1 pertemuan 4 statistik deskriptif-2 matakuliah: a0064 / statistik ekonomi tahun: 2005 versi: 1/1

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Pertemuan 4Statistik Deskriptif-2

Matakuliah : A0064 / Statistik EkonomiTahun : 2005 Versi : 1/1

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Learning Outcomes

Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu :• Menunjukkan hubungan antara ukuran

pemusatan (mean, median, dan modus denganukuran kemiringan (skewness) dan keruncingan (kurtosis)

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Outline Materi

• Ukuran Kemiringan (Skewness) dan Kerruncingan (Kurtosis) Data

• Metode-metode Penyajian Data

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Skewness– Measure of asymmetry of a frequency distribution

• Skewed to left• Symmetric or unskewed• Skewed to right

Kurtosis– Measure of flatness or peakedness of a frequency

distribution• Platykurtic (relatively flat)• Mesokurtic (normal)• Leptokurtic (relatively peaked)

1-6 Skewness and Kurtosis

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Skewed to left

Skewness

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Skewness

Symmetric

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Skewness

Skewed to right

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Kurtosis

Platykurtic - flat distribution

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Kurtosis

Mesokurtic - not too flat and not too peaked

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Kurtosis

Leptokurtic - peaked distribution

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Chebyshev’s TheoremApplies to any distribution, regardless of shapePlaces lower limits on the percentages of observations

within a given number of standard deviations from the mean

Empirical RuleApplies only to roughly mound-shaped and

symmetric distributionsSpecifies approximate percentages of observations

within a given number of standard deviations from the mean

1-7 Relations between the Mean and Standard Deviation

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1 12

1 14

34 75%

1 13

1 19

89 89%

1 14

1 116

1516 94%

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2

2

At least of the elements of any distribution lie within k standard deviations of the mean

At least

Lie within

Standarddeviationsof the mean

2

3

4

Chebyshev’s Theorem

2

11k

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For roughly mound-shaped and symmetric distributions, approximately:

68% 1 standard deviation of the mean

95% Lie within

2 standard deviations of the mean

All 3 standard deviations of the mean

Empirical Rule

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Pie ChartsCategories represented as percentages of total

Bar GraphsHeights of rectangles represent group frequencies

Frequency Polygons Height of line represents frequency

OgivesHeight of line represents cumulative frequency

Time PlotsRepresents values over time

1-8 Methods of Displaying Data

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Pie Chart

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Bar Chart

Average Revenues

Average Expenses

Fig. 1-11 Airline Operating Expenses and Revenues

1 2

1 0

8

6

4

2

0

A i r li n e

American Continental Delta Northwest Southwest United USAir

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Relative Frequency Polygon Ogive

Frequency Polygon and Ogive

50403020100

0.3

0.2

0.1

0.0

Rel

ativ

e Fr

eque

ncy

Sales50403020100

1.0

0.5

0.0

Cum

ulat

ive

Rel

ativ

e Fr

eque

ncy

Sales

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OSAJJMAMFJDNOSAJJMAMFJDNOSAJJMAMFJ

8.5

7.5

6.5

5.5

Month

Milli

ons

of T

ons

M o nthly S te e l P ro d uc tio n(P ro b le m 1 -4 6 )

Time Plot

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Stem-and-Leaf Displays Quick-and-dirty listing of all observations Conveys some of the same information as a histogram

Box Plots Median Lower and upper quartiles Maximum and minimum

Techniques to determine relationships and trends, identify outliers and influential observations, and quickly describe or summarize data sets.

1-9 Exploratory Data Analysis - EDA

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1 122355567 2 0111222346777899 3 012457 4 11257 5 0236 6 02

Example 1-8: Stem-and-Leaf Display

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X X *o

MedianQ1 Q3InnerFence

InnerFence

OuterFence

OuterFence

Interquartile Range

Smallest data point not below inner fence

Largest data point not exceeding inner fence

Suspected outlierOutlier

Q1-3(IQR)Q1-1.5(IQR) Q3+1.5(IQR)

Q3+3(IQR)

Elements of a Box Plot

Box Plot

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Example: Box Plot

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1-10 Using the Computer – The Template Output

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Using the Computer – Template Output for the Histogram

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Using the Computer – Template Output for Histograms for Grouped Data

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Using the Computer – Template Output for Frequency Polygons & the Ogive for Grouped Data

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Using the Computer – Template Output for Two Frequency Polygons for Grouped Data

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Using the Computer – Pie Chart Template Output

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Using the Computer – Bar Chart Template Output

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Using the Computer – Box Plot Template Output

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Using the Computer – Box Plot Template to Compare Two Data Sets

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Using the Computer – Time Plot Template

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Using the Computer – Time Plot Comparison Template

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Penutup

• Materi Statistik Deskriptif ini pada hakekatnya adalah prosedur atau metode dasar untuk pengumpulan, penyusunan, pengolahan, serta penyajian (display) data