Cross tabulations and scatter diagrams. . Exploratory data analysis. consists of simple arithmetic and easy-to-draw graphs that can be used to summarize data quickly. The Stem and Leaf Display. . A stem-and-leaf display shows both the . ID: 655486

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Slide1

x

y

Exploratory data analysis

Cross tabulations and scatter diagrams

Slide2

Exploratory data analysis

consists of simple arithmetic and easy-to-draw graphs that can be used to summarize data quickly

Slide3The Stem and Leaf Display

A stem-and-leaf display shows both the

rank order

and shape of the distribution of the data.

It is

similar to a histogram on its side, but it has the advantage of showing the actual data values.

The first digits of each data item are arranged to the

left of a vertical line.

To the right of the vertical line we record the last digit for each item in rank order.

Slide4Example: 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 nextslide.

Slide5Stretched Stem and Leaf

If we believe the original stem-and-leaf display has condensed the data too much, we can

stretch the display

by using two stems for each leading digit(s).

Whenever a stem value is stated twice, the first value corresponds to leaf values of 0 - 4, and the second value corresponds to leaf values of 5 - 9.

Slide6Sample parts cost for 50 tune-ups

Slide75

6

789

10

2 7

2 2 2 2 5 6 7 8 8 8 9 9

1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9

0 0 2 3 5 8 9

A Stem and Leaf Display for the Auto Parts Cost data

1 3 7 7 7 8 9

1 4 5 5 9

Stem

Leaf

Slide85

56

677

889

91010

Stretched Stem and Leaf for Hudson Auto parts data

7

2

5 6 7 8 8 8 9 9

2 2 2 2

1 1 2 2 3 4 4

5 5 5 6 7 8 9 9 9

0 0 2 3

5 8 9

7 7 7 8 9

1 3

5 5 9

1 4

Slide9Leaf Units

A single digit is used to define each leaf. In the preceding example, the

leaf unit was 1. But it does not

have to be 1. The leaf unit can be 0.1, 10, or 100.

Slide10Example: Leaf unit = .1

Suppose we have the following data:

8.6 11.7 9.4 10.2 11.0 8.8

The leaf unit is .1. Thus:

8

91011

6 8

4

2

0 7

Slide11Example: Leaf Unit = 10

If we have data with values such as

16

17

18

19

Leaf Unit = 10

8

1 9

0 3

1 7

1806 1717 1974 1791 1682 1910 1838

a stem-and-leaf display of these data will be

The 82 in 1682

is rounded down

to 80 and is

represented as an 8.

Slide12Crosstabulations and Scatter Diagrams

So far we have considered only ONE variable (parts cost, audit time). But often we are interested in tabular and graphical data that uncover the relationship between TWO variables.

Slide13Crosstabulations

A tabular method for summarizing the data for two variables simultaneously

Crosstabulations can be used when

one variable is qualitative and the other is quantitative,

both variables are qualitative, or

both variables are quantitative.

Slide14Price

Range

Colonial Log Split

A-Frame

Total

<

$99,000

> $99,000

18 6 19 12

55

45

30 20 35 15

Total

100

12 14 16 3

Home Style

Example: Finger Lakes Homes

Crosstabulation

The number of Finger Lakes homes sold for each style and price for the past two years is shown below.

quantitative

variable

qualitative

variable

Slide15Crosstabulation: Row or Column Percentages

Converting the entries in the table into row percentages or column percentages can provide additional insight about the relationship between the two variables.

Slide16Price

Range

Colonial Log Split A-Frame

Total

<

$99,000

> $99,000

32.73 10.91 34.55 21.82

100

100

Note: row totals are actually 100.01 due to rounding.

26.67 31.11 35.56 6.67

Home Style

(Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100

Crosstabulation: Row Percentages

Slide17Price

Range

Colonial Log Split A-Frame

<

$99,000

> $99,000

60.00 30.00 54.29 80.00

40.00 70.00 45.71 20.00

Home Style

100 100 100 100

Total

(Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100

Crosstabulation: Column Percentages

Slide18Using Excel’s PivotTable Report

to Construct a Crosstabulation

Step 3

When the Create Pivot Table dialog box appears:

Choose

Select a table or range

Enter A1:C301 in the

Table/Range

b

ox

Select

New Worksheet

Click

OK

Step

2: In the

Tables group, click the icon above

PivotTable

Step

1: Click on the

Insert

tab on the ribbon

Chapter 2 file

Restaurant.xlsx

Slide19Using the Pivot table Field List

Step 1: In the PivotTable Field List, go to

Choose Fields to add to report: Drag the

Quality Rating Field to the Row Labels

area.Drag the ($)Meal Price field to the

Column Labels area.Drag the Restaurant field to the

Values area.Step 2: Click Sum of Restaurant

in the Values areaSelect

Value Field Settings.Step 3: When the Value Field Settings dialog box appears:

Under Summarize value field by, choose Count

Click OK

Slide20Finalizing the

PivtotTable ReportStep 1: Right-click in cell B4 (or any other cell containing meal prices)Select

GroupStep 2: When the Grouping dialog box appears:Enter 10 in the Starting at

boxEnter 49 in the Ending at

boxEnter 10 in the By box

Step 3: Right-click on Excellent in cell A5

Choose MoveSelect Move “Excellent” to EndStep 4: Close the PivotTable Field List box

Slide21Crosstabulation for the LA

Restaurant Example

Meal Price ($)

Quality Rating

10-19

20-29

30-39

40-49

Grand Total

Good

42

40

2

84

Very Good

34

64

46

6

150

Excellent

2

14

28

22

66

Grand Total

78

118

76

28

300

Chapter 2 file

Restaurant.xlsx

Slide22Crosstabulation: Simpson’s Paradox

Simpson’ Paradox

: In some cases the conclusions

based upon an aggregated

crosstabulation

can be

completely reversed if we look at the

unaggregated

data.

We must be careful in drawing conclusions about the

relationship between the two variables in the

aggregated

crosstabulation

.

Data in two or more

crosstabulations

are often

aggregated to produce a summary crosstabulation

.

Slide23Judge

Verdict

Kendall

Luckett

Total

Upheld

Reversed

129 (86%)

21 (14%)

110 (88%)

15 (12%)

239

36

Total (%)

150 (100%)

125 (100%)

275

You might think

Luckett

is the better Judge. However,

a larger share of Kendall’s cases were in municipal court—where the likelihood of being overturned on appeal is higher.

Slide24

The general pattern of the plotted points suggests the

overall relationship between the variables.

One variable is shown on the horizontal axis and the

other variable is shown on the vertical axis.

A

scatter diagram

is a graphical presentation of the

relationship between two

quantitative

variables.

Scatter Diagram and Trendline

A trendline

is an approximation of the relationship.

Slide25A Positive Relationship

Y

X

0

Slide26A Negative Relationship

Y

X

0

Slide27No Apparent Relationship

Y

X

0

Slide28Example: Panthers Football Team

Scatter Diagram

The Panthers football team is interested in investigating the relationship, if any,

between interceptions made and points scored.

1

32

1

3

1424

18

1730

x

= Number of

Interceptions

y = Number of

Points Scored

Slide29Scatter Diagram

y

x

Number of Interceptions

Number of Points Scored

5

10

15

20

25

30

0

35

1

2

3

0

4

Slide30Insights Gained from the Preceding Scatter Diagram

The relationship is not perfect; all plotted points in

the scatter diagram are not on a straight line.

Higher points scored are associated with a higher

number of interceptions.

The scatter diagram indicates a positive relationship

between the number of interceptions and the

number of points scored.

Example: Panthers Football Team

Slide31Using Excel’s Chart Wizard to Construct

a Scatter Diagram and Trendline

Formula Worksheet (showing data entered)

Slide32Step 1 Select cells A1:B6

Step

2 Click the Chart Wizard

button on standard toolbar

Step 3 When the Chart Wizard - Step 1 of 4 -

Chart Type dialog box appears:

Choose

XY (Scatter) in the

Chart Type list

Choose Scatter

from the Chart subtype

display

Click Next >

Using Excel’s Chart Wizard

to Construct a Scatter Diagram

. . . continue

Slide33Using Excel’s Chart Wizard

to Construct a Scatter Diagram

Step 4 When the

Chart Wizard

- Step 2 of 4 -

Chart

Source Data

dialog box appears:

Click Next >

. . . continue

Slide34Using Excel’s Chart Wizard

to Construct a Scatter Diagram

Step 5 When the

Chart Wizard - Step 3 of 4 – Chart

Options

dialog box appears:

Select the

Titles tab and then

Type

Scatter Diagram for the Panthers

in the Chart title:

box

Type Number of Interceptions

in the

Value (X) axis:

box

Type Number of Points Scored in the

Value (Y) axis:

box

. . . continue

Slide35Step 5 (continued)

Select the

Legend

tab and then

Remove the check in the Show Legend

box Click

Next >

Using Excel’s Chart Wizard

to Construct a Scatter Diagram

Step 6 When the

Chart Wizard – Step 4 of 4 - Chart

Location

dialog box appears:

Specify a location for the new chart

Click

Finish

Slide36Using Excel’s Chart Wizard

to Construct a Scatter Diagram

Slide37Adding a Trendline

Using Excel’s Chart Wizard to Construct

a Scatter Diagram

and Trendline

Step 3 When the

Add Trendline

dialog box appears:

Select the

Type

tab and then

Choose Linear from the

Trend/

Regression type

display

Click

OK

Step 2 Choose the

Add Trendline option

Step 1 Position the mouse pointer over any data

point in the scatter diagram and right click

Slide38Using Excel’s Chart Wizard to Construct

a Scatter Diagram

and Trendline

Slide39Scatter Diagram for the Stereo and Sound

Equipment Store Example

Slide40Scatter Diagram for the Stereo and Sound

Equipment Store Example—with a Trendline

Next Slides