CHAPTER-1

Definition:

• Collection, summarization, analysis, and reporting of numerical findings

Statistics is concerned with data Collection; Organization; SummarizationPresentation and Scientific Analysis

drawing valid conclusions making informed decisions

1.1. What is Statistics? 1.1. What is Statistics?

Applications of Statistics Applications of Statistics in in

Business and EconomicsBusiness and Economics

Accounting

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.

Applications in Applications in Business and EconomicsBusiness and Economics

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 point-of-sale scanners atElectronic point-of-sale 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

Applications in Applications in Business and EconomicsBusiness and Economics

Financial advisors use price-earnings ratios andFinancial advisors use price-earnings ratios and

dividend yields to guide their investmentdividend yields to guide their investment

recommendations.recommendations.

FinanceFinance

Data:Data:Elements, Variables, and Elements, Variables, and

ObservationsObservations

Data refers to facts and figures that are collected, summarized, analyzed, and interpreted.

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

EElementslements:: are the entities on which data are collected.are the entities on which data are collected.

VVariableariable:: is a characteristic of interest for the elements.is a characteristic of interest for the elements.

ObservationObservation: : the set of collected for a particular element.the set of collected for a particular element.

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

Data: Elements, Variables, and Data: Elements, Variables, and ObservationsObservations

Stock Annual Earn/Stock Annual Earn/Exchange Sales($M) Share($)Exchange Sales($M) Share($)

Data: Data: Elements, Variables, and ObservationsElements, Variables, and Observations

CompanyCompany

DataramDataram

EnergySouthEnergySouth

KeystoneKeystone

LandCareLandCare

PsychemedicsPsychemedics

AMEXAMEX 73.10 73.10 0.86 0.86

OTCOTC 74.00 74.00 1.67 1.67

NYSENYSE 365.70365.70 0.86 0.86

NYSENYSE 111.40111.40 0.33 0.33

AMEXAMEX 17.60 17.60 0.13 0.13

VariableVariablessElemenElemen

tt NamesNames

Data SetData Set

ObservatioObservationn

Four commonly used Scales of measurementFour commonly used Scales of measurementFour commonly used Scales of measurementFour commonly used Scales of measurement

NominalNominal

OrdinalOrdinal

IntervalInterval

RatioRatio

Scales of measurement determine the Scales of measurement determine the amount of information contained in the data.amount of information contained in the data. Scales of measurement determine the Scales of measurement determine the amount of information contained in the data.amount of information contained in the data.

They determine the nature of data summarizationThey determine the nature of data summarization and statistical analyses that are most appropriate.and statistical analyses that are most appropriate. They determine the nature of data summarizationThey determine the nature of data summarization and statistical analyses that are most appropriate.and statistical analyses that are most appropriate.

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

Data Data labels or nameslabels or names used to identify an used to identify an attribute of the element.attribute of the element. Data Data labels or nameslabels or names used to identify an used to identify an attribute of the element.attribute of the element.

Example:Example: Classification of University students by theClassification of University students by the school in which they are enrolledschool in which they are enrolled using using labels such as Business, Humanities,labels such as Business, Humanities, Education, and so on. (Non-numeric)Education, and so on. (Non-numeric)

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used for the 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, and so on).so on).

Example:Example: Classification of University students by theClassification of University students by the school in which they are enrolledschool in which they are enrolled using using labels such as Business, Humanities,labels such as Business, Humanities, Education, and so on. (Non-numeric)Education, and so on. (Non-numeric)

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used for the 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, and so on).so on).

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

Data Measured using Ordinal scalesData Measured using Ordinal scaleshave the properties of nominal data. However,have the properties of nominal data. However, the the order or rank of the data is meaningfulorder or rank of the data is meaningful..

Data Measured using Ordinal scalesData Measured using Ordinal scaleshave the properties of nominal data. However,have the properties of nominal data. However, the the order or rank of the data is meaningfulorder or rank of the data is meaningful..

Example:Example: Classification of University students by theirClassification of University students by their class standingclass standing using a nonnumeric label such as using a nonnumeric label such as FreshmanFreshman, , SophomoreSophomore, , JuniorJunior, or , or SeniorSenior..

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

Example:Example: Classification of University students by theirClassification of University students by their class standingclass standing using a nonnumeric label such as using a nonnumeric label such as FreshmanFreshman, , SophomoreSophomore, , JuniorJunior, or , or SeniorSenior..

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

Interval data are Interval data are always numericalways numeric.. 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, and the interval between observations is expressed inthe interval between observations is expressed in terms of a fixed unit of measure.terms of a fixed unit of measure.

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

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

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

The data have all the properties of interval dataThe data have all the properties of interval data and the and the ratio of two values is meaningfulratio of two values is meaningful.. The data have all the properties of interval dataThe data have all the properties of interval data and 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 time use the ratio scale.use the ratio scale. Variables such as distance, height, weight, and timeVariables such as distance, height, weight, and time use the ratio scale.use the ratio scale.

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

Example:Example: Melissa’s college record shows 36 credit hoursMelissa’s college record shows 36 credit hours earned, 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 credit hours earned as Melissa.hours earned as Melissa.

Example:Example: Melissa’s college record shows 36 credit hoursMelissa’s college record shows 36 credit hours earned, 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 credit hours earned as Melissa.hours earned as Melissa.

Data are often classified into one of the following two categoriesData are often classified into one of the following two categories Data are often classified into one of the following two categoriesData are often classified into one of the following two categories

Quantitative DataQuantitative DataQuantitative DataQuantitative Data

Qualitative DataQualitative DataQualitative DataQualitative Data

Data TypesData Types

The statistical analysis that is appropriate dependsThe statistical analysis that is appropriate depends on whether the data for the variable are qualitativeon whether the data for the variable are qualitative or quantitative.or quantitative.

The statistical analysis that is appropriate dependsThe statistical analysis that is appropriate depends on whether the data for the variable are qualitativeon whether the data for the variable are qualitative or quantitative.or quantitative.

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

Qualitative and Quantitative DataQualitative and Quantitative Data

Labels or namesLabels or names are used to identify an attribute of each are used to identify an attribute of each elementelement Labels or namesLabels or names are used to identify an attribute of each are used to identify an attribute of each elementelement

Often referred to as Often referred to as categorical datacategorical data Often referred to as Often referred to as categorical datacategorical data

Use either the nominal or ordinal scalesUse either the nominal or ordinal scales Use either the nominal or ordinal scalesUse either the nominal or ordinal scales

Can be either numeric or nonnumericCan be either numeric or nonnumeric Can be either numeric or nonnumericCan be either numeric or nonnumeric

Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited

Features of Quantitative Features of Quantitative DataData

Quantitative data indicate Quantitative data indicate how many or how much:how many or how much: 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 discretediscrete, if measuring how many, if measuring how many

continuouscontinuous, if measuring how much, if measuring how much continuouscontinuous, if measuring how much, if measuring how much

Quantitative data are Quantitative data are always numericalways numeric.. Quantitative data are Quantitative data are always numericalways numeric..

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

Data and Scales of Measurement: Data and Scales of Measurement: SummarySummary

QualitativeQualitativeQualitativeQualitative QuantitativQuantitativee

QuantitativQuantitativee

NumericalNumericalNumericalNumerical NumericalNumericalNumericalNumericalNonnumericalNonnumericalNonnumericalNonnumerical

DataDataDataData

NominaNominallNominaNominall

OrdinaOrdinallOrdinaOrdinall

NominalNominalNominalNominal OrdinalOrdinalOrdinalOrdinal IntervalIntervalIntervalInterval RatioRatioRatioRatio

1. Cross-Sectional Data1. Cross-Sectional Data

Cross-sectional dataCross-sectional data are collected at the same or are collected at the same or approximately the same point in time over a range ofapproximately the same point in time over a range of different subjects.different subjects.

Cross-sectional dataCross-sectional data are collected at the same or are collected at the same or approximately the same point in time over a range ofapproximately the same point in time over a range of different subjects.different subjects.

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in a given year in each of the countiespermits issued in a given year in each of the counties of Minnesotaof Minnesota

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in a given year in each of the countiespermits issued in a given year in each of the counties of Minnesotaof Minnesota

2. Time Series Data2. Time Series Data

Time series dataTime series data are collected over several time are collected over several time periods.periods. Time series dataTime series data are collected over several time are collected over several time periods.periods.

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in a given country of Minnesota permits issued in a given country of Minnesota during each of the last 5 yearsduring each of the last 5 years

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in a given country of Minnesota permits issued in a given country of Minnesota during each of the last 5 yearsduring each of the last 5 years

3. Panel (Longitudinal) Data3. Panel (Longitudinal) Data

Panel (longitudinal) dataPanel (longitudinal) data are data collected over the are data collected over the same set of several Subjects for several time periods.same set of several Subjects for several time periods. Panel (longitudinal) dataPanel (longitudinal) data are data collected over the are data collected over the same set of several Subjects for several time periods.same set of several Subjects for several time periods.

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in each county in the state of permits issued in each county in the state of Minnesota over the last 36 yearsMinnesota over the last 36 years

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in each county in the state of permits issued in each county in the state of Minnesota over the last 36 yearsMinnesota over the last 36 years

Existing Sources (Secondary Sources)

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

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

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

Industry associationsIndustry associations – Travel Industry Association – Travel Industry Association of Americaof America

Special-interest organizationsSpecial-interest organizations – Graduate Management – Graduate Management Admission CouncilAdmission Council

InternetInternet – more and more firms – more and more firms

Statistical Studies (Primary Sources)

In In experimental studiesexperimental studies the variables of interest the variables of interestare first identified. Then one or more factors areare first identified. Then one or more factors arecontrolled so that data can be obtained about howcontrolled so that data can be obtained about howthe factors influence the variables.the factors influence the variables.

In In experimental studiesexperimental studies the variables of interest the variables of interestare first identified. Then one or more factors areare first identified. Then one or more factors arecontrolled so that data can be obtained about howcontrolled so that data can be obtained about howthe factors influence the variables.the factors influence the variables.

In In observationalobservational (non-experimental) (non-experimental) studiesstudies no no attempt is made to control or influence theattempt is made to control or influence the variables of interest.variables of interest.

In In observationalobservational (non-experimental) (non-experimental) studiesstudies no no 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 agood good

exampleexample

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 it

is available.is available.

• Organizations often charge for information evenOrganizations often charge for information even when 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 or that were acquired with little care can lead to poorthat were acquired with little care can lead to poor and misleading information.and misleading information.

Data are acquired! What Next?

Extracting the Information Contained in the Data.

How Can we extract the information content of a data?

Three different methods:

1.Tabular Methods, 2.Graphical Methods,3.Numerical Methods

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 understanding of the COST the COST

of PARTS used in the engineof PARTS used in the engine

tune-upstune-ups performed at the performed at the

shop. shop.

She randomly selects 50 customer invoices for She randomly selects 50 customer invoices for which tune-ups were performed. which tune-ups were performed.

Data in the following table refers to the costs of Data in the following table refers to the costs of parts, rounded to the nearest dollar.parts, rounded to the nearest dollar.

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

Example: Hudson Auto RepairExample: Hudson Auto Repair

Sample of Parts Cost for 50 Tune-upsSample of Parts Cost for 50 Tune-ups

The data presented here contains the The data presented here contains the information the manger needs, but is not in a information the manger needs, but is not in a usable format. The usable format. The information content of information content of the data needs to be extractedthe data needs to be extracted. How? . How?

50-5950-59

60-6960-69

70-7970-79

80-8980-89

90-9990-99

100-109100-109

22

1313

1616

77

77

55

5050

44

2626

3232

1414

1414

1010

100100

(2/50)X100(2/50)X100

PartsParts Cost ($)Cost ($)

PartsParts FrequencyFrequency

PercentPercentFrequencyFrequency

22

44

66

88

1010

1212

1414

1616

1818

PartsCost ($) PartsCost ($)

Fre

qu

en

cy

Fre

qu

en

cy

5059 6069 7079 8089 9099 100-1105059 6069 7079 8089 9099 100-110

Tune-up Parts CostTune-up Parts Cost

Hudson’s average cost of parts, based on the 50Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing thetune-ups studied, is $79 (found by summing the 50 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 statistic is the is the averageaverage (or (or meanmean).).

Statistical InferenceStatistical Inference

- - the process of using data obtained the process of using data obtained from a sample to make estimates and from a sample to make estimates and test hypotheses about the test hypotheses about the characteristics of a populationcharacteristics of a population

What do we do with InformationWhat do we do with InformationExtracted from data?Extracted from data?

1.Population1.Population (All tune-ups). Average(All tune-ups). Average

cost of parts iscost of parts isunknownunknown.

22. Sample. Sample (of 50 (of 50engine tune-ups engine tune-ups

is examined.)is examined.)

33. The sample data . The sample data Provides an average Provides an average

parts costparts costof $79 per tune-up.of $79 per tune-up.

44. The sample average. The sample averageis used to make inference is used to make inference

about the population average.about the population average.

Statistical analysis often involves working withStatistical analysis often involves working with large amounts of datalarge amounts of data..

Computer softwareComputer software is typically used to conduct the is typically used to conduct the analysis.analysis.

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

Instructions for using Excel in chapter appendices.Instructions for using Excel in chapter appendices.