Descriptive Statistics:
Tabular and Graphical Presentations
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Summarizing Qualitative Data
Summarizing Quantitative Data
Summarizing Qualitative Data
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Frequency Distribution
Relative Frequency Distribution
Cumulative Frequency
Cumulative Relative Frequency
Bar Graph
Pie Chart
Example: Marada Inn
Guests staying at Marada Inn were
asked to rate the quality of their
accommodations as being excellent,
above average, average, below average, or
poor. The ratings provided by a sample of 20 guests are:
Below Average
Above Average
Above Average
Average
Above Average
Average
Above Average
Average
Above Average
Below Average
Poor
Excellent
Above Average
Average
Above Average
Above Average
Below Average
Poor
Above Average
Average
Frequency Distribution
Cumulative
Frequency Frequency
Rating
2
2
Poor
3
5
Below Average
5
10
Average
19
9
Above Average
1
20 2+3+5 =10
Excellent
Total
20
Relative Frequency and
Percent Frequency Distributions
Relative
Frequency
Rating
.10
Poor
.15
Below Average
.25
Average
.45
Above Average
.05
Excellent
Total
1.00
Cumulative
Relative
Frequency
.10
.25
.50
.95 .10+.15 =.25
1.0
1/20 = .05
Bar Graph
Marada Inn Quality Ratings
10
9
Frequency
8
7
6
5
4
3
2
1
Poor
Below Average Above Excellent
Average
Average
Rating
Pie Chart
Marada Inn Quality Ratings
Excellent
5%
Poor
10%
Above
Average
45%
Below
Average
15%
Average
25%
Summarizing Quantitative Data
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Frequency Distribution
Relative Frequency Distributions
Histogram
Cumulative Distributions
Example: Hudson Auto Repair
The manager of Hudson Auto
would like to have a better
understanding of the cost
of parts used in the engine
tune-ups performed in the
shop. She examines 50
customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the next
slide.
Example: Hudson Auto Repair
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Sample of Parts Cost for 50 Tune-ups
91
71
104
85
62
78
69
74
97
82
93
72
62
88
98
57
89
68
68
101
75
66
97
83
79
52
75
105
68
105
99
79
77
71
79
80
75
65
69
69
97
72
80
67
62
62
76
109
74
73
Frequency Distribution
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Guidelines for Selecting Number of Classes
• Use between 5 and 20 classes.
•
Data sets with a larger number of elements
usually require a larger number of classes.
•
Smaller data sets usually require fewer classes
Frequency Distribution
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Guidelines for Selecting Width of Classes
•Use classes of equal width.
•Approximate Class Width =
Largest Data Value − Smallest Data Value
Number of Classes
Frequency Distribution
For Hudson Auto Repair, if we choose six classes:
Approximate Class Width = (109 - 52)/6 = 9.5 ≅ 10
Parts Cost ($) Frequency
50-59
2
60-69
13
70-79
16
80-89
7
90-99
7
100-109
5
Total
50
Relative Frequency Distribution
Parts
Relative
Cost ($) Frequency
50-59
.04
60-69
.26
2/50
70-79
.32
80-89
.14
90-99
.14
100-109
.10
Total 1.00
Cumulative Distributions
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Hudson Auto Repair
Cumulative Cumulative
Cumulative
Relative
Percent
Frequency
Cost ($) Frequency Frequency
Frequency
2
2
.04
50 - 59
4
13
15
.30
60 - 69
30
16
31 2 + 13 .62 15/50 62 .30(100)
70 - 79
.76
7
38
80 - 89
76
.90
7
45
90 - 99
90
1.00
5
50
100 - 109
100
Histogram
Tune-up Parts Cost
18
16
Frequency
14
12
10
8
6
4
2
Parts
50−59 60−69 70−79 80−89 90−99 100-110 Cost ($)
Histogram
Symmetric
• Left tail is the mirror image of the right tail
• Examples: heights and weights of people
.35
Relative Frequency
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.30
.25
.20
.15
.10
.05
0
Histogram
Moderately Skewed Left
• A longer tail to the left
• Example: exam scores
.35
Relative Frequency
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.30
.25
.20
.15
.10
.05
0
Histogram
Moderately Right Skewed
• A Longer tail to the right
• Example: housing values
.35
Relative Frequency
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.30
.25
.20
.15
.10
.05
0
Histogram
Highly Skewed Right
• A very long tail to the right
• Example: executive salaries
.35
Relative Frequency
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.30
.25
.20
.15
.10
.05
0
Scatter Diagram
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A Positive Relationship
y
x
Scatter Diagram
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A Negative Relationship
y
x
Scatter Diagram
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No Apparent Relationship
y
x
Example: Panthers Football Team
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Scatter Diagram
The Panthers football team is interested
in investigating the relationship, if any,
between interceptions made and points scored.
x = Number of
Interceptions
1
3
2
1
3
y = Number of
Points Scored
14
24
18
17
30
Scatter Diagram
Number of Points Scored
y
35
30
25
20
15
10
5
0
0
1
x
2
3
Number of Interceptions
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Tabular and Graphical Procedures
Data
Qualitative Data
Tabular
Methods
Graphical
Methods
•Frequency
•Bar Graph
Distribution
•Pie Chart
•Rel. Freq. Dist.
•Cumulative Freq.
Distribution
•Cumulative Rel. Freq.
Distribution
Quantitative Data
Tabular
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•Cum. Freq. Dist.
•Cum. Rel. Freq.
Distribution
Graphical
Methods
•Histogram
•Scatter
Diagram