch02
28/28
Copyright 2008 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation
of this work beyond that permitted in section 117of the 1976 United States Copyright Act without
express permission of the copyright owner isunlawful. Request for further information shouldbe addressed to the Permissions Department, JohnWiley & Sons, Inc. The purchaser may makeback-up copies for his/her own use only and notfor distribution or resale. The Publisher assumesno responsibility for errors, omissions, or damagescaused by the use of these programs or from theuse of the information herein.