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11SlideSlide© 2005 Thomson/South© 2005 Thomson/South--WesternWestern

Chapter 1Chapter 1Data and StatisticsData and Statistics

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■■ Applications in Business and EconomicsApplications in Business and Economics

■■ DataData

■■ Data SourcesData Sources

■■ Descriptive StatisticsDescriptive Statistics

■■ Statistical InferenceStatistical Inference

■■ Computers and Computers and

Statistical AnalysisStatistical Analysis


Applications in Applications in Business and EconomicsBusiness and Economics

■■ AccountingAccounting

■■ EconomicsEconomics

Public accounting firms use statisticalPublic accounting firms use statistical

sampling procedures when conductingsampling procedures when conducting

audits for their clients.audits for their clients.

Economists use statistical informationEconomists use statistical information

in making forecasts about the future ofin making forecasts about the future of

the economy or some aspect of it.the economy or some aspect of it.

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A variety of statistical quality A variety of statistical quality

control charts are used to monitorcontrol charts are used to monitor

the output of a production process.the output of a production process.

■■ ProductionProduction

Electronic pointElectronic point--ofof--sale scanners atsale scanners at

retail checkout counters are used toretail checkout counters are used to

collect data for a variety of marketingcollect data for a variety of marketing

research applications.research applications.

■■ MarketingMarketing



Financial advisors use priceFinancial advisors use price--earnings ratios andearnings ratios and

dividend yields to guide their investmentdividend yields to guide their investment

recommendations.recommendations.

�� FinanceFinance

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Data and Data SetsData and Data Sets

■■ DataData are the facts and figures collected, summarized,are the facts and figures collected, summarized,

analyzed, and interpreted.analyzed, and interpreted.

�� The data collected in a particular study are referredThe data collected in a particular study are referredto as the to as the data setdata set..


�� The The elementselements are the entities on which data areare the entities on which data arecollected.collected.

�� A A variablevariable is a characteristic of interest for the elements.is a characteristic of interest for the elements.

�� The set of measurements collected for a particularThe set of measurements collected for a particularelement is called an element is called an observationobservation..

�� The total number of data values in a data set is theThe total number of data values in a data set is thenumber of elements multiplied by the number ofnumber of elements multiplied by the number ofvariables.variables.

Elements, Variables, and ObservationsElements, Variables, and Observations

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Stock Annual Earn/Stock Annual Earn/

Exchange Sales($M) Share($)Exchange Sales($M) Share($)

Data, Data Sets, Data, Data Sets, Elements, Variables, and ObservationsElements, Variables, and Observations

CompanyCompany

DataramDataram

EnergySouthEnergySouth

KeystoneKeystone

LandCareLandCare

PsychemedicsPsychemedics

AMEXAMEX 73.1073.10 0.860.86

OTCOTC 74.0074.00 1.671.67

NYSENYSE 365.70365.70 0.86 0.86

NYSENYSE 111.40111.40 0.330.33

AMEXAMEX 17.6017.60 0.130.13

VariablesVariables

ElementElementNamesNames

Data SetData Set


Scales of MeasurementScales of Measurement

The scale indicates the data summarization andThe scale indicates the data summarization andstatistical analyses that are most appropriate.statistical analyses that are most appropriate.

The scale determines the amount of informationThe scale determines the amount of informationcontained in the data.contained in the data.

Scales of measurement include:Scales of measurement include:

NominalNominal

OrdinalOrdinal

IntervalInterval

RatioRatio

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■■ NominalNominal

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used.may be used.

Data are Data are labels or nameslabels or names used to identify anused to identify anattribute of the element.attribute of the element.


Example:Example:Students of a university are classified by theStudents of a university are classified by theschool in which they are enrolled using aschool in which they are enrolled using anonnumeric label such as Business, Humanities,nonnumeric label such as Business, Humanities,Education, and so on.Education, and so on.

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used forthe school variable (e.g. 1 denotes Business,the school variable (e.g. 1 denotes Business,2 denotes Humanities, 3 denotes Education, and2 denotes Humanities, 3 denotes Education, andso on).so on).


■■ NominalNominal

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■■ OrdinalOrdinal

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used.may be used.

The data have the properties of nominal data andThe data have the properties of nominal data andthe the order or rank of the data is meaningfulorder or rank of the data is meaningful..



■■ OrdinalOrdinal

Example:Example:Students of a university are classified by theirStudents of a university are classified by theirclass standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.Freshman, Sophomore, Junior, or Senior.

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used forthe class standing variable (e.g. 1 denotesthe class standing variable (e.g. 1 denotesFreshman, 2 denotes Sophomore, and so on).Freshman, 2 denotes Sophomore, and so on).

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■■ IntervalInterval

Interval data are Interval data are always numericalways numeric..

The data have the properties of ordinal data, andThe data have the properties of ordinal data, andthe interval between observations is expressed inthe interval between observations is expressed interms of a fixed unit of measure.terms of a fixed unit of measure.



■■ IntervalInterval

Example:Example:Melissa has an SAT score of 1205, while KevinMelissa has an SAT score of 1205, while Kevinhas an SAT score of 1090. Melissa scored 115has an SAT score of 1090. Melissa scored 115points more than Kevin.points more than Kevin.

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■■ RatioRatio

The data have all the properties of interval dataThe data have all the properties of interval dataand the and the ratio of two values is meaningfulratio of two values is meaningful..

Variables such as distance, height, weight, and timeVariables such as distance, height, weight, and timeuse the ratio scale.use the ratio scale.

This This scale must contain a zero valuescale must contain a zero value that indicatesthat indicatesthat nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point.



■■ RatioRatio

Example:Example:Melissa’s college record shows 36 credit hoursMelissa’s college record shows 36 credit hoursearned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credithours earned. Kevin has twice as many credithours earned as Melissa.hours earned as Melissa.

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Data can be further classified as being qualitativeData can be further classified as being qualitativeor quantitative.or quantitative.

The statistical analysis that is appropriate dependsThe statistical analysis that is appropriate dependson whether the data for the variable are qualitativeon whether the data for the variable are qualitativeor quantitative.or quantitative.

In general, there are more alternatives for statisticalIn general, there are more alternatives for statisticalanalysis when the data are quantitative.analysis when the data are quantitative.

Qualitative and Quantitative DataQualitative and Quantitative Data


Qualitative DataQualitative Data

Labels or namesLabels or names used to identify an attribute of eachused to identify an attribute of eachelementelement

Often referred to as Often referred to as categorical datacategorical data

Use either the nominal or ordinal scale ofUse either the nominal or ordinal scale ofmeasurementmeasurement

Can be either numeric or nonnumericCan be either numeric or nonnumeric

Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited

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Quantitative DataQuantitative Data

Quantitative data indicate Quantitative data indicate how many or how much:how many or how much:

discretediscrete, if measuring how many, if measuring how many

continuouscontinuous, if measuring how much, if measuring how much

Quantitative data are Quantitative data are always numericalways numeric..

Ordinary arithmetic operations are meaningful forOrdinary arithmetic operations are meaningful forquantitative data.quantitative data.



QualitativeQualitative QuantitativeQuantitative

NumericalNumerical NumericalNumericalNonnumericalNonnumerical

DataData

NominalNominal OrdinalOrdinal NominalNominal OrdinalOrdinal IntervalInterval RatioRatio

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CrossCross--Sectional DataSectional Data

CrossCross--sectional datasectional data are collected at the same orare collected at the same orapproximately the same point in time.approximately the same point in time.

ExampleExample: data detailing the number of building: data detailing the number of buildingpermits issued in June 2003 in each of the countiespermits issued in June 2003 in each of the countiesof Ohioof Ohio


Time Series DataTime Series Data

Time series dataTime series data are collected over several timeare collected over several timeperiods.periods.

ExampleExample: data detailing the number of building: data detailing the number of buildingpermits issued in Lucas County, Ohio in each ofpermits issued in Lucas County, Ohio in each ofthe last 36 monthsthe last 36 months

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Data SourcesData Sources

■■ Existing SourcesExisting Sources

Within a firmWithin a firm –– almost any departmentalmost any department

Business database servicesBusiness database services –– Dow Jones & Co.Dow Jones & Co.

Government agenciesGovernment agencies -- U.S. Department of LaborU.S. Department of Labor

Industry associationsIndustry associations –– Travel Industry AssociationTravel Industry Associationof Americaof America

SpecialSpecial--interest organizationsinterest organizations –– Graduate ManagementGraduate ManagementAdmission CouncilAdmission Council

InternetInternet –– more and more firmsmore and more firms


■■ Statistical StudiesStatistical Studies

Data SourcesData Sources

In In experimental studiesexperimental studies the variables of interestthe variables of interest

are first identified. Then one or more factors areare first identified. Then one or more factors are

controlled so that data can be obtained about howcontrolled so that data can be obtained about how

the factors influence the variables.the factors influence the variables.

In In observationalobservational (nonexperimental) (nonexperimental) studiesstudies nono

attempt is made to control or influence theattempt is made to control or influence the

variables of interest.variables of interest.a survey is aa survey is a

good examplegood example

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Data Acquisition ConsiderationsData Acquisition Considerations

Time RequirementTime Requirement

Cost of AcquisitionCost of Acquisition

Data ErrorsData Errors

•• Searching for information can be time consuming.Searching for information can be time consuming.

•• Information may no longer be useful by the time itInformation may no longer be useful by the time itis available.is available.

•• Organizations often charge for information evenOrganizations often charge for information evenwhen it is not their primary business activity.when it is not their primary business activity.

•• Using any data that happens to be available orUsing any data that happens to be available orthat were acquired with little care can lead to poorthat were acquired with little care can lead to poorand misleading information.and misleading information.


Descriptive StatisticsDescriptive Statistics

■■ Descriptive statisticsDescriptive statistics are the tabular, graphical, and are the tabular, graphical, and numerical methods used to numerical methods used to summarizesummarize data.data.

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Example: Hudson Auto RepairExample: Hudson Auto Repair

The manager of Hudson AutoThe manager of Hudson Auto

would like to have a betterwould like to have a better

understanding of the costunderstanding of the cost

of parts used in the engineof parts used in the engine

tunetune--ups performed in theups performed in the

shop. She examines 50shop. She examines 50

customer invoices for tunecustomer invoices for tune--ups. The costs of parts,ups. The costs of parts,

rounded to the nearest dollar, are listed on the nextrounded to the nearest dollar, are listed on the next

slide.slide.


91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 74

62 82 98 101 79 105 79 69 62 73

Example: Hudson Auto RepairExample: Hudson Auto Repair

■■ Sample of Parts Cost for 50 TuneSample of Parts Cost for 50 Tune--upsups

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Tabular Summary:Tabular Summary:Frequency and Percent FrequencyFrequency and Percent Frequency

5050--5959

6060--6969

7070--7979

8080--8989

9090--9999

100100--109109

22

1313

1616

77

77

55

5050

44

2626

3232

1414

1414

1010

100100

(2/50)100(2/50)100

PartsPartsCost ($)Cost ($)

PartsPartsFrequencyFrequency

PercentPercentFrequencyFrequency


Graphical Summary: HistogramGraphical Summary: Histogram

22

44

66

88

1010

1212

1414

1616

1818

PartsCost ($)Parts

Cost ($)

Fre

qu

en

cyF

req

ue

ncy

50−59 60−69 70−79 80−89 90−99 100-11050−59 60−69 70−79 80−89 90−99 100-110

TuneTune--up Parts Costup Parts Cost

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Numerical Descriptive StatisticsNumerical Descriptive Statistics

�� Hudson’s average cost of parts, based on the 50Hudson’s average cost of parts, based on the 50tunetune--ups studied, is $79 (found by summing theups studied, is $79 (found by summing the50 cost values and then dividing by 50).50 cost values and then dividing by 50).

�� The most common numerical descriptive statisticThe most common numerical descriptive statisticis the is the averageaverage (or (or meanmean).).


Statistical InferenceStatistical Inference

PopulationPopulation

SampleSample

Statistical inferenceStatistical inference

CensusCensus

Sample surveySample survey

−− the set of all elements of interest in athe set of all elements of interest in aparticular studyparticular study

−− a subset of the populationa subset of the population

−− the process of using data obtainedthe process of using data obtainedfrom a sample to make estimatesfrom a sample to make estimatesand test hypotheses about theand test hypotheses about thecharacteristics of a populationcharacteristics of a population

−− collecting data for a populationcollecting data for a population

−− collecting data for a samplecollecting data for a sample

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Process of Statistical InferenceProcess of Statistical Inference

11. Population . Population consists of allconsists of all

tunetune--ups. Averageups. Averagecost of parts iscost of parts is

unknownunknown.

22. A sample of 50. A sample of 50engine tuneengine tune--ups ups

is examined.is examined.

33. The sample data . The sample data provide a sampleprovide a sampleaverage parts costaverage parts costof $79 per tuneof $79 per tune--up.up.

44. The sample average. The sample averageis used to estimate theis used to estimate the

population average.population average.


Computers and Statistical AnalysisComputers and Statistical Analysis

�� Statistical analysis often involves working withStatistical analysis often involves working withlarge amounts of datalarge amounts of data..

�� Computer softwareComputer software is typically used to conduct theis typically used to conduct theanalysis.analysis.

�� Statistical software packages such as Statistical software packages such as Microsoft ExcelMicrosoft Exceland and MinitabMinitab are capable of data management, analysis,are capable of data management, analysis,and presentation.and presentation.

�� Instructions for using Excel and Minitab are providedInstructions for using Excel and Minitab are providedin chapter appendices.in chapter appendices.

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End of Chapter 1End of Chapter 1

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