© 2003 Prentice-Hall, Inc. Chapter 2 Presenting Data in Tables and Charts Business Statistics (9 th Edition)

© 2003 Prentice-Hall, Inc.

Chapter 2Presenting Data in Tables

and Charts

Business Statistics(9th Edition)


Chapter Topics

Guidelines to Analyze data Organizing Numerical Data

The Ordered Array and Stem-Leaf Display

Tabulating and Graphing Univariate Numerical Data Frequency Distributions: Tables, Histograms, Polygons Describing Distribution:

Shape, Center and Spread Cumulative Distributions: Tables, the Ogive

Graphing Bivariate Numerical Data


Chapter Topics Displaying Categorical Data Tabulating and Graphing Univariate Categorical

Data The Summary Table Bar and Pie Charts, the Pareto Diagram

Tabulating and Graphing Bivariate Categorical Data Contingency Tables Side by Side Bar Charts

Case Study: Titanic Data Graphical Excellence and Common Errors in

Presenting Data

(continued)


Guidelines to Analyze data

First learn something about the context: What was measured? What are the units? How was the measurement carried out? Where the data measured for a particular purpose?

Then make a picture. It is sometimes said that there are three rules for

starting a data analysis: Plot the data, plot the data, and plot the data. Look for an overall pattern and for deviations from

that pattern. Such deviations are called outliers.

4.1 See a real world problem in which a distribution is needed.


Organizing Numerical Data

2 144677

3 028

4 1

Numerical Data

Ordered Array

Stem and LeafDisplay

Frequency DistributionsCumulative Distributions

Histograms

Polygons

Ogive

Tables

41, 24, 32, 26, 27, 27, 30, 24, 38, 21

21, 24, 24, 26, 27, 27, 30, 32, 38, 41


Data in RawRaw Form (as Collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38

Data in Ordered ArrayOrdered Array from Smallest to Smallest to LargestLargest:

21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Stem-and-Leaf Display:

Organizing Numerical Data(continued)

2 1 4 4 6 7 7

3 0 2 8

4 1


Tabulating and Graphing Numerical Data

O g ive

0

20

40

60

80

100

120

10 20 30 40 50 60

0

1

2

3

4

5

6

7

10 20 30 40 50 60

2 144677

3 028

4 1

Numerical Data

Ordered Array

Stem and LeafDisplay

Histograms Ogive

Tables

41, 24, 32, 26, 27, 27, 30, 24, 38, 21

21, 24, 24, 26, 27, 27, 30, 32, 38, 41

Frequency DistributionsCumulative Distributions

Polygons


Tabulating Numerical Data: Frequency Distributions

Sort Raw Data in Ascending Order12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find Range: 58 - 12 = 46

Select Number of Classes: 5 (usually between 5 and 15)

Compute Class Interval (Width): 10 (46/5 then round up)

Determine Class Boundaries (Limits):10, 20, 30, 40,

50, 60

Compute Class Midpoints: 15, 25, 35, 45, 55

Count Observations & Assign to Classes


Frequency Distributions, Relative Frequency Distributions and

Percentage Distributions

Class Frequency

10 but under 20 3 .15 15

20 but under 30 6 .30 30

30 but under 40 5 .25 25

40 but under 50 4 .20 20

50 but under 60 2 .10 10

Total 20 1 100

RelativeFrequency

Percentage

Data in Ordered Array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58


Graphing Numerical Data: The Histogram

Histogram

0

3

65

4

2

001234567

5 15 25 35 45 55 More

Fre

qu

en

cy


No Gaps Between

Bars

Class MidpointsClass Boundaries


Bar Chart

How tall are the tallest soldiers in this group?

1. How many in this group are between 65 and 67 inches tall?

2. If we selected a soldier at random from this group, would you estimate that he or she is more likely to be taller than 65 inches or shorter than 65 inches? (Hint: No calculation is needed. Judge from the way the display looks.)


Graphing Numerical Data: The Frequency Polygon

Frequency

0

1

2

3

4

5

6

7

5 15 25 35 45 55 More

Class Midpoints



Tabulating Numerical Data: Cumulative Frequency

Lower Cumulative CumulativeLimit Frequency % Frequency

10 0 0

20 3 15

30 9 45

40 14 70

50 18 90

60 20 100



Graphing Numerical Data: The Ogive (Cumulative %

Polygon)

Ogive

0

20

40

60

80

100

10 20 30 40 50 60

Class Boundaries (Not Midpoints)

Data in Ordered Array :12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58


Graphing Bivariate Numerical Data (Scatter

Plot)

Mutual Funds Scatter Plot

0

10

20

30

40

0 10 20 30 40

Net Asset Values

Tota

l Yea

r to

Dat

e R

etur

n (%

)


Tabulating and Graphing Univariate Categorical Data

Categorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts


Univariate and Bivariate Analysis by Tables and Charts

of Car Data

Variables: •Miles per Gallon•Type of Drive•Weight


Variables

We will be looking at 3 variables relating to cars

We Will use Histograms Frequency and Percentage Polygon Ogives Scatter Plots (Bivariate Data)


The following Data Relates to Front and Rear Wheel Drive

Cars

Drive Type and Miles per Gallon (Rear)Cumulative Frequency

12 to under 14 13 2 8.0% 12 0 0.00%14 to under 16 15 4 16.0% 14 0 0.00%16 to under 18 17 3 12.0% 16 4 17.39%18 to under 20 19 8 32.0% 18 7 30.43%20 to under 22 21 4 16.0% 20 15 65.22%22 to under 24 23 2 8.0% 22 19 82.61%24 to under 26 25 2 8.0% 24 21 91.30%26 to under 28 27 0 0.0% 26 23 100.00%28 to under 30 29 0 0.0% 28 23 100.00%30 to under 32 31 0 0.0% 30 23 100.00%32 to under 34 33 0 0.0% 32 23 100.00%

Total 25 100.0%

Cumulative %Frequency

DistributionPercentage Distribution

Lower Limit

Cumulative Frequency

Lower Upper Limit Mid points

Drive Type and Miles per Gallon (Front)Cumulative Frequency

12 to under 14 13 0 0.00% 12 0 0.00%14 to under 16 15 3 3.70% 14 0 0.00%16 to under 18 17 1 1.23% 16 3 3.70%18 to under 20 19 12 14.81% 18 4 4.94%20 to under 22 21 19 23.46% 20 16 19.75%22 to under 24 23 22 27.16% 22 35 43.21%24 to under 26 25 11 13.58% 24 57 70.37%26 to under 28 27 6 7.41% 26 68 83.95%28 to under 30 29 4 4.94% 28 74 91.36%30 to under 32 31 3 3.70% 30 78 96.30%32 to under 34 33 0 0.00% 32 81 100.00%

Cumulative %

Frequency Distribution

Percentage Distribution Lower Limit

Cumulative Frequency

Lower limit

Upper Limit

Mid points


0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

12 14 16 18 20 22 24 26 28 30

Midpoints

Perc

enta

ge

Ogive: Front Wheel Drive

What percentage of the Front wheel Drive Cars do: -

•More than 19 miles per gallon

•Less than 27 Miles per gallon

Estimate the miles per gallon for: -

•50 Percentile of Front Wheel Drive Cars:

•25 Percentile of Front Wheel Drive Cars


0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

12 14 16 18 20 22 24 26 28 30

Midpoints

Perc

enta

ge

Ogive: Rear Wheel Drive

What percentage of the Rear wheel Drive Cars do: -

•More than 19 miles per gallon

•Less than 27 Miles per gallon

Estimate the miles per gallon for: -

•50 Percentile of Rear Wheel Drive Cars:

•Rear Percentile of Front Wheel Drive Cars


To Compare Distributions

Compare Frequency and Percentage Polygons for Front and Rear Drive Cars

Compare Ogives for Front and Rear Drive Cars


Frequency Polygon: Drive Type and Miles per Gallon

0

5

10

15

20

25

11 13 15 17 19 21 23 25 27 29 31 33

Miles per Gallon

Front Rear

Answer the Following True or False. This graph shows:

• There are more Rear Wheel Cars than Front Wheel Cars

•No Front Wheel Drive Cars Do more than 25 Miles per gallon

•There are more Front Wheel Drive Cars that do 21 Miles per gallon than Rear Wheel Drive Cars


0%

5%

10%

15%

20%

25%

30%

35%

11 13 15 17 19 21 23 25 27 29 31 33

Miles per Gallon

Front Rear

Percentage Polygon: Drive Type and Miles per GallonAnswer the Following True or False.

This graph shows:

• Overall the miles per gallon for Rear Wheel is not as good as Front Wheel Drive Cars

• 40% of Front Wheel Drive Cars do 21 Miles per gallon

•There are more Front Wheel Drive Cars that do 21 Miles per gallon than Rear Wheel Drive Cars


0%

20%

40%

60%

80%

100%

120%

12 14 16 18 20 22 24 26 28 30 32

Miles per Gallon

Front Rear

Cumulative Percentage Polygon: Drive Type and Miles

per Gallon


• Overall the miles per gallon for Front Wheel is better than Rear Wheel Drive Cars

• 80% of Front Wheel Drive Cars do less than 21 Miles per gallon


Car Weight (lbs) V’s Miles per Gallon

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0 5 10 15 20 25 30 35

Miles per Gallon

Weight (lbs)


• Overall the Weight of the car is associated with the Miles per gallon

• The Heavier the car the greater the miles per gallon


Displaying Categorical Data

Three Rules of Data Analysis: - Make a picture – It will reveal things you can

not see on a table and will help you think clearly

Make a picture – Well designed display will show the important features and patterns in your data i.e. missing wrong data or unexpected patterns

Make Picture –It is the best way to tell others what about your data.


Frequency Tables1. What is the most common hair color in this group of children?

2. What is the second most common color?

3. Are the categories given here well-defined?

4. If not, how would you improve them?

5. Does this distribution of hair colors resemble the distribution you see among people in Cambodia?

6. If not, how does it differ?

Fair Red Medium Dark Black

27% 5.3% 39.7% 25.8%

2.2%


0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Red Medium Dark Black

Bar Chart1. What is the most common hair color in this group of children?

2. What is the second most common color?

3. Is there a greater difference between the relative frequencies of Red and Black, or between the relative frequencies of Medium and Dark?


Graphing Univariate Categorical Data

0 1 0 2 0 3 0 4 0 5 0

S to c k s

B o n d s

S a vin g s

C D

Categorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

S to c k s B o n d s S a vin g s C D

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0


Tabulating and Graphing Bivariate Categorical Data

Contingency Tables:

Standard of Living A B C TotalRich 8 5 0 13Medium 15 10 1 26Poor 39 39 25 103Poorest 37 41 50 128Total 99 95 76 270

Standard of Living A B C TotalRich 8% 5% 0% 5%Medium 15% 11% 1% 10%Poor 39% 41% 33% 38%Poorest 37% 43% 66% 47%Total 100% 100% 100% 100%

Cummune

Cummune


Pie Chart (Analyzing Standard of Living in 4

Communes)

Rich5%

Medium10%

P oor38%

P oorest47%

Rich

Medium

Poor

Poorest

Standar d of Living


Bivariate Categorical Data(for Standard of Living by Commune)

0 10 20 30 40 50 60

Rich

Medium

Poor

Poorest

C

B

A

Commune

Frequency


Stacked Bar Chart Bivariate Categorical Data

0%

20%

40%

60%

80%

100%

A B C

Poorest

Poor

Medium

Rich

Which commune has the highest percentage of Poor


Pareto Diagram

Axis for line graph shows

cumulative % invested

Axis for bar

chart shows

number in each

category

Pateto of Returned Phones

0

1

2

3

4

5

6

Returned Phones

Co

un

t

0

20

40

60

80

100

120

%

Count Cumulative Percentage


Case Study: Titanic Data

Survived Age Sex ClassDead Adult Male ThirdDead Adult Male CrewDead Adult Male ThirdDead Adult Male CrewDead Adult Male CrewDead Adult Male CrewAlive Adult Female FirstDead Adult Male ThirdDead Adult Male Crew

•Part of a table detailing the Titanic

•Problem with this table - in fact all tables like this – is that you can not really see what is going on

•We need to show patterns, relationships, trends and even exceptions

What are the variables?


Frequency Tables

•The Count provides the Frequency of each category.

•The Variable CLASS has only 4 categories so it is very easy to read

•The Percentage Provides the Relative Frequency

What percentage was not crew ?


Example: Create a Frequency Table

Survived Age Sex ClassDead Adult Male ThirdAlive Adult Male CrewDead Adult Male ThirdDead Child Male CrewDead Adult Male CrewAlive Child Male CrewAlive Adult Female FirstDead Adult Male ThirdDead Adult Male Crew

Example: Create 3 Frequency Tables

1. Survived

2. Age

3. Class


Bar Charts

Displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison

What does this graph tell us?

People on the Titanic by Ticket Class

0

200

400

600

800

Count

Fre

qu

ency First

Second

ThirdExample: Create 6 bar Charts for data on previous

slide.

1. Survived: A Frequency B Percentage

2. Age : A Frequency B Percentage

3. Class : A Frequency B Percentage


Pie Charts

Pie Chars show us the whole group of cases as a circle. They slice into pieces whose size is proportional to the fraction of the whole in each category

Where are there more crew or Third class passengers?

First15%

Second13%

Third32%

Crew40%

Example: Draw 6 Pie Charts for data on previous slide.

1. Survived: A Frequency B Percentage

2. Age : A Frequency B Percentage

3. Class : A Frequency B Percentage


Bivariate Table (Cross Tabulations)

Was there a relationship between the CLASS and the chance of surviving?

We need to look at Class and Survival together on a contingency table.

Marginal Distribution


Example: Cross Tabulations

Create a cross tabulation for:

1. Survived and Age

2. Survived and Sex

3. Age and Sex



Row Percentages indicate Chance

How can the presentation can be improved?


Conditional Distributions makes it clearer

•We have redefined the WHO of the study into two groups: Who was ALIVE and Who was DEAD

•Conditional distributions is when one variable has been selected which satisfies some condition?

If % of ROW same it shows the distributions are INDEPENDENT of Class How can the presentation can be improved?


Clustered Bar Chart of comparing percentage of Alive and Dead in Titanic

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Alive Dead

Crew

Third

Second

First

Did the Crew, Third Class, Second Class and First Class have the same Chance of Survival (being Alive or Dead)?

Class

Each bar as the ”Whole” and divides it proportionally into segments corresponding to the percentage in each group.


Data changed to show an Equal Chance of Survival

Survival First Second Third Crew TotalAlive 202 118 178 212 710Dead 101 59 89 106 355Total 303 177 267 318 1065

Class

First Second Third Crew TotalAlive 202 118 178 212 710% Row 28% 17% 25% 30% 100%

First Second Third Crew TotalDead 101 59 89 106 355% Row 28% 17% 25% 30% 100%

•The Conditional Distributions is based on Category Survival.•Note now the % Row are equal

This means the chance of being alive and dead is the same in each Class. Thus, Survival is independent of Class

Modified


Clustered Bar Chart for Equal Chance of Survival

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Alive Dead

Crew

Third

Second

First

Class


Alternatively, create Conditional Distributions split on Class (By Columns)

First % ColumnAlive 202 67%Dead 101 33%Total 303 100%

Second % ColumnAlive 118 67%Dead 59 33%Total 177 100%

Third % ColumnAlive 178 67%Dead 89 33%Total 267 100%

Crew % ColumnAlive 212 67%Dead 106 33%Total 318 100%

Modified Data to show equal Chance

The Passengers in Category First Class have an equal chance of survival…..

… as they do in Second Class…

… as they do in Third Class…

… as they do in Crew …


Pie Charts are also a good choice when you are primarily interested in percentage

ALIVE

First

Second

Third

Crew

DEAD

First

Second

Third

Crew

What does this show? (See Hidden Slide)

The Dead (non survivors) are mostly crew and 3rd class passengers, survivors on the other hand are nearly evenly split across the classes.

These Pie Charts use original Titanic Data


Examining Contingency tables STEP-BY-STEP

Think Variable – Identify the Variables are report the W’s. be certain that the data are counts and the categories do not overlap

Show Mechanics – Make an appropriate display to see whether there is a difference in the relative proportions. Bar Charts may work equally well

Tell Interpretation – Discuss the pattern in the tables and display and if you can flag any issues to managers to inform them of any consequences. This is extremely important when conducting research.


Example: Cross Tabulations and Graphs

You have created a cross tabulation for:

1. Survived and Age2. Survived and Sex3. Age and Sex Workout Row

percentages and then display them on a Stacked bar or Pie Chart



Principles of Graphical Excellence

Well-Designed Presentation of Data that Provides: Substance Statistics Design

Communicate Complex Ideas with Clarity, Precision and Efficiency

Gives the Largest Number of Ideas in the Most Efficient Manner

Almost Always Involves Several Dimensions Telling the Truth about the Data


Errors in Presenting Data

Using ‘Chart Junk’ No Relative Basis in Comparing Data

between Groups Compressing the Vertical Axis No Zero Point on the Vertical Axis


‘Chart Junk’

Good Presentation

1960: $1.00

1970: $1.60

1980: $3.10

1990: $3.80

Minimum Wage Minimum Wage

0

2

4

1960 1970 1980 1990

$

Bad Presentation


No Relative Basis

Good PresentationA’s received by

studentsA’s received by

students

Bad Presentation

0

200

300

FR SO JR SR

Freq.

10

30

FR SO JR SR

%

FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior


Compressing Vertical Axis

Good Presentation

Quarterly Sales Quarterly Sales

Bad Presentation

0

25

50

Q1 Q2 Q3 Q4

$

0

100

200

Q1 Q2 Q3 Q4

$


No Zero Point on Vertical Axis

Good Presentation

Monthly SalesMonthly Sales

Bad Presentation

0

39

42

45

J F M A M J

$

36

39

42

45

J F M A M J

$

Graphing the first six months of sales

36


Chapter Summary

Organized Numerical Data The Ordered Array and Stem-Leaf Display

Tabulated and Graphed Univariate Numerical Data Frequency Distributions: Tables, Histograms,

Polygons Cumulative Distributions: Tables, the Ogive

Graphed Bivariate Numerical Data


Chapter Summary

Tabulated and Graphed Univariate Categorical Data The Summary Table Bar and Pie Charts, the Pareto Diagram

Tabulated and Graphed Bivariate Categorical Data Contingency Tables Side by Side Charts

Discussed Graphical Excellence and Common Errors in Presenting Data

(continued)

Documents

© 2003 Prentice-Hall, Inc. Chapter 2 Presenting Data in Tables and Charts Business Statistics (9 th Edition)