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Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-1

Chapter 2

Organizing and Visualizing Data

Statistics for Managers usingMicrosoft Excel 6 th Edition


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Learning Objectives

In this chapter you learn:

The sources of data used in business

The types of data used in businessTo develop tables and charts for numericaldata

To develop tables and charts for categoricaldata

The principles of properly presenting graphs


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A Step by Step Process For Examining &Concluding From Data Is Helpful

In this book we will use DCOVA

Define the variables for which you want to reach

conclusionsCollect the data from appropriate sourcesOrganize the data collected by developing tablesVisualize the data by developing chartsAnalyze the data by examining the appropriatetables and charts (and in later chapters by usingother statistical methods) to reach conclusions


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Types of Variables

Categorical (qualitative ) variables have values thatcan only be placed into categories, such as yes andno.

Numerical (quantitative ) variables have values thatrepresent quantities.

Discrete variables arise from a counting processContinuous variables arise from a measur ing process

DCOVA


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Types of Variables

Variables

Categorical Numerical

Discrete Continuous

Examples:

Marital StatusPolitical PartyEye Color

(Defined categories) Examples:

Number of ChildrenDefects per hour

(Counted items)

Examples:

WeightVoltage

(Measured characteristics)

DCOVA


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Levels of Measurement

A nominal scale classifies data into distinctcategories in which no ranking is implied.

Categorical Variables Categories

Personal ComputerOwnership

Type of Stocks Owned

Internet Provider

Yes / No

Microsoft Network / AOL/ Other

Growth / Value / Other

DCOVA


7/65Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-7

Levels of Measurement (cont.)

An ordinal scale classifies data into distinctcategories in which ranking is implied

Catego rical Variable Ordered Categories

Student class designation Freshman, Sophomore, Junior,Senior

Product satisfaction Satisfied, Neutral, Unsatisfied

Faculty rank Professor, Associate Professor, Assistant Professor, Instructor

Standard & Poors bond ratings AAA, AA, A, BBB, BB, B, CCC, CC,C, DDD, DD, D

Student Grades A, B, C, D, F

DCOVA



Levels of Measurement (cont.)

An interval scale is an ordered scale in which thedifference between measurements is a meaningfulquantity but the measurements do not have a true

zero point.

A ratio scale is an ordered scale in which thedifference between the measurements is ameaningful quantity and the measurements have atrue zero point.

DCOVA



Interval and Ratio ScalesDCOVA



Why Collect Data?

A marketing research analyst needs to assess the effectivenessof a new television advertisement.

A pharmaceutical manufacturer needs to determine whether anew drug is more effective than those currently in use.

An operations manager wants to monitor a manufacturing process to find out whether the quality of the product beingmanufactured is conforming to company standards.

An auditor wants to review the financial transactions of acompany in order to determine whether the company is incompliance with generally accepted accounting principles.

DCOVA



Sources of Data

Primary Sources : The data collector is the one using the datafor analysis

Data from a political survey

Data collected from an experimentObserved data

Secondary Sources : The person performing data analysis isnot the data collector

Analyzing census dataExamining data from print journals or data published on the internet.

DCOVA



Sources of data fall into fourcategories

Data distributed by an organization or anindividual

A designed experiment

A survey

An observational study

DCOVA



Examples Of Data DistributedBy Organizations or Individuals

Financial data on a company provided byinvestment services.

Industry or market data from market researchfirms and trade associations.

Stock prices, weather conditions, and sportsstatistics in daily newspapers.

DCOVA



Examples of Data From ADesigned Experiment

Consumer testing of different versions of aproduct to help determine which product shouldbe pursued further.

Material testing to determine which suppliersmaterial should be used in a product.

Market testing on alternative productpromotions to determine which promotion to

use more broadly.

DCOVA



Examples of Survey Data

Political polls of registered voters during politicalcampaigns.

People being surveyed to determine theirsatisfaction with a recent product or serviceexperience.

DCOVA



Examples of Data FromObservational Studies

Market researchers utilizing focus groups toelicit unstructured responses to open-endedquestions.

Measuring the time it takes for customers to beserved in a fast food establishment.

Measuring the volume of traffic through anintersection to determine if some form of

advertising at the intersection is justified.

DCOVA



Categorical Data Are Organized ByUtilizing Tables

CategoricalData

Tallying Data

SummaryTable

DC OVA

OneCategorical

Variable

TwoCategorical

Variables

ContingencyTable



Organizing Categorical Data:Summary Table

A summary table indicates the frequency, amount, or percentage of itemsin a set of categories so that you can see differences between categories.

Banking Preference? PercentATM 16%

Automated or live telephone 2%

Drive-through service at branch 17%

In person at branch 41%

Internet 24%

DC OVA

Summary Table From A Survey of 1000 Banking Customers



A Contingency Table Helps OrganizeTwo or More Categorical Variables

Used to study patterns that may exist betweenthe responses of two or more categoricalvariables

Cross tabulates or tallies jointly the responsesof the categorical variables

For two variables the tallies for one variable arelocated in the rows and the tallies for thesecond variable are located in the columns

DC OVA



Contingency Table - Example

A random sample of 400invoices is drawn.Each invoice is categorized

as a small, medium, or largeamount.Each invoice is alsoexamined to identify if there

are any errors.This data are then organizedin the contingency table tothe right.

DC OVA

NoErrors Errors Total

Small Amount

170 20 190

Medium

Amount

100 40 140

Large Amount

65 5 70

Total335 65 400

Contingency Table ShowingFrequency of Invoices Categorized

By Size and The Presence Of Errors



Contingency Table Based OnPercentage Of Overall Total


Small Amount

170 20 190

Medium

Amount

100 40 140

Large Amount

65 5 70

Total335 65 400

DC OVA


Small Amount

42.50% 5.00% 47.50%

Medium Amount

25.00% 10.00% 35.00%

Large Amount

16.25% 1.25% 17.50%

Total83.75% 16.25% 100.0%

42.50% = 170 / 40025.00% = 100 / 40016.25% = 65 / 400

83.75% of sampled invoiceshave no errors and 47.50%of sampled invoices are forsmall amounts.



Contingency Table Based OnPercentage of Row Totals


Small Amount

170 20 190

Medium

Amount

100 40 140

Large Amount

65 5 70

Total335 65 400

DC OVA


Small Amount

89.47% 10.53% 100.0%

Medium Amount

71.43% 28.57% 100.0%

Large Amount

92.86% 7.14% 100.0%

Total83.75% 16.25% 100.0%

89.47% = 170 / 19071.43% = 100 / 14092.86% = 65 / 70

Medium invoices have a largerchance (28.57%) of havingerrors than small (10.53%) orlarge (7.14%) invoices.



Contingency Table Based OnPercentage Of Column Total


Small Amount

170 20 190

Medium

Amount

100 40 140

Large Amount

65 5 70

Total335 65 400

DC OVA


Small Amount

50.75% 30.77% 47.50%

Medium Amount

29.85% 61.54% 35.00%

Large Amount

19.40% 7.69% 17.50%

Total100.0% 100.0% 100.0%

50.75% = 170 / 33530.77% = 20 / 65

There is a 61.54% chancethat invoices with errors areof medium size.


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Tables Used For OrganizingNumerical Data

Numerical Data

Ordered Array

DC OVA

CumulativeDistributions

FrequencyDistributions


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Organizing Numerical Data:Ordered Array

An ordered array is a sequence of data, in rank order, from thesmallest value to the largest value.Shows range (minimum value to maximum value)May help identify outliers (unusual observations)

Age ofSurveyedCollegeStudents

Day Students

16 17 17 18 18 18

19 19 20 20 21 22

22 25 27 32 38 42Night Students

18 18 19 19 20 21

23 28 32 33 41 45

DC OVA


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Organizing Numerical Data:Frequency Distribution

The frequency distribution is a summary table in which the data arearranged into numerically ordered classes.

You must give attention to selecting the appropriate number of class

groupings for the table, determining a suitable width of a class grouping,and establishing the boundaries of each class grouping to avoidoverlapping.

The number of classes depends on the number of values in the data. Witha larger number of values, typically there are more classes. In general, afrequency distribution should have at least 5 but no more than 15 classes.

To determine the width of a class interval, you divide the range (Highestvalue Lowest value) of the data by the number of class groupings desired.

DC OVA


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Organizing Numerical Data:Frequency Distribution Example

Example: A manufacturer of insulation randomly selects 20winter days and records the daily high temperature

24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27

DC OVA


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Organizing Numerical Data:Frequency Distribution Example

Sort raw data in ascending order:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Find range: 58 - 12 = 46Select number of classes: 5 (usually between 5 and 15)

Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits):Class 1: 10 to less than 20Class 2: 20 to less than 30Class 3: 30 to less than 40Class 4: 40 to less than 50Class 5: 50 to less than 60

Compute class midpoints: 15, 25, 35, 45, 55Count observations & assign to classes

DC OVA


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Organizing Numerical Data: FrequencyDistribution Example

Class Midpoints Frequency

10 but less than 20 15 3


30 but less than 40 35 540 but less than 50 45 4


Total 20

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

DC OVA


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Organizing Numerical Data: Relative &Percent Frequency Distribution Example

Class Frequency

10 but less than 20 3 .15 15

20 but less than 30 6 .30 30

30 but less than 40 5 .25 2540 but less than 50 4 .20 20

50 but less than 60 2 .10 10

Total 20 1.00 100

RelativeFrequency Percentage


DC OVA


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Organizing Numerical Data: CumulativeFrequency Distribution Example

Class

10 but less than 20 3 15% 3 15%20 but less than 30 6 30% 9 45%

30 but less than 40 5 25% 14 70%40 but less than 50 4 20% 18 90%50 but less than 60 2 10% 20 100%

Total 20 100 20 100%

Percentage CumulativePercentage


Frequency CumulativeFrequency

DC OVA


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Why Use a Frequency Distribution?

It condenses the raw data into a moreuseful form

It allows for a quick visual interpretation ofthe data

It enables the determination of the majorcharacteristics of the data set includingwhere the data are concentrated /clustered

DC OVA

b


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Frequency Distributions:Some Tips

Different class boundaries may provide different pictures forthe same data (especially for smaller data sets)

Shifts in data concentration may show up when differentclass boundaries are chosen

As the size of the data set increases, the impact ofalterations in the selection of class boundaries is greatlyreduced

When comparing two or more groups with different samplesizes, you must use either a relative frequency or apercentage distribution

DC OVA


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Visualizing Categorical DataThrough Graphical Displays

CategoricalData

Visualizing Data

BarChart

SummaryTable For One

Variable

ContingencyTable For Two

Variables

Side By SideBar Chart

DCO V A

Pie Chart

ParetoChart

Vi li i C i l D


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Visualizing Categorical Data:The Bar Chart

In a bar chart, a bar shows each category, the length of whichrepresents the amount, frequency or percentage of values falling intoa category which come from the summary table of the variable.

Banking Preference

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

ATM

Automated or live telephone

Drive-through service at branch

In person at branch

Internet

DCO V A

Banking Preference? %

ATM 16%

Automated or livetelephone

2%

Drive-through service at

branch

17%


Internet 24%

Vi li i C t i l D t


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Visualizing Categorical Data:The Pie Chart

The pie chart is a circle broken up into slices that represent categories.The size of each slice of the pie varies according to the percentage ineach category.

Banking Prefere nce

16%

2%

17%

41%

24% ATM


Drive-through s ervice atbranch

In person at branch

Internet

DCO V A

Banking Preference? %

ATM 16%


2%

Drive-through service at branch

17%


Internet 24%

Vi li i C i l D


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Visualizing Categorical Data:The Pareto Chart

Used to portray categorical data (nominal scale)

A vertical bar chart, where categories are

shown in descending order of frequency A cumulative polygon is shown in the samegraph

Used to separate the vital few from the trivialmany

DCO V A

Visualizing Categorical Data:


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Visualizing Categorical Data:The Pareto Chart (cont)

Pareto Chart For Banking Preference

0%

20%

40%

60%

80%

100%

In personat branch

Internet Drive-through

service atbranch

ATM Automatedor live

telephone

% i

n e a c h c a

t e g o r y

( b a r g r a p

h )

0%

20%

40%

60%

80%

100%

C u m u

l a t i v e

%

( l i n e g r a p

h )

DCO V A


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Visualizing Numerical DataBy Using Graphical Displays

Numerical Data

Ordered Array

Stem-and-LeafDisplay Histogram Polygon Ogive

Frequency Distributionsand

Cumulative Distributions

DCO V A


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Stem-and-Leaf Display

A simple way to see how the data are distributedand where concentrations of data exist

METHOD: Separate the sorted data seriesinto leading digits (the stems ) and

the trailing digits (the leaves )

DCO V A

Organizing Numerical Data:


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Organizing Numerical Data:Stem and Leaf Display

A stem-and-leaf display organizes data into groups (calledstems) so that the values within each group (the leaves)

branch out to the right on each row.

Stem Leaf

1 67788899

2 0012257

3 28

4 2

Age of College Students

Day Students Night Students

Stem Leaf

1 8899

2 0138

3 23

4 15

Age ofSurveyedCollegeStudents

Day Students

16 17 17 18 18 18

19 19 20 20 21 22

22 25 27 32 38 42

Night Students18 18 19 19 20 21

23 28 32 33 41 45

DCO V A

Visualizing Numerical Data:


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Visualizing Numerical Data:The Histogram

A vertical bar chart of the data in a frequency distribution iscalled a histogram.

In a histogram there are no gaps between adjacent bars.

The class boundaries (or class midpoints ) are shown on thehorizontal axis.

The vertical axis is either frequency, relative frequency, or percentage .

The height of the bars represent the frequency, relativefrequency, or percentage.

DCO V A



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Visualizing Numerical Data:The Histogram

Class Frequency

10 but less than 20 3 .15 15

20 but less than 30 6 .30 3030 but less than 40 5 .25 2540 but less than 50 4 .20 2050 but less than 60 2 .10 10

Total 20 1.00 100

RelativeFrequency Percentage

0

2

4

6

8

5 15 25 35 45 55 More

F r e q u e n c y

Histogram: Age Of Students

(In a percentagehistogram the verticalaxis would be defined toshow the percentage ofobservations per class)

DCO V A



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Visualizing Numerical Data:The Polygon

A percentage polygon is formed by having the midpoint ofeach class represent the data in that class and then connectingthe sequence of midpoints at their respective class

percentages.

The cumulative percentage polygon, or ogive, displays thevariable of interest along the X axis, and the cumulative

percentages along theY

axis.

Useful when there are two or more groups to compare.

DCO V A

l l


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01234567

5 15 25 35 45 55 65

F r e q u e n c y

Frequency Polygon: Age Of Students

Visualizing Numerical Data:The Frequency Polygon

Class Midpoints

Class

10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 5


FrequencyClass

Midpoint

(In a percentagepolygon the vertical axiswould be defined toshow the percentage ofobservations per class)

DCO V A

Vi li i N i l D t


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Visualizing Numerical Data:The Ogive (Cumulative % Polygon)

Class

10 but less than 20 10 1520 but less than 30 20 4530 but less than 40 30 70


% lessthan lowerboundary

Lowerclass

boundary

02040

6080

100

10 20 30 40 50 60 C u m u

l a t i v e

P e r c e n

t a g e

Ogive: Age Of Students

Lower Class Boundary

(In an ogive the percentageof the observations lessthan each lower classboundary are plotted versusthe lower class boundaries.

DCO V A

Vi li i g T N i l


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Visualizing Two NumericalVariables: The Scatter Plot

Scatter plots are used for numerical data consisting of pairedobservations taken from two numerical variables

One variable is measured on the vertical axis and the othervariable is measured on the horizontal axis

Scatter plots are used to examine possible relationships

between two numerical variables

DCO V A


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Scatter Plot Example

Volumeper day

Cost perday

23 125

26 14029 146

33 160

38 167

42 170

50 188

55 195

60 200

Cost per Day vs. Production Volume

0

50

100

150

200

250

20 30 40 50 60 70

Volume per Day

C o s

t p e r

D a y

DCO V A

Vi li i T N i l


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A Time Series Plot is used to studypatterns in the values of a numeric

variable over time

The Time Series Plot:Numeric variable is measured on thevertical axis and the time period ismeasured on the horizontal axis

Visualizing Two NumericalVariables: The Time Series Plot

DCO V A


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Time Series Plot Example

Number of Franchises, 1996-2004

0

20

40

6080

100

120

1994 1996 1998 2000 2002 2004 2006

Ye ar

N u m

b e r o

f

F r a n c

h i s e s

YearNumber ofFranchises

1996 43

1997 541998 60

1999 73

2000 82

2001 95

2002 1072003 99

2004 95

DCO V A

U i Pi T bl T E l


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Using Pivot Tables To ExploreMultidimensional Data

Can be used to discover possible patterns andrelationships in multidimensional data.

An Excel tool for creating tables that summarize data.

Simple applications used to create summary orcontingency tables

Can also be used to change and / or add variables to atable

All of the examples that follow can be created usingSection EG2.3

DC OV A

Pivot Table Version of


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Pivot Table Version ofContingency Table For Bond Data

Type Assets Fees Expense Ratio Return 2008 3-Year Return 5-Year Return Risk

Intermediate Government 158.2 No 0.61 7.6 6.3 5.0 Average


Intermediate Government 243.1 No 0.93 11.1 7.4 5.0 Above AverageIntermediate Government 24.7 No 0.49 7.3 6.5 5.4 Above Average


Intermediate Government 497.7 No 0.27 11.4 7.7 5.9 Above Average

First Six Data Points In The Bond Data SetDC OV A

Can Easily Convert To An


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Can Easily Convert To AnOverall Percentages Table

Intermediate government funds are much morelikely to charge a fee.

DC OV A

Can Easily Add Variables To


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Can Easily Add Variables To An Existing Table

Is the pattern of risk the same for all combinations offund type and fee charge?

DC OV A

Can Easily Change The


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Can Easily Change TheStatistic Displayed

This table computes the sum of a numerical variable (Assets)for each of the four groupings and divides by the overall sumto get the percentages displayed.

DC OV A

Tables Can Compute & Display


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Tables Can Compute & DisplayOther Descriptive Statistics

This table computes and displays averages of 3-year returnfor each of the twelve groupings.

DC OV A

Can Drill Down Into Any Cell


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Can Drill Down Into Any CellIn A Pivot Table

Double click in any cell to see a worksheet displayingthe data that is used in that cell. Below is the worksheetcreated by drilling down in the short term corporate bond /fee yes cell.

DC OV A


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Principles of Excellent Graphs

The graph should not distort the data.The graph should not contain unnecessary adornments(sometimes referred to as chart junk ).

The scale on the vertical axis should begin at zero.All axes should be properly labeled.The graph should contain a title.The simplest possible graph should be used for a given set ofdata.

DCO V A


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Graphical Errors: Chart Junk

1960: $1.00

1970: $1.60

1980: $3.10

1990: $3.80

Minimum Wage

Bad Presentation

Minimum Wage

0

2

4

1960 1970 1980 1990

$

Good Presentation

DCO V A

Graphical Errors:


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Graphical Errors:No Relative Basis

As received bystudents.

As received bystudents.

Bad Presentation

0

200

300

FR SO JR SR

Freq.

10%

30%

FR SO JR SR

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

100

20%

0%

%

Good Presentation

DCO V A

Graphical Errors:


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Graphical Errors:Compressing the Vertical Axis

Good Presentation

Quarterly Sales Quarterly Sales

Bad Presentation

0

25

50

Q1 Q2 Q3 Q4

$

0

100

200

Q1 Q2 Q3 Q4

$

DCO V A

Graphical Errors: No Zero Point


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G ap ca o s: o e o o ton the Vertical Axis

Monthly Sales

36

39

42

45

J F M A M J

$

Graphing the first six months of sales

Monthly Sales

0

394245

J F M A M J

$

36

Good PresentationsBad Presentation

DCO V A


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Chapter Summary

Organized categorical using a summary table or acontingency table.Organized numerical data using an ordered array, a frequencydistribution, a relative frequency distribution, a percentagedistribution, and a cumulative percentage distribution.Visualized categorical data using the bar chart, pie chart, andPareto chart.Visualized numerical data using the stem-and-leaf display,

histogram, percentage polygon, and ogive.Developed scatter plots and time series graphs.Looked at examples of the use of Pivot Tables in Excel formultidimensional data.

Examined the dos and don'ts of graphically displaying data.

In this chapter, we have


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