Basic Concepts of Statistics

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Basic Concepts Basic Concepts of of

Statistical Statistical StudiesStudies

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IntroductionIntroduction Decision makers make better decisions Decision makers make better decisions

when they use all available information in when they use all available information in an effective and meaningful way. The an effective and meaningful way. The primary role of statistics is to to provide primary role of statistics is to to provide decision makers with methods for decision makers with methods for obtaining and analyzing information to obtaining and analyzing information to help make these decisions. Statistics is help make these decisions. Statistics is used to answer long-range planning used to answer long-range planning questions, such as when and where to questions, such as when and where to locate facilities to handle future sales.locate facilities to handle future sales.

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DefinitionDefinition

Statistics is defined as the Statistics is defined as the science of collecting, science of collecting, organizing, presenting, organizing, presenting, analyzing and interpreting analyzing and interpreting numerical data for the numerical data for the purpose of assisting in purpose of assisting in making a more effective making a more effective decision. decision.

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Applications in ManagementApplications in Management 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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Applications in ManagementApplications in Management

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

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Types of StatisticsTypes of Statistics There are two types of statisticsThere are two types of statistics

1. 1. Descriptive StatisticsDescriptive Statistics is concerned with is concerned with summary calculations, graphs, charts and summary calculations, graphs, charts and tables.tables.

2. 2. Inferential StatisticsInferential Statistics is a method used is a method used to generalize from a sample to a population. to generalize from a sample to a population. For example, the average income of all For example, the average income of all families (the population) in India can be families (the population) in India can be estimated from figures obtained from a few estimated from figures obtained from a few hundred (the sample) families. hundred (the sample) families.

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Statistical PopulationStatistical Population

A A PopulationPopulation is a collection of all is a collection of all distinct individuals or objects or distinct individuals or objects or items under study. The number of items under study. The number of entities in a population, Called the entities in a population, Called the Population Size, is denoted by Population Size, is denoted by NN

A descriptive measure of a A descriptive measure of a population is called a population is called a ParameterParameter

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SampleSample

A A SampleSample is a part of a is a part of a population and the sample population and the sample size is denoted by n. A size is denoted by n. A sample should be a sample should be a representative of the representative of the population.population.

A descriptive measure of a A descriptive measure of a population is called a population is called a StatisticStatistic

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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 referred to as the to as the data setdata set..

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The The elementselements are the entities on which data are are the entities on which data are collected.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 particular element is called an element is called an observationobservation..

The total number of data values in a complete dataThe total number of data values in a complete data set is the number of elements multiplied by theset is the number of elements multiplied by the number of variables.number of 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

NQNQ 73.10 73.10 0.86 0.86

NN 74.00 74.00 1.67 1.67

NN 365.70365.70 0.86 0.86

NQNQ 111.40111.40 0.33 0.33

NN 17.60 17.60 0.13 0.13

VariableVariablessElemenElemen

tt NamesNames

Data SetData Set

ObservatioObservationn

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Scales of MeasurementScales of Measurement

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

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

Scales of measurement include:Scales of measurement include: Scales of measurement include:Scales of measurement include:

NominalNominal

OrdinalOrdinal

IntervalInterval

RatioRatio

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Scales of MeasurementScales of Measurement NominalNominal

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

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Example:Example: Students of a university are classified by theStudents of a university are classified by the school in which they are enrolled using aschool in which they are enrolled using a nonnumeric 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 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: Students of a university are classified by theStudents of a university are classified by the school in which they are enrolled using aschool in which they are enrolled using a nonnumeric 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 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).

Scales of MeasurementScales of Measurement

NominalNominal

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Scales of MeasurementScales of Measurement OrdinalOrdinal

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.

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

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Scales of MeasurementScales of Measurement OrdinalOrdinal

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

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 Juniors and so on).Freshman, 2 denotes Juniors and so on).

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

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 Juniors and so on).Freshman, 2 denotes Juniors and so on).

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Scales of MeasurementScales of Measurement IntervalInterval

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.

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Scales of MeasurementScales of Measurement IntervalInterval

Example:Example: Shruti has an MAT score of 605, while RajShruti has an MAT score of 605, while Raj has an MAT score of 655. Raj scored 50has an MAT score of 655. Raj scored 50 points more than Shruti.points more than Shruti.

Example:Example: Shruti has an MAT score of 605, while RajShruti has an MAT score of 605, while Raj has an MAT score of 655. Raj scored 50has an MAT score of 655. Raj scored 50 points more than Shruti.points more than Shruti.

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Scales of MeasurementScales of Measurement RatioRatio

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.

This This 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. This This 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.

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Scales of MeasurementScales of Measurement RatioRatio

Example:Example: Raj’s college record shows 36 credit hoursRaj’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 hours earned as Raj’sRaj’s..

Example:Example: Raj’s college record shows 36 credit hoursRaj’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 hours earned as Raj’sRaj’s..

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

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

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Qualitative DataQualitative Data

Labels or namesLabels or names used to identify an attribute of each used to identify an attribute of each elementelement Labels or namesLabels or names used to identify an attribute of each 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 scale ofUse either the nominal or ordinal scale of measurementmeasurement Use either the nominal or ordinal scale ofUse either the nominal or ordinal scale of measurementmeasurement

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

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Quantitative DataQuantitative Data

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.

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Scales of MeasurementScales of Measurement

QualitativeQualitativeQualitativeQualitative QuantitativQuantitativee

QuantitativQuantitativee

NumericalNumericalNumericalNumerical NumericalNumericalNumericalNumericalNon-Non-numericalnumerical

Non-Non-numericalnumerical

DataDataDataData

NominaNominallNominaNominall

OrdinaOrdinallOrdinaOrdinall

NominalNominalNominalNominal OrdinalOrdinalOrdinalOrdinal IntervalIntervalIntervalInterval RatioRatioRatioRatio

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Cross-Sectional DataCross-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.approximately the same point in time. Cross-sectional dataCross-sectional data are collected at the same or are collected at the same or approximately the same point in time.approximately the same point in time.

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in June 2007 in each of the Districtspermits issued in June 2007 in each of the Districts of UPof UP

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in June 2007 in each of the Districtspermits issued in June 2007 in each of the Districts of UPof UP

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Time Series DataTime 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 Districts of UP in each ofpermits issued in Districts of UP in each of the last 36 monthsthe last 36 months

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in Districts of UP in each ofpermits issued in Districts of UP in each of the last 36 monthsthe last 36 months

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Data SourcesData Sources Existing SourcesExisting 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 - Department of Labor - Department of Labor

Industry associationsIndustry associations – Travel Industry Association – Travel Industry Association

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

InternetInternet – more and more firms – more and more firms

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Descriptive StatisticsDescriptive Statistics Descriptive statisticsDescriptive statistics are the tabular, are the tabular,

graphical, and numerical methods used to graphical, and numerical methods used to summarize and presentsummarize and present 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

tune-ups performed in thetune-ups performed in the

shop. She examines 50shop. She examines 50

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

rounded to the nearest dollar, are listed on the rounded to the nearest dollar, are listed on the nextnext

slide.slide.

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Example: Hudson Auto RepairExample: Hudson Auto Repair

Sample of Parts Cost ($) for 50 Tune-Sample of Parts Cost ($) for 50 Tune-upsups

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

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

FrequencyFrequency

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)10(2/50)1000

(2/50)10(2/50)1000

PartsParts Cost ($)Cost ($)

PartsParts FrequencyFrequency

PercentPercentFrequencyFrequency

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Graphical Summary: Graphical Summary: HistogramHistogram

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 CostTune-up Parts CostTune-up Parts Cost

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Numerical Descriptive Numerical Descriptive StatisticsStatistics

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).).

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Statistical InferenceStatistical Inference

PopulationPopulationPopulationPopulation

SampleSampleSampleSample

Statistical inferenceStatistical inferenceStatistical inferenceStatistical inference

CensusCensusCensusCensus

Sample surveySample surveySample surveySample survey

the set of all elements of interest in athe set of all elements of interest in a particular studyparticular study

a subset of the populationa subset of the population

the process of using data obtainedthe process of using data obtained from a sample to make estimatesfrom a sample to make estimates and test hypotheses about theand test hypotheses about the characteristics 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 Process of Statistical InferenceInference

11. Population . Population consists of all tune-consists of all tune-

ups. Average cost ofups. Average cost ofparts is unknownparts is unknown.

11. Population . Population consists of all tune-consists of all tune-

ups. Average cost ofups. Average cost ofparts is unknownparts is unknown.

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

is examined.is examined.

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

is examined.is examined.

3.3. The sample dataThe sample dataprovide a sampleprovide a sample

average parts costaverage parts costof $79 per tune-up.of $79 per tune-up.

3.3. The sample dataThe sample dataprovide a sampleprovide a sample

average parts costaverage parts costof $79 per tune-up.of $79 per tune-up.

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

population average.population average.

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

population average.population average.

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Computers and Statistical Computers and Statistical AnalysisAnalysis

Statistical analysis typically involves working withStatistical analysis typically 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. Instructions are provided in chapter appendices forInstructions are provided in chapter appendices for carrying out many of the statistical procedurescarrying out many of the statistical procedures using Minitab and Excel.using Minitab and Excel.