1 1 Slide © 2006 Thomson/South-Western Chapter 1 Data and Statistics I need help! Applications in...

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© 2006 Thomson/South-Western© 2006 Thomson/South-Western

Chapter 1Chapter 1 Data and Statistics Data and Statistics

I need I need help!help!Applications in Business and Economics

Data

Data Sources

Descriptive Statistics

Statistical Inference

Computers and Statistical Analysis

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Data and Data SetsData and Data Sets

DataData are the facts and figures collected, are the facts and figures collected, summarized, analyzed, and interpreted.summarized, analyzed, and interpreted.

The data collected in a particular study The data collected in a particular study areare referred to as the referred 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 the elements. is a characteristic of 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..

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 73.10 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

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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

OrdinalOrdinalIntervalInterval

RatioRatio

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Nominal = name categories, count Nominal = name categories, count frequenciesfrequencies

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may may be used.be used. A A nonnumeric labelnonnumeric label or or numeric codenumeric code may may be used.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 schoolschool in which they are enrolled using a 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.

Example:Example: Students of a university are classified by theStudents of a university are classified by the schoolschool in which they are enrolled using a 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.


NominalNominal

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Ordinal = rank categories in order, but Ordinal = rank categories in order, but no meaningful distanceno meaningful distance

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

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

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OrdinalOrdinal

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

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

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Interval = equal distance between Interval = equal distance between scores; numericalscores; numerical

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,The data have the properties of ordinal data, and the interval between observations is and the interval between observations is a fixed unit of measure.a fixed unit of measure.

The data have the properties of ordinal data,The data have the properties of ordinal data, and the interval between observations is and the interval between observations is a fixed unit of measure.a fixed unit of measure.

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IntervalInterval

Example:Example: Melissa has an Melissa has an SAT scoreSAT score of 1205, while Kevin 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 Melissa has an SAT scoreSAT score of 1205, while Kevin 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.

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Ratio = equal distance, meaningful zeroRatio = equal distance, meaningful zero

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

Distance, height, weight, and timeDistance, height, weight, and time use the ratio scale.use the ratio scale.

Distance, height, weight, and timeDistance, 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 for for which nothing exists for the variablewhich nothing exists for the variable This This scale must contain a zero valuescale must contain a zero value for for which nothing exists for the variablewhich nothing exists for the variable

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RatioRatio

Example:Example: Melissa’s college record shows 36 Melissa’s college record shows 36 credit hourscredit 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 Melissa’s college record shows 36 credit hourscredit 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.

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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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QualitativeQualitativeQualitativeQualitative QuantitativQuantitativee

QuantitativQuantitativee

NumericalNumericalNumericalNumerical NumericalNumericalNumericalNumericalNonnumericalNonnumericalNonnumericalNonnumerical

DataDataDataData

NominaNominallNominaNominall

OrdinaOrdinallOrdinaOrdinall

NominalNominalNominalNominal OrdinalOrdinalOrdinalOrdinal IntervalIntervalIntervalInterval RatioRatioRatioRatio

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Descriptive StatisticsDescriptive Statistics

Descriptive statisticsDescriptive statistics are the tabular, are the tabular, graphical, and numerical methods used graphical, and numerical methods used to 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

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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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

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

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

PartsParts Cost ($)Cost ($)

PartsParts FrequencyFrequency

PercentPercentFrequencyFrequency

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Graphical Summary: HistogramGraphical Summary: Histogram

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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

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Inferential StatisticsInferential Statistics

Uses samples from larger populationsUses samples from larger populations Draw conclusions from sample dataDraw conclusions from sample data Conclusions apply to whole populationConclusions apply to whole population Estimate a population valueEstimate a population value Test a hypothesisTest a hypothesis State probability of errorState probability of error

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