1 Pertemuan 3 Statistik Deskriptif-1 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.
1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.
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Transcript of 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.
![Page 1: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/1.jpg)
1
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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3
Outline Materi
• Ukuran Kemiringan (Skewness) dan Kerruncingan (Kurtosis) Data
• Metode-metode Penyajian Data
![Page 4: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/4.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-4
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
![Page 5: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/5.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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Skewed to left
Skewness
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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-6
Skewness
Symmetric
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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-7
Skewness
Skewed to right
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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-8
Kurtosis
Platykurtic - flat distribution
![Page 9: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/9.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-9
Kurtosis
Mesokurtic - not too flat and not too peaked
![Page 10: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/10.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-10
Kurtosis
Leptokurtic - peaked distribution
![Page 11: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/11.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-11
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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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-12
1 12
1 14
34 75%
1 13
1 19
89 89%
1 14
1 116
1516 94%
2
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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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-13
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
![Page 14: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/14.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
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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
![Page 15: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/15.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-15
Pie Chart
![Page 16: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/16.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-16
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
![Page 17: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/17.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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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
![Page 18: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/18.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-18
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
![Page 19: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/19.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-19
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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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-20
1 122355567 2 0111222346777899 3 012457 4 11257 5 0236 6 02
Example 1-8: Stem-and-Leaf Display
![Page 21: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/21.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
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1-21
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
![Page 22: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/22.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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Example: Box Plot
![Page 23: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/23.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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1-10 Using the Computer – The Template Output
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COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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Using the Computer – Template Output for the Histogram
![Page 25: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/25.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-25
Using the Computer – Template Output for Histograms for Grouped Data
![Page 26: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/26.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-26
Using the Computer – Template Output for Frequency Polygons & the Ogive for Grouped Data
![Page 27: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/27.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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Using the Computer – Template Output for Two Frequency Polygons for Grouped Data
![Page 28: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/28.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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Using the Computer – Pie Chart Template Output
![Page 29: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/29.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
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Using the Computer – Bar Chart Template Output
![Page 30: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/30.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-30
Using the Computer – Box Plot Template Output
![Page 31: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/31.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-31
Using the Computer – Box Plot Template to Compare Two Data Sets
![Page 32: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/32.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-32
Using the Computer – Time Plot Template
![Page 33: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/33.jpg)
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-33
Using the Computer – Time Plot Comparison Template
![Page 34: 1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.](https://reader035.fdokumen.com/reader035/viewer/2022062601/5a4d1bf47f8b9ab0599e73eb/html5/thumbnails/34.jpg)
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Penutup
• Materi Statistik Deskriptif ini pada hakekatnya adalah prosedur atau metode dasar untuk pengumpulan, penyusunan, pengolahan, serta penyajian (display) data