Chapter-2: Descriptive Statistics:
This presentation is the property of its rightful owner.
Sponsored Links
1 / 29

Chapter-2: Descriptive Statistics: PowerPoint PPT Presentation


  • 95 Views
  • Uploaded on
  • Presentation posted in: General

Chapter-2: Descriptive Statistics:. Tabular and Graphical Presentations Part A. Exploratory Data Analysis Cross-tabulations; Scatter Diagrams. Tabular and Graphical Procedures. Data. Qualitative Data. Quantitative Data. Tabular Methods. Graphical Methods. Tabular Methods.

Download Presentation

Chapter-2: Descriptive Statistics:

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 2 descriptive statistics

Chapter-2: Descriptive Statistics:

Tabular and Graphical PresentationsPart A

Exploratory Data Analysis

Cross-tabulations; Scatter Diagrams


Tabular and graphical procedures

Tabular and Graphical Procedures

Data

Qualitative Data

Quantitative Data

Tabular

Methods

Graphical

Methods

Tabular

Methods

Graphical

Methods

  • Bar Graph

  • Pie Chart

  • Frequency

  • Distribution

  • Rel. Freq. Dist.

  • Percent Freq.

  • Distribution

  • Crosstabulation

  • Dot Plot

  • Histogram

  • Ogive

  • Scatter

  • Diagram

  • Frequency

  • Distribution

  • Rel. Freq. Dist.

  • Cum. Freq. Dist.

  • Cum. Rel. Freq.

  • Distribution

  • Stem-and-Leaf

  • Display

  • Crosstabulation


Stem and leaf display

Stem-and-Leaf Display

  • A stem-and-leaf display is an exploratory data

    analysis method that shows both the rank order

  • and shape of the distribution of the data.

  • It is similar to a histogram, but it has the

  • advantage of showing the actual data values.


Chapter 2 descriptive statistics

Example: Hudson Auto Repair

  • Sample of Parts Cost for 50 Tune-ups


Chapter 2 descriptive statistics

Stem-and-Leaf Display

5

6

7

8

9

10

2 7

2 2 2 2 5 6 7 8 8 8 9 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

1 3 7 7 7 8 9

1 4 5 5 9


Steps to construct a stem and leaf display

Steps to Construct a Stem-and-Leaf Display

  • Arrange the first digits of each data to the

  • left of a vertical line.

  • To the right of the vertical line, record the last

  • digit for each item in rank order.

  • Each line in the display is referred to as a stem.

  • Each digit on a stem is a leaf.


Chapter 2 descriptive statistics

Stem-and-Leaf Display

5

6

7

8

9

10

2 7

2 2 2 2 5 6 7 8 8 8 9 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

1 3 7 7 7 8 9

1 4 5 5 9

a stem

a leaf


Stretched stem and leaf display

Stretched Stem-and-Leaf Display

  • If we believe the display has condensed the data too

    much, we can stretch thedisplay by using two stems

    for each leading digit(s).

  • Whenever stretched, the first value of a stem

    corresponds to leaf values of 0 - 4, and the second

  • value of a stem corresponds to leaf values of 5 - 9.


Chapter 2 descriptive statistics

Stretched Stem-and-Leaf Display

5

5

6

6

7

7

8

8

9

9

10

10

2

7

2 2 2 2

5 6 7 8 8 8 9 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

1 3

7 7 7 8 9

1 4

5 5 9


Chapter 2 descriptive statistics

Stem-and-Leaf Display—Some notes

  • Leaf Units

  • A single digit is used to define each leaf.

  • In the preceding example, the leaf unit was 1.

  • Leaf units may be 100, 10, 1, 0.1, and so on.

  • Where the leaf unit is not shown, it is assumed

  • to equal 1.


Example leaf unit 0 1

Example: Leaf Unit = 0.1

If we have data with values such as

8.6 11.79.49.110.211.08.8

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

Leaf Unit = 0.1

8

9

10

11

6 8

1 4

2

0 7


Chapter 2 descriptive statistics

Example: Leaf Unit = 10

If we have data with values such as

1806171719741791168219101838

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

Leaf Unit = 10

16

17

18

19

8

The 82 in 1682

is rounded down

to 80 and is

represented as an 8.

1 9

0 3

1 7


Crosstabulations and scatter diagrams

Crosstabulations and Scatter Diagrams


Crosstabulations and scatter diagrams1

Crosstabulations and Scatter Diagrams

  • Thus far we have focused on methods that are used

  • to summarize the data on one variable at a time.

  • Cross tabulationand a scatter diagram are methods for

  • summarizing the data on two (or more) variables

  • simultaneously.

  • Help us understand the relationship between two variables.


Chapter 2 descriptive statistics

Crosstabulation

  • A crosstabulation is a tabular summary of data for

    two variables.

  • Crosstabulation can be used when:

    • one variable is qualitative and the other is

    • quantitative,

    • both variables are qualitative, or

    • both variables are quantitative.

  • The left and top margin labels define the classes for

  • the two variables.


Chapter 2 descriptive statistics

Cross-tabulation

  • Example:

    The number of Homes sold by style and price for the past two years is shown below.

qualitative

variable

quantitative

variable

Home Style

Price

Range

Colonial Log Split A-Frame

Total

18 6 19 12

55

45

< $99,000

> $99,000

12 14 16 3

30 20 35 15

Total

100


Cross tabulation

Cross-tabulation

  • Insights Gained from Preceding Cross-tabulation

  • The greatest number of homes in the sample (19)

  • are a split-level style and priced at less than or

  • equal to $99,000.

  • Only three homes in the sample are an A-Frame

  • style and priced at more than $99,000.


Cross tabulation row or column percentages

Cross-tabulation: 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.


Chapter 2 descriptive statistics

Cross-tabulation

Frequency distribution

for the price variable

Home Style

Price

Range

Colonial Log Split A-Frame

Total

18 6 19 12

55

45

< $99,000

> $99,000

12 14 16 3

30 20 35 15

Total

100

Frequency distribution

for the home style variable


Chapter 2 descriptive statistics

Cross-tabulation: Row Percentages

Home Style

Price

Range

Colonial Log Split A-Frame

Total

32.73 10.91 34.55 21.82

100

100

< $99,000

> $99,000

26.67 31.11 35.56 6.67

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


Chapter 2 descriptive statistics

Simpson’s Paradox

  • Often Times data in two or more cross-tabulations are

    aggregated to produce a summary cross-tabulation.

  • We must be careful in drawing conclusions about the

  • relationship between the two variables in the

  • aggregated cross-tabulation.

  • Simpson’ Paradox: In some cases the conclusions

    based upon an aggregated cross-tabulation can be

    completely different from the un-aggregated

    data.


Chapter 2 descriptive statistics

Scatter Diagram and Trend line


Chapter 2 descriptive statistics

Scatter Diagram and Trend line

  • A scatter diagram is a graphical presentation of the

  • relationship between two quantitative variables.

  • One variable is shown on the horizontal axis and the

  • other variable is shown on the vertical axis.

  • The general pattern of the plotted points suggests the

  • overall relationship between the variables.

  • A trend line is an approximation of the relationship.


Scatter diagram

Scatter Diagram

  • A Positive Relationship

y

x


Scatter diagram1

Scatter Diagram

  • A Negative Relationship

y

x


Scatter diagram2

Scatter Diagram

  • No Apparent Relationship

y

x


Example panthers football team

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

14

24

18

17

30

1

3

2

1

3


Scatter diagram3

35

30

25

20

15

10

5

0

1

0

2

3

4

Scatter Diagram

y

Number of Points Scored

x

Number of Interceptions


Chapter 2 descriptive statistics

Example: Panthers Football Team

  • Insights Gained from the Preceding Scatter Diagram

  • 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.


  • Login