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Descriptive Statistics: Descriptive Statistics: Tabular and Graphical Presentations Tabular and Graphical Presentations Summarizing Qualitative Data Summarizing Qualitative Data Summarizing Quantitative Data Summarizing Quantitative Data

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Descriptive Statistics:Descriptive Statistics:Tabular and Graphical PresentationsTabular and Graphical Presentations

Summarizing Qualitative DataSummarizing Qualitative Data Summarizing Quantitative DataSummarizing Quantitative Data

Summarizing Qualitative DataSummarizing Qualitative Data

Frequency DistributionFrequency Distribution Relative Frequency DistributionRelative Frequency Distribution Cumulative FrequencyCumulative Frequency Cumulative Relative Frequency Cumulative Relative Frequency Bar GraphBar Graph Pie ChartPie Chart

Example: Marada InnExample: Marada Inn

Guests staying at Marada Inn wereGuests staying at Marada Inn wereasked to rate the quality of their asked to rate the quality of their accommodations as being accommodations as being excellentexcellent,,above averageabove average, , averageaverage, , below averagebelow average, or, orpoorpoor. The ratings provided by a sample of 20 . The ratings provided by a sample of 20

guests are:guests are:

Below AverageBelow Average

Above AverageAbove Average

Above AverageAbove Average

AverageAverage

Above Average Above Average

AverageAverage

Above AverageAbove Average

Average Average

Above AverageAbove Average

Below AverageBelow Average

PoorPoor

Excellent Excellent

Above AverageAbove Average

AverageAverage

Above AverageAbove Average

Above AverageAbove Average

Below AverageBelow Average

PoorPoor

Above Average Above Average

AverageAverage

Frequency DistributionFrequency Distribution

PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent

22 33 55 99 11

TotalTotal 20 20

RatingRating FrequencyFrequencyCumulativeCumulative

FrequencyFrequency 22 55 1010 1919 2020

2+3+5 2+3+5

=10=10

Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions

PoorPoor

Below AverageBelow Average

AverageAverage

Above AverageAbove Average

ExcellentExcellent

.10.10

.15.15

.25.25

.45.45

.05.05

TotalTotal 1.00 1.00

.10.10

.25.25

.50.50

.95.95

1.01.0

RelativeRelativeFrequencyFrequency

CumulativeCumulativeRelativeRelativeFrequencyFrequencyRatingRating

.10+.15 .10+.15 =.25=.25

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

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 Ratings

BelowAverage 15%

BelowAverage 15%

Average 25%Average 25%

AboveAverage 45%

AboveAverage 45%

Poor10%Poor10%

Excellent 5%Excellent 5%

Marada InnMarada Inn Quality Quality RatingsRatings

Marada InnMarada Inn Quality Quality RatingsRatings

Pie ChartPie Chart

Summarizing Quantitative DataSummarizing Quantitative Data

Frequency DistributionFrequency Distribution Relative Frequency DistributionsRelative Frequency Distributions HistogramHistogram Cumulative DistributionsCumulative Distributions

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.

Example: Hudson Auto RepairExample: Hudson Auto Repair

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

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

Frequency DistributionFrequency Distribution

Guidelines for Selecting Number of ClassesGuidelines for Selecting Number of Classes

• Use between 5 and 20 classes.Use between 5 and 20 classes.

• Data sets with a larger number of elementsData sets with a larger number of elements usually require a larger number of classes.usually require a larger number of classes.

• Smaller data sets usually require fewer classesSmaller data sets usually require fewer classes

Frequency DistributionFrequency Distribution

Guidelines for Selecting Width of ClassesGuidelines for Selecting Width of Classes

Largest Data Value Smallest Data ValueNumber of Classes

Largest Data Value Smallest Data ValueNumber of Classes

•Use classes of equal width.Use classes of equal width.

•Approximate Class Width =Approximate Class Width =

Frequency DistributionFrequency Distribution

For Hudson Auto Repair, if we choose six classes: For Hudson Auto Repair, if we choose six classes:

50-5950-59

60-69 60-69 70-7970-79 80-8980-89 90-9990-99

100-109100-109

22 1313 1616 77 77 55

Total 50Total 50

Parts Cost ($)Parts Cost ($) FrequencyFrequency

Approximate Class Width = (109 - 52)/6 = 9.5 Approximate Class Width = (109 - 52)/6 = 9.5 1010

Relative Frequency DistributionRelative Frequency Distribution

50-5950-59

60-69 60-69

70-7970-79

80-8980-89

90-9990-99

100-109100-109

PartsPartsCost ($)Cost ($)

.04.04

.26.26

.32.32

.14.14

.14.14

.10.10

Total 1.00 Total 1.00

RelativeRelativeFrequencyFrequency

2/502/50

Cumulative DistributionsCumulative Distributions

Hudson Auto RepairHudson Auto Repair

5050 - 59- 59

60 - 69 60 - 69

70 - 7970 - 79

80 - 8980 - 89

90 - 9990 - 99

100 - 109100 - 109

Cost ($)Cost ($) CumulativeCumulativeFrequencyFrequency

CumulativeCumulativeRelativeRelative

FrequencyFrequency

CumulativeCumulativePercentPercent

FrequencyFrequency 22

1515

3131

3838

4545

50 50

.04.04

.30.30

.62.62

.76.76

.90.90

1.00 1.00

44

3030

6262

7676

9090

100 100

2 + 2 + 1313

15/5015/50 .30(10.30(100)0)

FrequencyFrequency 22

1313

1616

77

77

5 5

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 Cost

SymmetricSymmetric

• Left tail is the mirror image of the right tailLeft tail is the mirror image of the right tail

• Examples: heights and weights of peopleExamples: heights and weights of people

HistogramHistogram

Rela

tive F

req

uen

cyR

ela

tive F

req

uen

cy

.05.05

.10.10

.15.15

.20.20

.25.25

.30.30

.35.35

00

HistogramHistogram

Moderately Skewed LeftModerately Skewed Left

• A longer tail to the leftA longer tail to the left

• Example: exam scoresExample: exam scoresR

ela

tive F

req

uen

cyR

ela

tive F

req

uen

cy

.05.05

.10.10

.15.15

.20.20

.25.25

.30.30

.35.35

00

Moderately Right SkewedModerately Right Skewed

• A Longer tail to the rightA Longer tail to the right

• Example: housing valuesExample: housing values

HistogramHistogram

Rela

tive F

req

uen

cyR

ela

tive F

req

uen

cy

.05.05

.10.10

.15.15

.20.20

.25.25

.30.30

.35.35

00

HistogramHistogram

Highly Skewed RightHighly Skewed Right

• A very long tail to the rightA very long tail to the right

• Example: executive salariesExample: executive salaries

Rela

tive F

req

uen

cyR

ela

tive F

req

uen

cy

.05.05

.10.10

.15.15

.20.20

.25.25

.30.30

.35.35

00

Scatter DiagramScatter Diagram

A Positive RelationshipA Positive Relationship

xx

yy

Scatter DiagramScatter Diagram

A Negative RelationshipA Negative Relationship

xx

yy

Scatter DiagramScatter Diagram

No Apparent RelationshipNo Apparent Relationship

xx

yy

Example: Panthers Football TeamExample: Panthers Football Team

Scatter DiagramScatter Diagram

The Panthers football team is interestedThe Panthers football team is interested

in investigating the relationship, if any,in investigating the relationship, if any,

between interceptions made and points between interceptions made and points scored.scored.

1133221133

14142424181817173030

xx = Number of = Number ofInterceptionsInterceptions

yy = Number of = Number of Points ScoredPoints Scored

Scatter DiagramScatter Diagram

yy

xx

Number of InterceptionsNumber of Interceptions

Num

ber

of

Poin

ts S

core

dN

um

ber

of

Poin

ts S

core

d

551010

1515202025253030

00

3535

11 22 3300 44

Tabular and Graphical ProceduresTabular and Graphical Procedures

Qualitative DataQualitative DataQualitative DataQualitative Data Quantitative DataQuantitative DataQuantitative DataQuantitative Data

TabularTabularMethodsMethods TabularTabularMethodsMethods

TabularTabularMethodsMethods TabularTabularMethodsMethods

GraphicalGraphical MethodsMethodsGraphicalGraphical MethodsMethods

GraphicalGraphical MethodsMethodsGraphicalGraphical MethodsMethods

•FrequencyFrequency DistributionDistribution•Rel. Freq. Dist.Rel. Freq. Dist.•Cumulative Freq. Cumulative Freq. DistributionDistribution•Cumulative Rel. Freq.Cumulative Rel. Freq. DistributionDistribution

•Bar GraphBar Graph•Pie ChartPie Chart •FrequencyFrequency

DistributionDistribution•Rel. Freq. Dist.Rel. Freq. Dist.•Cum. Freq. Dist.Cum. Freq. Dist.•Cum. Rel. Freq.Cum. Rel. Freq. Distribution Distribution

•HistogramHistogram•ScatterScatter DiagramDiagram

DataDataDataData