1. 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:
Above Average
Below Average
Poor
Average
Below Average
Above Average
Average
Average
Above Average
Below Average
Poor
Excellent 3 9 5 2 1

2. Categorical Data Example: Marada Inn Poor Below Average Average
Above Average
Excellent
Rating
Frequency 2 3 5 9 1
Total

3. Categorical Data Example: Marada Inn Relative Frequency Percent
Poor
Below Average
Average
Above Average
Excellent
Rating
Frequency 2
.10 10 15 25 45 5
100 3
.15 5
.25 9
.45 1
.05
Total
1.00

4. Marada Inn Quality Ratings
Categorical Data
Marada Inn Quality Ratings 1 2 3 4 5 6 7 8 9 10
Frequency
What is the scale of Marada Inn Quality Rating?
Nominal
When a variable has nominal scale, the shape of the distribution is meaningless.
When a variable has ordinal scale, the shape of the distribution is important.
Rating
Poor
Below
Average
Average
Above
Average
Excellent

5. Marada Inn Quality Ratings
Categorical Data
Marada Inn Quality Ratings
Excellent 5%
Poor
10%
Below
Average
15%
Above
Average
45%
INSIGHTS: One-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent.” This might please the manager.
For each customer who gave an “excellent” rating, there were two customers who gave a rating of “poor.” This should displease the manager.
Average
25%

6. Customer 5 purchased 2 items,
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 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.
Customer 5 purchased 2 items,
… which cost her $54

7. Pelican Stores data_pelican.xls
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 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
Using graphs and tables, summarize the qualitative variables.
A large majority of the customers use National Clothing’s proprietary credit card.
The overwhelming majority of customers are female.
Most of the customers are married.
data_pelican.xls

8. 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 tune-ups 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 79 76
104 74 68
105 77 65
109 85 88 83 67 82 98
101 73

9. Quantitative Data sorted minimum maximum 52 57 62 65 66 67 68 69 71 72
Example: Hudson Auto Repair
minimum 52 57 62 65 66 67 68 69 71 72 73 74 75 76 77 78 79 80 82 83 85 88 89 91 93 97 98 99
101
104
105
109
maximum

10. Quantitative Data Cost ($) Frequency 50-59 60-69 70-79 80-89 90-99 2 13 16 7 7 5 52 57 62 65 66 67 68 69 71 72 73 74 75 76 77 78 79 80 82 83 85 88 89 91 93 97 98 99
101
104
105
109
Frequency distribution
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.
Class Width = ( )/6 ~ 10

11. Quantitative Data Cost ($) Frequency Relative Freq Percent Freq 50-59
60-69
70-79
80-89
90-99
2/50 2
.04 4
13/50 13
.26 26
16/50 16
.32 32
7/50 7
.14 14
7/50 7
.14 14
5/50 5
.10 10
1.00
100 50

12. Quantitative Data Tune-up Parts Cost Frequency Parts Cost ($) 18 16 142 4 6 8 10 12 14 16 18
Frequency
Parts
Cost ($)

13. Quantitative Data
Symmetric
Moderately Skewed Left
Highly Skewed Right

14. Quantitative Data Ogive for Hudson Auto Repair Parts Cumulative Parts
Cost ($)
Parts
Frequency
Cumulative
Frequency
< 60
< 70
< 80
< 90
< 100
< 110
Cost ($)
50-59
60-69
70-79
80-89
90-99 2 13 16 7 5 2 15 31
oh - jive 38 45 50 50

15. Quantitative Data Ogive for Hudson Auto Repair Cumulative Cumulative
Relative
Frequency
Cumulative
Percent
Frequency
< 60
< 70
< 80
< 90
< 100
< 110
Cost ($)
Cumulative
Frequency 2 15 31 38 45 50 4 30 62 76 90
100
.04
.30
.62
.76
.90
1.00

16. Quantitative Data Example: Hudson Auto Repair Tune-up Parts Cost
($110, 100%)
Tune-up Parts Cost 20 40 60 80
100
($100, 90%)
($90, 76%)
Cumulative Percent Frequency
($50, 0%)
($80, 62%)
($70, 30%)
Parts
Cost ($)
($60, 4%)

17. 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 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
Using graphs and tables, summarize the qualitative variables.
Using graphs and tables, summarize the quantitative variables.
Over half of the customers purchase 1 or 2 items, but a few make numerous purchases.
The percent frequency distribution of net sales shows that 61% of the customers spent $50 or more.
Customers are distributed across all adult age groups.
data_pelican.xls

18. Summarizing Two variables
Price
Range
Colonial Log Split A-Frame
Total
< $99,000
> $99,000
Home Style 55 45 30 20 35 15
100
Example:
Finger Lakes Homes.xls
The number of Finger Lakes homes sold for each
style and price for the past two years is shown below.
qualitative
variable
Quantitative
variable

19. Summarizing Two variables
Home Style
Price
Range
Colonial Log Split A-Frame
Total
< $99,000
> $99,000 55 45
Total 30 20 35 15
100
Example:
Finger Lakes Homes.xls

20. Summarizing Two variables
Home Style
Price
Range
Colonial Log Split A-Frame
Total
< $99,000
> $99,000 55 45
Total 30 20 35 15
100
Price
Range
Home Style
Colonial Log Split A-Frame
Total
0.3273
0.1091
0.3455
0.2182
< $99,000
> $99,000
1.0000
0.2667
0.3111
0.3556
0.0667
1.0000

21. Summarizing Two variables
Home Style
Price
Range
Colonial Log Split A-Frame
< $99,000
> $99,000
Total 30 20 35 15
Price
Range
Home Style
Colonial Log Split A-Frame
0.6000
0.30
0.5429
0.8000
< $99,000
> $99,000
0.4000
0.70
0.4571
0.2000
Total
1.0000
1.0000
1.0000
1.0000

22. Male acceptance rate is higher when data is aggregated.
Summarizing Two variables
The crosstabulation for the aggregated UC-Berkley data is
Admitted
Denied
Total
Male
3738
4704
8442
Female
1494
2827
4321
5232
7531
12763
Male acceptance rate is higher when data is aggregated.
Dividing all of the frequencies above by the number of observations yields what the joint probability table below
Simpson’s Paradox Example:
In the Fall of 1973, an observational study on possible gender bias was conducted at UC-Berkeley. 
There were 12,763 applicants for graduate admission, of whom 8442 were male and 4321 were female.
Of the male applicants, 3738 were admitted, whereas of the female applicants only 1494 were admitted.
Admitted
Denied
Total
Male
0.2929
0.3686
0.6614
Female
0.1171
0.2215
0.3386
0.4099
0.5901
1.0000

23. Summarizing Two variables
Male
Admitted
Denied
Total A
512
313
825 B
207
520
1345
Female
Admitted
Denied
Total A 89 19
108 B 17 8 25
106 27
133
Compute the row percentages to show the Simpson’s Paradox
Male
Admitted
Denied
Total A
0.6206
0.3794
1.0000 B
0.6019
0.3981
Female
Admitted
Denied
Total A
0.8241
0.1759
1.0000 B
0.6800
0.3200
At UC-Berkeley graduate admission decisions are made at the department level. 
In 1973, UC-Berkeley had 101 different graduate departments.
For simplicity, we look at only the 2 largest departments.
The tables represent the top two departments (A and B).
data_simpson.xls

24. Summarizing Two variables
A Negative Relationship
QBigMacs y 21 2 x
PBigMacs
0.50
5.00

25. Summarizing Two variables
No Apparent Relationship
QNoseHairTrimmers y x
PBigMacs

26. 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
y = Number of
Points Scored 1 3 2 14 24 18 17 30

27. Summarizing Two variablesy 5 10 15 20 25 30 35
Number of Points Scored
The scatter diagram indicates a positive relationship
between the number of interceptions and the
number of points scored.
Higher points scored are associated with a higher
number of interceptions
The relationship is not perfect; all plotted points in
the scatter diagram are not on a straight line. x 1 2 3 4
Number of Interceptions

28. 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 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
Using graphs and tables, summarize the qualitative variables.
Using graphs and tables, summarize the quantitative variables.
Using pivot tables and scatter plots, summarize the variables.
From the crosstabulation it appears that net sales are larger for promotional customers.
Age is not a factor in determining net sales.
data_pelican.xls