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Pertemuan 02Analisis Data

Matakuliah : I0272 – Statistik Probabilitas

Tahun : 2005

Versi : Revisi

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Learning Outcomes

Pada akhir pertemuan ini, diharapkan mahasiswa

akan mampu :

• Mahasiswa akan dapat menjelaskan cara menentukan data pencilan dengan diagram kotak - garis

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Outline Materi

• Kuantil suatu sebaran

• Kuantil sebaran empiris

• Statistik urutan dan kuartil

• Diagram kotak-garis

• Ukuran pemusatan dan variabilitas

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Descriptive Statistics:Tabular and Graphical Methods

• Summarizing Qualitative Data• Summarizing Quantitative Data• Exploratory Data Analysis• Crosstabulations

and Scatter Diagrams

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Summarizing Qualitative Data

• Frequency Distribution

• Relative Frequency

• Percent Frequency Distribution

• Bar Graph

• Pie Chart

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• Frequency Distribution

Rating Frequency

Poor 2

Below Average 3

Average 5

Above Average 9

Excellent 1

Total 20

Contoh Soal: Marada Inn

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Contoh Soal: Marada Inn

• Relative Frequency and Percent Frequency Distributions

Relative Percent

Rating Frequency Frequency

Poor .10 10

Below Average .15 15

Average .25 25

Above Average .45 45

Excellent .05 5

Total 1.00 100

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Contoh Soal: Marada Inn

• Bar Graph

1122

33

44

55

66

77

88

99

PoorPoor BelowAverageBelow

AverageAverageAverage Above

AverageAbove

AverageExcellentExcellent

Fre

qu

en

cy

Fre

qu

en

cy

RatingRating

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Summarizing Quantitative Data

• Frequency Distribution

• Relative Frequency and Percent Frequency Distributions

• Dot Plot

• Histogram

• Cumulative Distributions

• Ogive

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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

Contoh Soal: Hudson Auto Repair

The manager of Hudson Auto would like to get a

better picture of the distribution of costs for engine

tune-up parts. A sample of 50 customer invoices has

been taken and the costs of parts, rounded to the

nearest dollar, are listed below.

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Contoh Soal: Hudson Auto Repair

• Ogive with Cumulative Percent Frequencies

PartsPartsCost ($)Cost ($) PartsPartsCost ($)Cost ($)

2020

4040

6060

8080

100100

Cu

mu

lati

ve P

erc

en

t Fr

eq

uen

cyC

um

ula

tive P

erc

en

t Fr

eq

uen

cyC

um

ula

tive P

erc

en

t Fr

eq

uen

cyC

um

ula

tive P

erc

en

t Fr

eq

uen

cy

50 60 70 80 90 100 11050 60 70 80 90 100 11050 60 70 80 90 100 11050 60 70 80 90 100 110

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Contoh Soal: Hudson Auto Repair

• Stem-and-Leaf Display

5 2 7

6 2 2 2 2 5 6 7 8 8 8 9 9 9

7 1 1 2 2 3 4 4 5 5 5 6 7 8 9 9

8 0 0 2 3 5 8 9

9 1 3 7 7 7 8 9

10 1 4 5 5 9

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Contoh Soal: Hudson Auto Repair

• Stretched Stem-and-Leaf Display 5 2 5 7 6 2 2 2 2 6 5 6 7 8 8 8 9 9 9 7 1 1 2 2 3 4 4 7 5 5 5 6 7 8 9 9 9 8 0 0 2 3 8 5 8 9 9 1 3 9 7 7 7 8 9

10 1 4 10 5 5 9

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Scatter Diagram

• A Positive Relationship

xx

yy

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Scatter Diagram

• A Negative Relationship

xx

yy

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Tabular and Graphical Procedures

DataData

Qualitative DataQualitative DataQualitative DataQualitative Data Quantitative DataQuantitative Data

TabularTabularMethodsMethods

TabularTabularMethodsMethods

GraphicalGraphical MethodsMethods

GraphicalGraphical MethodsMethods

•FrequencyFrequency DistributionDistribution•Rel. Freq. Dist.Rel. Freq. Dist.•% Freq. Dist.% Freq. Dist.•CrosstabulationCrosstabulation

•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 •Stem-and-LeafStem-and-Leaf DisplayDisplay•CrosstabulationCrosstabulation

•Dot PlotDot Plot•HistogramHistogram•OgiveOgive•ScatterScatter DiagramDiagram

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Measures of Location

• Mean

• Median

• Mode

• Percentiles

• Quartiles

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Mean

• The mean of a data set is the average of all the data values.

• If the data are from a sample, the mean is denoted by

.

• If the data are from a population, the mean is denoted by (mu).

xxnixxni

xNi x

Ni

xx

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Quartiles

• Quartiles are specific percentiles

• First Quartile = 25th Percentile

• Second Quartile = 50th Percentile = Median

• Third Quartile = 75th Percentile

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Measures of Variability

• Range

• Interquartile Range

• Variance

• Standard Deviation

• Coefficient of Variation

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Variance

• The variance is the average of the squared differences between each data value and the mean.

• If the data set is a sample, the variance is denoted by s2.

• If the data set is a population, the variance is denoted by 2.

sxi x

n2

2

1

( )s

xi x

n2

2

1

( )

22

( )xNi 2

2

( )xNi

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Coefficient of Variation

• The coefficient of variation indicates how large the standard deviation is in relation to the mean.

• If the data set is a sample, the coefficient of variation is computed as follows:

• If the data set is a population, the coefficient of variation is computed as follows:

sx

( )100sx

( )100

( )100

( )100

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• Selamat Belajar Semoga Sukses.