1 1 Slide Tuesday August 28 Class 2 Text problems for August 30: Chapter 2 - 2,6 & 10 Aplia Graded...

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Tuesday August 28Tuesday August 28Class 2Class 2

Text problems for August 30: Chapter 2 - 2,6 Text problems for August 30: Chapter 2 - 2,6 & 10& 10

Aplia Graded Assignment: Aplia Graded Assignment: ““IntroductionIntroduction”” due due September 4, 9:00 amSeptember 4, 9:00 am

Practice Problems for Chapter 1 & 2 are now Practice Problems for Chapter 1 & 2 are now availableavailable

Please note that a tutorial for basic math Please note that a tutorial for basic math concepts is available if neededconcepts is available if needed

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Introduction Statistics: the languageIntroduction Statistics: the language

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Data and Data SetsData and Data Sets

DataData are the facts and or numbers collected, are the facts and or numbers collected, summarized, analyzed, and interpreted.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..

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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 how the data can be summarized The scale indicates how the data can be summarized and statistical analyses that are most appropriate.and statistical analyses that are most appropriate. The scale indicates how the data can be summarized The scale indicates how the data can be summarized and statistical analyses that are most appropriate.and 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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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).


NominalNominal

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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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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, Sophomore, Junior, or Senior.Freshman, Sophomore, 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 Sophomore, and so on).Freshman, 2 denotes Sophomore, 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, Sophomore, Junior, or Senior.Freshman, Sophomore, 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 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.. 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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IntervalInterval

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.

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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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RatioRatio

Example:Example: MelissaMelissa’’s college record shows 36 credit hourss college record shows 36 credit hours earned, while Kevinearned, while Kevin’’s record shows 72 credit 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: MelissaMelissa’’s college record shows 36 credit hourss college record shows 36 credit hours earned, while Kevinearned, while Kevin’’s record shows 72 credit 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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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

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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 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 countiespermits issued in June 2007 in each of the counties of Ohioof Ohio

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in June 2007 in each of the countiespermits issued in June 2007 in each of the counties of Ohioof Ohio

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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 Lucas County, Ohio in each ofpermits issued in Lucas County, Ohio 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 Lucas County, Ohio in each ofpermits issued in Lucas County, Ohio in each of the last 36 monthsthe last 36 months

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Statistical StudiesStatistical Studies

Types of Statistical StudiesTypes of Statistical Studies

In In experimental studiesexperimental studies the variable of interest is the variable of interest isfirst identified. Then one or more other variablesfirst identified. Then one or more other variablesare identified and controlled so that data can beare identified and controlled so that data can beobtained about how they influence the variable ofobtained about how they influence the variable ofinterest.interest.

In In experimental studiesexperimental studies the variable of interest is the variable of interest isfirst identified. Then one or more other variablesfirst identified. Then one or more other variablesare identified and controlled so that data can beare identified and controlled so that data can beobtained about how they influence the variable ofobtained about how they influence the variable ofinterest.interest.

In In observationalobservational (nonexperimental) (nonexperimental) 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 (nonexperimental) (nonexperimental) 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 a surveysurvey is a good is a good

exampleexamplea a surveysurvey is a good is a good

exampleexample

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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 Auto would like to The manager of Hudson Auto would like to have ahave a

better understanding of the cost of parts used in better understanding of the cost of parts used in thethe

engine tune-ups performed in the shop. She engine tune-ups performed in the shop. She examinesexamines

50 customer invoices for tune-ups. The costs of 50 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 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

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

PartsParts Cost ($)Cost ($)

PartsParts FrequencyFrequency

PercentPercentFrequencyFrequency

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Graphical Summary: HistogramGraphical Summary: Histogram

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 StatisticsNumerical Descriptive Statistics

HudsonHudson’’s average cost of parts, based on the 50s 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 collection of all the elements ofthe collection of all the elements of interestinterest

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 InferenceProcess of Statistical Inference

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 AnalysisComputers and Statistical Analysis

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.

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Tainted TruthTainted Truth

““ If someone is misusing numbers and scaring us If someone is misusing numbers and scaring us with those numbers to get us to do something, with those numbers to get us to do something, however good that something is, we have lost the however good that something is, we have lost the power of numberspower of numbers””

WE ALL NEED TO BE CRITICAL.WE ALL NEED TO BE CRITICAL.

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Reported InformationReported Information Eating oat brand is a cheap and easy way to Eating oat brand is a cheap and easy way to

reduce your cholesterol count (Quaker Oats)reduce your cholesterol count (Quaker Oats)

Actual Study InformationActual Study Information Diet must consist of nothing but oat bran to Diet must consist of nothing but oat bran to

achieve a slightly lower cholesterol count.achieve a slightly lower cholesterol count.

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Reported InformationReported Information Only 29% of high school girls are happy with Only 29% of high school girls are happy with

themselves, compared to 66% of elementary themselves, compared to 66% of elementary school girls. (American Association of school girls. (American Association of University Women)University Women)

Actual Study InformationActual Study Information Of 3000 high school girls 29% responded Of 3000 high school girls 29% responded

““Always trueAlways true”” to the statement, to the statement, ““I am happy I am happy with the way I am.with the way I am.”” Most answered, Most answered, ““Sort of Sort of truetrue”” and and ““Sometimes true.Sometimes true.””

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?????? Credible ?????? Credible

Four out of five people in Columbia prefer Four out of five people in Columbia prefer Wendys over McDonalds (according to a recent Wendys over McDonalds (according to a recent survey)survey)

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Ethical Guidelines for Statistical Ethical Guidelines for Statistical Practice Practice

American Statistical AssociationAmerican Statistical Association

www.amstat.org

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Association vs CausationAssociation vs Causation

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Chapter 2Chapter 2Descriptive Statistics:Descriptive Statistics:

Tabular and Graphical PresentationsTabular and Graphical Presentations

Summarizing Qualitative DataSummarizing Qualitative Data Summarizing Quantitative DataSummarizing Quantitative Data

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Summarizing Qualitative DataSummarizing Qualitative Data

Frequency DistributionFrequency Distribution Relative Frequency Distribution Relative Frequency Distribution Percent Frequency DistributionPercent Frequency Distribution Bar GraphsBar Graphs Pie ChartsPie Charts

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A A frequency distributionfrequency distribution is a tabular summary of is a tabular summary of data showing the frequency (or number) of itemsdata showing the frequency (or number) of items in each of several non-overlapping classes.in each of several non-overlapping classes.

A A frequency distributionfrequency distribution is a tabular summary of is a tabular summary of data showing the frequency (or number) of itemsdata showing the frequency (or number) of items in each of several non-overlapping classes.in each of several non-overlapping classes.

The objective is to The objective is to provide insightsprovide insights about the data about the data that cannot be quickly obtained by looking only atthat cannot be quickly obtained by looking only at the original data.the original data.

The objective is to The objective is to provide insightsprovide insights about the data about the data that cannot be quickly obtained by looking only atthat cannot be quickly obtained by looking only at the original data.the original data.

Frequency DistributionFrequency Distribution

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Example: Marada InnExample: Marada Inn

Guests staying at Marada Inn were asked to rate theGuests staying at Marada Inn were asked to rate the

quality of their accommodations as being quality of their accommodations as being excellentexcellent, , aboveabove

averageaverage, , averageaverage, , below averagebelow average, or , or poorpoor. The ratings. The ratings

provided by a sample of 20 guests are:provided by a sample of 20 guests are:

Below AverageBelow Average

Above AverageAbove Average


AverageAverage

Above Average Above Average

AverageAverage


Average Average



PoorPoor

Excellent Excellent


AverageAverage




PoorPoor

Above Average Above Average

AverageAverage

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Frequency DistributionFrequency Distribution

PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent

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TotalTotal 20 20

RatingRating FrequencyFrequency

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The The relative frequencyrelative frequency of a class is the fraction or of a class is the fraction or proportion of the total number of data itemsproportion of the total number of data items belonging to the class.belonging to the class.

The The relative frequencyrelative frequency of a class is the fraction or of a class is the fraction or proportion of the total number of data itemsproportion of the total number of data items belonging to the class.belonging to the class.

A A relative frequency distributionrelative frequency distribution is a tabular is a tabular summary of a set of data showing the relativesummary of a set of data showing the relative frequency for each class.frequency for each class.

A A relative frequency distributionrelative frequency distribution is a tabular is a tabular summary of a set of data showing the relativesummary of a set of data showing the relative frequency for each class.frequency for each class.

Relative Frequency DistributionRelative Frequency Distribution

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Percent Frequency DistributionPercent Frequency Distribution

The The percent frequencypercent frequency of a class is the relative of a class is the relative frequency multiplied by 100.frequency multiplied by 100. The The percent frequencypercent frequency of a class is the relative of a class is the relative frequency multiplied by 100.frequency multiplied by 100.

AA percent frequency distributionpercent frequency distribution is a tabular is a tabular summary of a set of data showing the percentsummary of a set of data showing the percent frequency for each class.frequency for each class.

AA percent frequency distributionpercent frequency distribution is a tabular is a tabular summary of a set of data showing the percentsummary of a set of data showing the percent frequency for each class.frequency for each class.

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Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions

PoorPoor


AverageAverage


ExcellentExcellent

.10.10

.15.15

.25.25

.45.45

.05.05

TotalTotal 1.00 1.00

1010

1515

2525

4545

55

100100

RelativeRelativeFrequencyFrequency

PercentPercentFrequencyFrequencyRatingRating

.10(100) = .10(100) = 1010

.10(100) = .10(100) = 1010

1/20 1/20 = .05= .051/20 1/20 = .05= .05

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Bar GraphBar Graph

A A bar graphbar graph is a graphical device for depicting is a graphical device for depicting qualitative data.qualitative data.

On one axis (usually the horizontal axis), we specifyOn one axis (usually the horizontal axis), we specify the labels that are used for each of the classes.the labels that are used for each of the classes. A A frequencyfrequency, , relative frequencyrelative frequency, or , or percent frequencypercent frequency scale can be used for the other axis (usually thescale can be used for the other axis (usually the vertical axis).vertical axis).

Using a Using a bar of fixed widthbar of fixed width drawn above each class drawn above each class label, we extend the height appropriately.label, we extend the height appropriately.

The The bars are separatedbars are separated to emphasize the fact that each to emphasize the fact that each class is a separate category.class is a separate category.

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PoorPoor BelowAverageBelow

AverageAverageAverage Above

Average Above

AverageExcellentExcellent

Fre

qu

en

cy

Fre

qu

en

cy

RatingRating

Bar GraphBar Graph

1122

33

44

55

66

77

88

991010

Marada Inn Quality RatingsMarada Inn Quality RatingsMarada Inn Quality RatingsMarada Inn Quality Ratings

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Pie ChartPie Chart

The The pie chartpie chart is another commonly used graphical device is another commonly used graphical device for presenting relative frequency distributions forfor presenting relative frequency distributions for qualitative data.qualitative data.

First draw a First draw a circlecircle; then use the relative frequencies; then use the relative frequencies to subdivide the circle into sectors that correspondto subdivide the circle into sectors that correspond to the relative frequency for each class.to the relative frequency for each class.

Since there are 360 degrees in a circle, a class with aSince there are 360 degrees in a circle, a class with a

relative frequency of .25 would consume .25(360) = 90relative frequency of .25 would consume .25(360) = 90

degrees of the circle.degrees of the circle.

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BelowAverage 15%

BelowAverage 15%

Average 25%Average 25%

AboveAverage 45%

AboveAverage 45%

Poor10%Poor10%

Excellent 5%Excellent 5%

Marada InnMarada Inn Quality Quality RatingsRatings


Pie ChartPie Chart

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Insights Gained from the Preceding Pie ChartInsights Gained from the Preceding Pie Chart

Example: Marada InnExample: Marada Inn

• One-half of the customers surveyed gave MaradaOne-half of the customers surveyed gave Marada a quality rating of a quality rating of ““above averageabove average”” or or ““excellentexcellent”” (looking at the left side of the pie). This might(looking at the left side of the pie). This might please the manager.please the manager.

• For For eacheach customer who gave an customer who gave an ““excellentexcellent”” rating, rating, there were there were twotwo customers who gave a customers who gave a ““poorpoor”” rating (looking at the top of the pie). This shouldrating (looking at the top of the pie). This should displease the manager.displease the manager.

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BelowAverage 15%

BelowAverage 15%

Average 25%Average 25%

AboveAverage 45%

AboveAverage 45%

Poor10%Poor10%

Excellent 5%Excellent 5%



Pie ChartPie Chart

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See Example 1 Class 2 data fileSee Example 1 Class 2 data file

Text problems for August 30: Chapter 2 – 2 , 6 Text problems for August 30: Chapter 2 – 2 , 6 & 10& 10

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