Descriptive charts and graphs

Descriptive charts and graphs - Transcript

Chapter 2 Descriptive Descriptive Charts and Charts Graphs Graphs

1

Learning Objectives
Construct a frequency distribution Determine the class midpoints relative Determine frequencies and cumulative frequencies of a frequency distribution frequencies Construct a histogram a frequency Construct polygon an ogive a pie chart polygon

2

Ungrouped vs Grouped Ungrouped Data Data
Ungrouped data
have not been summarized in any way are also called raw data are raw

Grouped data
have been organized into a frequency have distribution distribution

3

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

4

Frequency Distribution Frequency of Child Care Manager s Ages 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

5

Data Range 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

Range Largest Smallest 74 23 51

Smallest Largest

6

Number of Classes and Class Number Width Width
The number of classes should be between 5 The and 15 and
Fewer than 5 classes cause excessive Fewer summarization summarization More than 15 classes leave too much detail

Class Width
Divide the range by the number of classes for an approximate class width an Round up to a convenient number

51 Approximate Class Width 8 5 6 Class Width 10

7

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
8

Relative Frequency
Class Interval 20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80 Total Total Relative Relative Frequency Frequency 6 6 12 5 0 18 36 1 8 11 22 5 0 11 22 3 06 1 02 50 1 00
9

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

10 10

Class Midpoints Relative Frequencies and Class Cumulative Frequencies Cumulative
Cumulative Cumulative Class Interval Frequency Midpoint Relative Frequency Frequency

20 under 30 30 under 40 40 under 50 50 under 60 60 under 70 70 under 80 Total Total

6 18 11 11 3 1 50

25 35 45 55 65 75

12 36 22 22 06 02 1 00

6 24 35 46 49 50

11 11

Cumulative Relative Frequencies
Cumulative Cumulative Relative Cumulative Relative Relative Class IntervalFrequency 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 Total
12 12

Common Statistical Graphs
Histogram vertical bar chart of Histogram frequencies frequencies Frequency Polygon line graph of Frequency frequencies frequencies Ogive line graph of cumulative Ogive frequencies frequencies Pie Chart proportional representation Pie for categories of a whole for
13 13

Histogram
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
20 Frequency 0 0 10

10 20 30 40 50 60 70 80 Years

14 14

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
20 Frequency 0 0 10

10 20 30 40 50 60 70 80 Years

15 15

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
20 Frequency 0 0 10

10 20 30 40 50 60 70 80 Years

16 16

Ogive
Cumulative 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
60
Frequency

0 0

20

40

10

20

30

40 Years

50

60

70

80

17 17

Relative Frequency Ogive
Cumulative 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 10 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

18 18

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

19 19

Complaints by Amtrak Complaints Passengers Passengers
Personnel 14 Equipment 15 Schedules Etc 10

Train Performance 21

Stations Etc 40

20 20

Second Second Quarter Truck Production in the U S Hypothetical values values

Company A B C D E Totals

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

21 21

Second Quarter Second U S Truck Production
17 4 1

39 39

A

B

C

D

E

22 22

Pie Chart Calculations Pie for Truck Producer Company A for
Company A B C D E Totals 2d Quarter Truck Production 357 411 Proportion 388 386 175 Degrees 140 139 63 13 5 360
23 23

357 411 920 190

354 936 160 997 34 099 12 747 920 190

388 360 037
014 1 000