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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
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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
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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
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Interval and Ratio ScalesDCOVA
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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
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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
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Sources of data fall into fourcategories
Data distributed by an organization or anindividual
A designed experiment
A survey
An observational study
DCOVA
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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
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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
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Examples of Survey Data
Political polls of registered voters during politicalcampaigns.
People being surveyed to determine theirsatisfaction with a recent product or serviceexperience.
DCOVA
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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
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Categorical Data Are Organized ByUtilizing Tables
CategoricalData
Tallying Data
SummaryTable
DC OVA
OneCategorical
Variable
TwoCategorical
Variables
ContingencyTable
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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
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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
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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
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Contingency Table Based OnPercentage Of Overall Total
NoErrors Errors Total
Small Amount
170 20 190
Medium
Amount
100 40 140
Large Amount
65 5 70
Total335 65 400
DC OVA
NoErrors Errors Total
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.
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Contingency Table Based OnPercentage of Row Totals
NoErrors Errors Total
Small Amount
170 20 190
Medium
Amount
100 40 140
Large Amount
65 5 70
Total335 65 400
DC OVA
NoErrors Errors Total
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.
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Contingency Table Based OnPercentage Of Column Total
NoErrors Errors Total
Small Amount
170 20 190
Medium
Amount
100 40 140
Large Amount
65 5 70
Total335 65 400
DC OVA
NoErrors Errors Total
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
20 but less than 30 25 6
30 but less than 40 35 540 but less than 50 45 4
50 but less than 60 55 2
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
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: 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
Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
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%
In person at branch 41%
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
Automated or livetelephone
Drive-through s ervice atbranch
In person at branch
Internet
DCO V A
Banking Preference? %
ATM 16%
Automated or livetelephone
2%
Drive-through service at branch
17%
In person at branch 41%
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
Visualizing Numerical Data:
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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
Visualizing Numerical Data:
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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
40 but less than 50 45 450 but less than 60 55 2
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
40 but less than 50 40 9050 but less than 60 50 100
% 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 420.6 No 0.61 8.9 6.7 5.3 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 462.2 No 0.62 6.9 6.0 4.8 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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recording, or otherwise, without the prior written permission of the publisher.Printed in the United States of America.
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