Download - 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