descriptive statistics: tabular and graphical presentations n summarizing qualitative data n...
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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
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