Ken Black QA ch02

8/3/2019 Ken Black QA ch02

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Business Statistics, 5th ed.

by Ken Black

Chapter 2

Charts& Graphs

Discrete Distributions

PowerPoint presentations prepared by Lloyd Jaisingh,Morehead State University


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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


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


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


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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


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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.


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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


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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.


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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.


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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.


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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


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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.


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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


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Histogram


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


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Histogram Construction


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


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Frequency Polygon


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


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Ogive

Cumulative


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


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Relative Frequency Ogive

Cumulative

Relative


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


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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


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Complaints by Amtrak Passengers

Stations, Etc.

40%Train

Performance

21%

Equipment15%

Personnel

14%

Schedules,

Etc.

10%


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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


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39%

39%

17%

4%1%

A B C D E

Second Quarter

U.S. Truck Production


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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 =


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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


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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


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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


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Scatter Plot

Registered Vehicles (1000s)

GasolineSa

les(1000sofgallo

1614121086420

140

120

100

80

60

40

20

0


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