Charts Graphs

Charts Graphs - Transcript

Charts Graphs

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

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

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 Care Centers in the United States

Frequency Distribution of Child Care Manager s Ages
Class Interval 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80 Frequency 6 18 11 11 3 1

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

Range Largest Smallest 74 23 51

Smallest Largest

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

51 Approximate Class Width 8 5 6 Class Width 10

Class Midpoint
beginning class endpoint ending class endpoint Class Midpoint 2 30 40 2 35
1 Class Midpoint class beginning point class width 2 1 30 10 2 35

Relative Frequency
Class Interval 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80 Total Relative Frequency Frequency 6 12 6 18 36 5 0 11 22 1 8 5 0 11 22 3 06 1 02 50 1 00

Cumulative Frequency
Class Interval 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80 Total Total Frequency 6 18 11 11 3 1 50 Cumulative Cumulative Frequency 6 24 18 6 35 11 24 46 49 50

Class Midpoints Relative Frequencies and Cumulative Frequencies
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 Total 50 Total Relative Cumulative Relative Cumulative Midpoint Frequency Frequency 25 12 6 35 36 24 45 22 35 55 22 46 65 06 49 75 02 50 1 00

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 98 70 under 80 1 02 50 1 00 Total 50 1 00

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

Histogram
Class Interval Frequency 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80

6 18 11 11 3 1

Frequency

0 0

10

20

10 20 30 40 50 60 70 80 Years

Histogram Construction
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

Frequency

0 0

10

20

10 20 30 40 50 60 70 80 Years

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

Frequency

0 0

10

20

10 20 30 40 50 60 70 80 Years

Ogive
Cumulative Frequency 6 24 35 46 49 50

Class Interval 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80

Frequency

0 0

20

40

60

10

20

30

40 Years

50

60

70

80

Relative Frequency Ogive
Cumulative Relative Frequency 12 48 70 92 98 1 00
Cumulative Relative Frequency

Class Interval 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80

1 00 0 90 0 80 0 70 0 60 0 50 0 40 0 30 0 20 0 10 0 00 0 10 20 30 40 Years 50 60 70 80

Complaints by Amtrak Passengers
COMPLAINT Stations etc Train Performance Equipment Personnel Schedules etc Total NUMBER 28 000 14 700 10 500 9 800 7 000 70 000 PROPORTION 40 21 15 14 10 1 00 DEGREES 144 0 75 6 50 4 50 6 36 0 360 0

Complaints by Amtrak Passengers
Personnel 14 Equipment 15 Schedules Etc 10

Train Performance 21

Stations Etc 40

Second Quarter Truck Production in the U S Hypothetical values

Company A B C D E Totals

2d Quarter Truck Production 357 411 354 936 160 997 34 099 12 747 920 190

Second Quarter U S Truck Production
17 4 1

39 39

A

B

C

D

E

Pie Chart Calculations for Company A
2d Quarter Truck Production 357 411

Company A B C D E Totals

Proportion 388 386 175

Degrees 140 139 63 13 5 360

357 411 920 190

354 936 160 997 34 099 12 747 920 190

388 360 037
014 1 000

Safety Examination Scores for Plant Trainees
Raw Data
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

Stem 2 3 4 5 6 7 8 9 3 9 79 569

Leaf

07788 0245567789 11233689 11247

Construction of Stem and Leaf Plot
Raw Data
86 76 23 77 81 79 68 77 92 59 68 75 83 49 91 47 72 82 74 70 60 88 75 97 39

Stem

Leaf 3 9 79 569 07788 0245567789 11233689 11247

Stem
67 83

55

2 3 4 5 6 7 8 9

Leaf
67 91 81

89

Stem 78
94 Leaf

56

Pareto Chart
100 90 80 70 100 90 80 70 60 50 40 30 20 10 0 Poor Wiring Short in Coil Defective Plug Other

Frequency

60 50 40 30 20 10 0

Scatter Plot

Registered Vehicles 1000 s

Gasoline Sales 1000 s of Gallons
Ga so li ne Sa les

200

5 15 9 15 7

60 120 90 140 60

100

0 0 5 10 15 Registered Vehicles 20