Categorical Data
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:
3
9
5
Below Average
Above Average
Above Average
Average
Above Average
Average
Above Average
Average
Above Average
Below Average
Poor
1
Excellent
Above Average
Average
Above Average
Above Average
Below Average
Poor
Above Average
Average
2
Categorical Data
Example: Marada Inn
Rating
Poor
Below Average
Average
Above Average
Excellent
Total
Frequency
2
3
5
9
1
20
Categorical Data
Example: Marada Inn
Rating
Frequency
Poor
2
3
Below Average
Average
5
9
Above Average
1
Excellent
Total
20
Relative
Frequency
.10
.15
.25
.45
.05
1.00
Percent
Frequency
10
15
25
45
5
100
Categorical Data
Marada Inn Quality Ratings
10
9
Frequency
8
7
6
5
4
3
2
1
Poor
Below Average Above Excellent
Average
Average
Rating
Categorical Data
Marada Inn Quality Ratings
Excellent
5%
Above
Average
45%
Poor
10%
Below
Average
15%
Average
25%
Pelican Stores
Pelican Stores is chain of women’s apparel stores. It recently ran a promotion in which
discount coupons were set to customers of other National Clothing stores. Data collected for a
sample of 100 in-store credit card transactions at Pelican Stores during one day while the
promotion was running are shown in Table 2.18. Customers who made a purchase using a
discount coupon are referred to as promotional customers and customers who made a purchase
but did not use a discount coupon are referred to as regular customers. Because the
promotional coupons were not set to regular Pelican Stores customers, management considers
theCustomer
sales made 5to people presenting the promotional coupons as sales it would not otherwise
purchased
2 items,
make.
… which cost her $54
Pelican Stores
Pelican Stores is chain of women’s apparel stores. It recently ran a promotion in which
discount coupons were set to customers of other National Clothing stores. Data collected for a
sample of 100 in-store credit card transactions at Pelican Stores during one day while the
promotion was running are shown in Table 2.18. Customers who made a purchase using a
discount coupon are referred to as promotional customers and customers who made a purchase
but did not use a discount coupon are referred to as regular customers. Because the
promotional coupons were not set to regular Pelican Stores customers, management considers
the sales made to people presenting the promotional coupons as sales it would not otherwise
make.
Pelican’s management would like to use this sample data to learn about its customer
base and to evaluate the promotion involving discounts.
Managerial Report
1.Using graphs and tables, summarize the qualitative variables.
data_pelican.xls
Quantitative Data
Example: Hudson Auto Repair
The manager of Hudson Auto would like to have better
understanding of the cost of parts used in the engine tuneups performed in the shop. She examines 50 customer
invoices for tune-ups. The costs of parts, rounded to the
nearest dollar.
91
78
93
57
75
52
99
80
97
62
71
69
72
89
66
75
79
75
72
76
104
74
62
68
97
105
77
65
80
109
85
97
88
68
83
68
71
69
67
74
62
82
98
101
79
105
79
69
62
73
Quantitative Data
Example: Hudson Auto Repair
minimum
52
68
57
68
62
69
62
69
62
69
62
71
65
71
66
72
67
72
68
73
74
79
97
74
80
97
75
80
97
75
82
98
75
83
99
76 77 78 79 79
85 88 89 91 93
101 104 105 105 109
maximum
Quantitative Data
Cost ($) Frequency
50-59
2
60-69
13
70-79
16
80-89
7
90-99
7
100-109
5
52
68
74
79
97
57
68
74
80
97
62
69
75
80
97
62
69
75
82
98
62
69
75
83
99
62 65 66 67 68
71 71 72 72 73
76 77 78 79 79
85 88 89 91 93
101 104 105 105 109
Quantitative Data
Cost ($) Frequency
50-59
2
60-69
13
70-79
16
80-89
7
90-99
7
100-109
5
50
Relative Freq
.04
2/50
.26
13/50
16/50
.32
7/50
.14
7/50
.14
5/50
.10
1.00
Percent Freq
4
26
32
14
14
10
100
Quantitative Data
Tune-up Parts Cost
18
16
Frequency
14
12
10
8
6
4
2
50
60
70
80
90
100
Parts
110 Cost ($)
Quantitative Data
Symmetric
Moderately Skewed Left
Highly Skewed Right
Quantitative Data
Ogive for Hudson Auto Repair
Parts
Cost ($)
50-59
60-69
70-79
80-89
90-99
100-109
Parts
Frequency
2
13
16
7
7
5
50
Cost ($)
< 60
< 70
< 80
< 90
< 100
< 110
Cumulative
Frequency
2
15
31
38
45
50
Quantitative Data
Ogive for Hudson Auto Repair
Cost ($)
< 60
< 70
< 80
< 90
< 100
< 110
Cumulative Cumulative
Cumulative
Relative
Percent
Frequency Frequency
Frequency
2
.04
4
15
.30
30
31
.62
62
38
.76
76
.90
45
90
50
1.00
100
Quantitative Data
Example: Hudson Auto Repair
($110, 100%)
Cumulative Percent Frequency
Tune-up Parts Cost
100
($100, 90%)
80
60
($90, 76%)
($50,
40 0%)
($80, 62%)
($70, 30%)
20
50
60
70
80
($60, 4%)
90
100
110
Parts
Cost ($)
Pelican Stores -- continued
Pelican Stores is chain of women’s apparel stores. It recently ran a promotion in which
discount coupons were set to customers of other National Clothing stores. Data collected for a
sample of 100 in-store credit card transactions at Pelican Stores during one day while the
promotion was running are shown in Table 2.18. Customers who made a purchase using a
discount coupon are referred to as promotional customers and customers who made a purchase
but did not use a discount coupon are referred to as regular customers. Because the
promotional coupons were not set to regular Pelican Stores customers, management considers
the sales made to people presenting the promotional coupons as sales it would not otherwise
make.
Pelican’s management would like to use this sample data to learn about its customer
base and to evaluate the promotion involving discounts.
Managerial Report
1.Using graphs and tables, summarize the qualitative variables.
2.Using graphs and tables, summarize the quantitative variables.
data_pelican.xls
Summarizing Two variables
Home Style
Log Split A-Frame
Price
Range
Colonial
< $99,000
> $99,000
18
12
6
14
19
16
12
3
55
45
30
20
35
15
100
Total
Total
Example: Finger Lakes Homes.xls
Quantitative
variable
qualitative
variable
Summarizing Two variables
Home Style
Log Split A-Frame
Price
Range
Colonial
< $99,000
> $99,000
18
12
6
14
19
16
12
3
55
45
30
20
35
15
100
Total
Example: Finger Lakes Homes.xls
Total
Summarizing Two variables
Home Style
Log Split A-Frame
Price
Range
Colonial
< $99,000
> $99,000
18
12
6
14
19
16
12
3
55
45
30
20
35
15
100
Total
Price
Range
Colonial
< $99,000
> $99,000
0.3273
0.2667
Total
Home Style
Log Split A-Frame
Total
0.1091 0.3455 0.2182
0.3111 0.3556 0.0667
1.0000
1.0000
Summarizing Two variables
Home Style
Log Split A-Frame
Price
Range
Colonial
< $99,000
> $99,000
18
12
6
14
19
16
12
3
30
20
35
15
Total
Price
Range
Colonial
< $99,000
> $99,000
0.6000
0.4000
Total
1.0000
Home Style
Log Split A-Frame
0.30
0.70
0.5429 0.8000
0.4571 0.2000
1.0000 1.0000 1.0000
Summarizing Two variables
The crosstabulation for the aggregated UC-Berkley data is
Admitted
Denied
Total
Male
3738
4704
8442
Female
1494
2827
4321
Total
5232
7531
Male acceptance rate
is higher when data is
aggregated.
12763
Dividing all of the frequencies above by the number of observations yields
what the joint probability table below
Admitted
Denied
Total
Male
0.2929
0.3686
0.6614
Female
0.1171
0.2215
0.3386
Total
0.4099
0.5901
1.0000
Summarizing Two variables
Female
Male
Admitted
Denied
Total
A
89
19
108
520
B
17
8
25
1345
Total
106
27
133
Admitted
Denied
Total
Admitted
Denied
Total
A
512
313
825
B
313
207
Total
825
520
Compute the row percentages to show the Simpson’s Paradox
Female
Male
Admitted
Denied
Total
A
0.6206
0.3794
1.0000
A
0.8241
0.1759
1.0000
B
0.6019
0.3981
1.0000
B
0.6800
0.3200
1.0000
data_simpson.xls
Summarizing Two variables
A Negative Relationship
y
QBigMacs
21
2
0.50
5.00
x BigMacs
P
Summarizing Two variables
No Apparent Relationship
y
QNoseHairTrimmers
x BigMacs
P
Summarizing Two variables
Example: Panthers Football Team
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
Summarizing Two variables
Number of Points Scored
y
35
30
25
20
15
10
5
0
0
1
x
2
3
Number of Interceptions
4
Pelican Stores -- continued
Pelican Stores is chain of women’s apparel stores. It recently ran a promotion in which
discount coupons were set to customers of other National Clothing stores. Data collected for a
sample of 100 in-store credit card transactions at Pelican Stores during one day while the
promotion was running are shown in Table 2.18. Customers who made a purchase using a
discount coupon are referred to as promotional customers and customers who made a purchase
but did not use a discount coupon are referred to as regular customers. Because the
promotional coupons were not set to regular Pelican Stores customers, management considers
the sales made to people presenting the promotional coupons as sales it would not otherwise
make.
Pelican’s management would like to use this sample data to learn about its customer
base and to evaluate the promotion involving discounts.
Managerial Report
1.Using graphs and tables, summarize the qualitative variables.
2.Using graphs and tables, summarize the quantitative variables.
3.Using pivot tables and scatter plots, summarize the variables.
data_pelican.xls