below average above average above average average above average average above average

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

Example: Marada Inn

3 9

5 2 1

Categorical Data

1

PoorBelow AverageAverageAbove AverageExcellent

Rating Frequency

Example: Marada Inn

Total 20

2359

Categorical Data

PoorBelow AverageAverageAbove AverageExcellent

10 15 25 45 5 100

RelativeFrequency

PercentFrequencyRating

Example: Marada Inn

.051.00

.10

.15

.25

.45 1

Total 20

2359

Frequency

Categorical Data

Poor BelowAverage

Average AboveAverage

Excellent

Freq

uenc

y

Rating

Categorical Data

123456789

10 Marada Inn Quality Ratings

BelowAverage 15%

Average 25%

AboveAverage 45%

Poor10%

Excellent 5%

Marada Inn Quality Ratings

Categorical Data

Pelican StoresPelican 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.

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

Pelican StoresPelican 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 Report1. Using graphs and tables, summarize the qualitative variables.

data_pelican.xls

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 6271 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

Quantitative Data

sorted

52 57 62 62 62 62 65 66 67 6868 68 69 69 69 71 71 72 72 7374 74 75 75 75 76 77 78 79 7979 80 80 82 83 85 88 89 91 9397 97 97 98 99 101 104 105 105 109

minimum

maximum

Example: Hudson Auto Repair

Quantitative Data

13

52 57 62 62 62 62 65 66 67 6868 68 69 69 69 71 71 72 72 7374 74 75 75 75 76 77 78 79 7979 80 80 82 83 85 88 89 91 9397 97 97 98 99 101 104 105 105 109

2

1677

5

50-5960-6970-7980-8990-99

100-109

Cost ($) Frequency

Quantitative Data

2/50.04Relative Freq

1.00

13/5016/507/507/505/50

.26

.32

.14

.14 .10

4Percent Freq

100

26321414

10

Quantitative Data

50

50-5960-6970-7980-8990-99

100-109

Cost ($) Frequency

132

1677

5

2468

1012141618

PartsCost ($)

Freq

uenc

y

50 60 70 80 90 100 110

Tune-up Parts Cost

Quantitative Data

Moderately Skewed LeftSymmetric

Highly Skewed Right

Quantitative Data

Ogive for Hudson Auto Repair

< 60 < 70

< 80 < 90

< 100< 110

Cost ($) CumulativeFrequency

50-59 60-69 70-79 80-89 90-99 100-109

2 13 16 7 7 5

Parts Cost ($)

Parts Frequency

50

21531384550

Quantitative Data

CumulativeRelative

Frequency

CumulativePercent

Frequency 4 30 62 76 90

100

.04

.30

.62

.76

.90

1.00

Quantitative Data

Ogive for Hudson Auto Repair

< 60 < 70

< 80 < 90

< 100< 110

Cost ($) CumulativeFrequency

21531384550

PartsCost ($)

20

40

60

80

100

Cum

ulat

ive

Perc

ent F

requ

ency

50 60 70 80 90 100 110

($90, 76%)

Tune-up Parts CostExample: Hudson Auto Repair

($50, 0%)

($60, 4%)

($70, 30%)

($80, 62%)

($100, 90%)

($110, 100%)

Quantitative Data

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 Report1. Using graphs and tables, summarize the qualitative variables.2. Using graphs and tables, summarize the quantitative variables.

data_pelican.xls

Summarizing Two variables

Finger Lakes Homes.xls

Example:

18 6 19 12 55

30 10012 14 16 3

Quantitative variable

qualitative variable

45

20 35 15

PriceRange Colonial Log Split A-FrameTotal

< $99,000> $99,000

Total

Home Style

PriceRange Colonial Log Split A-FrameTotal

< $99,000> $99,000

18 6 19 12 55

30Total 10012 14 16 3

Home Style

45

20 35 15

Summarizing Two variables

Finger Lakes Homes.xls

Example:

PriceRange Colonial Log Split A-FrameTotal

< $99,000> $99,000

Home Style

PriceRange Colonial Log Split A-FrameTotal

< $99,000> $99,000

18 6 19 12 55

30Total 10012 14 16 3

Home Style

45

20 35 15

0.3273 1.00000.10910.34550.21820.2667 1.00000.31110.35560.0667

Summarizing Two variables

PriceRange Colonial Log Split A-Frame

Total

< $99,000> $99,000

Home Style

PriceRange Colonial Log Split A-Frame

< $99,000> $99,000

18 6 19 12

30Total12 14 16 3

Home Style

20 35 15

0.6000

1.0000

0.40000.30

1.0000

0.700.5429

1.0000

0.45710.8000

1.0000

0.2000

Summarizing Two variables

Summarizing Two variables

Admitted Denied TotalMale 3738 4704 8442

Female 1494 2827 4321Total 5232 7531 12763

Admitted Denied TotalMale 0.2929 0.3686 0.6614

Female 0.1171 0.2215 0.3386Total 0.4099 0.5901 1.0000

Dividing all of the frequencies above by the number of observations yields what the joint probability table below

The crosstabulation for the aggregated UC-Berkley data is

Male acceptance rate is higher when data is aggregated.

FemaleAdmitted Denied Total

A 89 19 108B 17 8 25

Total 106 27 133

MaleAdmitted Denied Total

A 512 313 825B 313 207 520

Total 825 520 1345

Female

Admitted Denied Total

A 0.8241 0.1759 1.0000

B 0.6800 0.3200 1.0000

Male

Admitted Denied Total

A 0.6206 0.3794 1.0000

B 0.6019 0.3981 1.0000

Compute the row percentages to show the Simpson’s Paradox

Summarizing Two variables

data_simpson.xls

A Negative Relationship

x

yQBigMacs

PBigMacs0.50

21

5.00

2

Summarizing Two variables

No Apparent Relationship

yQNoseHairTrimmers

xPBigMacs

Summarizing Two variables

Example: Panthers Football Team

13213

1424181730

x = Number ofInterceptions

y = Number of Points Scored

The Panthers football team is interested ininvestigating the relationship, if any, betweeninterceptions made and points scored.

Summarizing Two variables

y

x

Number of Interceptions

Num

ber o

f Poi

nts S

core

d

51015202530

0

35

1 2 30 4

Summarizing Two variables

data_pelican.xls

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 Report1. 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.