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© 2002 Thomson / South-Western Slide 2-1
Chapter 2
Descriptive Charts and
Graphs
© 2002 Thomson / South-Western Slide 2-2
Learning Objectives
• Construct a frequency distribution• Determine the class midpoints,
relative frequencies, and cumulative frequencies of a frequency distribution.
• Construct a histogram, a frequency polygon, an ogive, a pie chart.
© 2002 Thomson / South-Western Slide 2-3
Ungrouped vs 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
© 2002 Thomson / South-Western Slide 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 Care
Centers in theUnited States
© 2002 Thomson / South-Western Slide 2-5
Frequency Distribution of Child Care Manager’s Ages
Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1
© 2002 Thomson / South-Western Slide 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
© 2002 Thomson / South-Western Slide 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
© 2002 Thomson / South-Western Slide 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
© 2002 Thomson / South-Western Slide 2-9
Relative Frequency RelativeClass Interval FrequencyFrequency20-under 30 6 .1230-under 40 18 .3640-under 50 11 .2250-under 60 11 .2260-under 70 3 .0670-under 80 1 .02 Total 50 1.00
6
50
18
50
© 2002 Thomson / South-Western Slide 2-10
Cumulative Frequency
CumulativeClass Interval Frequency Frequency20-under 30 6 630-under 40 18 2440-under 50 11 3550-under 60 11 4660-under 70 3 4970-under 80 1 50 Total 50
18 + 611 + 24
© 2002 Thomson / South-Western Slide 2-11
Class Midpoints, Relative Frequencies, and Cumulative Frequencies
Relative
CumulativeClass Interval Frequency Midpoint FrequencyFrequency20-under 30 6 25 .12 630-under 40 18 35 .36 2440-under 50 11 45 .22 3550-under 60 11 55 .22 4660-under 70 3 65 .06 4970-under 80 1 75 .02 50 Total 50 1.00
© 2002 Thomson / South-Western Slide 2-12
Cumulative Relative Frequencies
Cumulative Relative Cumulative RelativeClass Interval Frequency Frequency FrequencyFrequency20-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
© 2002 Thomson / South-Western Slide 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
© 2002 Thomson / South-Western Slide 2-14
Histogram
Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1
010
20
0 10 20 30 40 50 60 70 80
Years
Freq
uenc
y
© 2002 Thomson / South-Western Slide 2-15
Histogram Construction
Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1 0
1020
0 10 20 30 40 50 60 70 80
Years
Freq
uenc
y
© 2002 Thomson / South-Western Slide 2-16
Frequency Polygon
Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1 0
1020
0 10 20 30 40 50 60 70 80
Years
Fre
qu
ency
© 2002 Thomson / South-Western Slide 2-17
Ogive
CumulativeClass Interval Frequency20-under 30 630-under 40 2440-under 50 3550-under 60 4660-under 70 4970-under 80 50
02
04
06
00 10 20 30 40 50 60 70 80
Years
Fre
qu
en
cy
© 2002 Thomson / South-Western Slide 2-18
Relative Frequency Ogive
Cumulative
RelativeClass IntervalFrequency20-under 30 .1230-under 40 .4840-under 50 .7050-under 60 .9260-under 70 .9870-under 80 1.00
0.000.100.200.300.400.500.600.700.800.901.001.10
0 10 20 30 40 50 60 70 80
Years
Cu
mu
lati
ve R
elat
ive
Fre
qu
ency
© 2002 Thomson / South-Western Slide 2-19
Complaints by Amtrak PassengersComplaints 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
© 2002 Thomson / South-Western Slide 2-20
Complaints by Amtrak PassengersComplaints by Amtrak Passengers
Stations, Etc.40%
Train Performance
21%
Equipment15%
Personnel14%
Schedules, Etc.10%
© 2002 Thomson / South-Western Slide 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
© 2002 Thomson / South-Western Slide 2-22
39%39%
17%4%
1%
A B C D E
Second Quarter U.S. Truck Production
© 2002 Thomson / South-Western Slide 2-23
Pie Chart Calculations for Truck Producer 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 =