Matakuliah
Tahun
Versi
: A0064 / Statistik Ekonomi
: 2005
: 1/1
Pertemuan 4
Statistik Deskriptif-2
1
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)
2
Outline Materi
• Ukuran Kemiringan (Skewness) dan
Kerruncingan (Kurtosis) Data
• Metode-metode Penyajian Data
3
COMPLETE
BUSINESS STATISTICS
1-4
5th edi tion
1-6 Skewness and Kurtosis

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)
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-5
5th edi tion
Skewness
Skewed to left
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-6
5th edi tion
Skewness
Symmetric
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-7
5th edi tion
Skewness
Skewed to right
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
5th edi tion
1-8
Kurtosis
Platykurtic - flat distribution
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-9
5th edi tion
Kurtosis
Mesokurtic - not too flat and not too peaked
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
5th edi tion
1-10
Kurtosis
Leptokurtic - peaked distribution
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
1-11
BUSINESS STATISTICS
5th edi tion
1-7 Relations between the Mean and
Standard Deviation

Chebyshev’s Theorem
 Applies to any distribution, regardless of shape
 Places lower limits on the percentages of observations
within a given number of standard deviations from the
mean

Empirical Rule
 Applies only to roughly mound-shaped and
symmetric distributions
 Specifies approximate percentages of observations
within a given number of standard deviations from the
mean
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
5th edi tion
1-12
BUSINESS STATISTICS
Chebyshev’s Theorem
At least 1  k1  of the elements of any
distribution lie within k standard deviations
of the mean

1
At
least
2
1
1 3

1

  75%
2
4 4
2
1
1 8
1  2  1    89%
9 9
3
1
1 15
1 2  1

 94%
16
16
4
McGraw-Hill/Irwin
Aczel/Sounderpandian
2
Lie
within
3
Standard
deviations
of the mean
4
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
1-13
BUSINESS STATISTICS
5th edi tion
Empirical Rule

For roughly mound-shaped and symmetric
distributions, approximately:
68%
95%
All
McGraw-Hill/Irwin
1 standard deviation
of the mean
Lie
within
2 standard deviations
of the mean
3 standard deviations
of the mean
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
1-14
BUSINESS STATISTICS
5th edi tion
1-8 Methods of Displaying Data

Pie Charts
 Categories represented as percentages of total

Bar Graphs
 Heights of rectangles represent group frequencies

Frequency Polygons
 Height of line represents frequency

Ogives
 Height of line represents cumulative frequency

Time Plots
 Represents values over time
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-15
5th edi tion
Pie Chart
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
5th edi tion
1-16
BUSINESS STATISTICS
Bar Chart
Fig. 1-11 Airline Operating Expenses and Revenues
12
Average Revenues
Average Expenses
10
8
6
4
2
0
American Continental Delta
Northwest Southwest United
USAir
A i r li n e
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
5th edi tion
1-17
BUSINESS STATISTICS
Frequency Polygon and Ogive
Relative Frequency Polygon
0.3
Ogive
1.0
0.2
0.5
0.1
0.0
0.0
0
10
20
30
40
50
Sales
McGraw-Hill/Irwin
0
10
20
30
40
50
Sales
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
5th edi tion
1-18
Time Plot
M o n thly S te e l P ro d uc tio n
(P ro b le m 1 -4 6 )
Millions of Tons
8.5
7.5
6.5
5.5
Month
McGraw-Hill/Irwin
J F M A M J J A S ON D J F M A M J J A S ON D J F M A M J J A S O
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
1-19
BUSINESS STATISTICS
5th edi tion
1-9 Exploratory Data Analysis - EDA
Techniques to determine relationships and trends,
identify outliers and influential observations, and
quickly describe or summarize data sets.

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
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
5th edi tion
1-20
BUSINESS STATISTICS
Example 1-8: Stem-and-Leaf Display
1
2
3
4
5
6
McGraw-Hill/Irwin
122355567
0111222346777899
012457
11257
0236
02
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
5th edi tion
1-21
BUSINESS STATISTICS
Box Plot
Elements of a Box Plot
Outlier
Smallest data
point not below
inner fence
o
Largest data point
Suspected
not exceeding
outlier
inner fence
X
Outer
Fence
Inner
Fence
Q1-1.5(IQR)
Q1-3(IQR)
McGraw-Hill/Irwin
X
Q1
Median
Interquartile Range
Q3
Inner
Fence
Q3+1.5(IQR)
*
Outer
Fence
Q3+3(IQR)
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
5th edi tion
1-22
Example: Box Plot
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-23
5th edi tion
1-10 Using the Computer – The
Template Output
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-24
5th edi tion
Using the Computer – Template Output
for the Histogram
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-25
5th edi tion
Using the Computer – Template Output
for Histograms for Grouped Data
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-26
5th edi tion
Using the Computer – Template Output for Frequency
Polygons & the Ogive for Grouped Data
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-27
5th edi tion
Using the Computer – Template Output for Two
Frequency Polygons for Grouped Data
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-28
5th edi tion
Using the Computer – Pie Chart
Template Output
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-29
5th edi tion
Using the Computer – Bar Chart
Template Output
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-30
5th edi tion
Using the Computer – Box Plot Template
Output
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-31
5th edi tion
Using the Computer – Box Plot Template
to Compare Two Data Sets
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-32
5th edi tion
Using the Computer – Time Plot
Template
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
1-33
5th edi tion
Using the Computer – Time Plot
Comparison Template
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
Penutup
• Materi Statistik Deskriptif ini pada
hakekatnya adalah prosedur atau metode
dasar untuk pengumpulan, penyusunan,
pengolahan, serta penyajian (display) data
34