1 Pertemuan 4 Statistik Deskriptif-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1

2 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)

3 Outline Materi Ukuran Kemiringan (Skewness) dan Kerruncingan (Kurtosis) Data Metode-metode Penyajian Data

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., l Skewness –Measure of asymmetry of a frequency distribution Skewed to left Symmetric or unskewed Skewed to right l Kurtosis –Measure of flatness or peakedness of a frequency distribution Platykurtic (relatively flat) Mesokurtic (normal) Leptokurtic (relatively peaked) 1-6 Skewness and Kurtosis

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Skewed to left Skewness

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Skewness Symmetric

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Skewness Skewed to right

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Kurtosis Platykurtic - flat distribution

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Kurtosis Mesokurtic - not too flat and not too peaked

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Kurtosis Leptokurtic - peaked distribution

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., l 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 l 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 1-7 Relations between the Mean and Standard Deviation

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., l At least of the elements of any distribution lie within k standard deviations of the mean At least Lie within Standard deviations of the mean Chebyshev’s Theorem

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., l For roughly mound-shaped and symmetric distributions, approximately: Empirical Rule

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., l Pie Charts Categories represented as percentages of total l Bar Graphs Heights of rectangles represent group frequencies l Frequency Polygons Height of line represents frequency l Ogives Height of line represents cumulative frequency l Time Plots Represents values over time 1-8 Methods of Displaying Data

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Pie Chart

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Bar Chart Average Revenues Average Expenses Fig Airline Operating Expenses and Revenues Airline AmericanContinentalDeltaNorthwestSouthwestUnitedUSAir

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Relative Frequency Polygon Ogive Frequency Polygon and Ogive Relative Frequency Sales Cumulative Relative Frequency Sales

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Time Plot

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., l Stem-and-Leaf Displays Quick-and-dirty listing of all observations Conveys some of the same information as a histogram l 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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Example 1-8: Stem-and-Leaf Display

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., XX *o Median Q1Q1 Q3Q3 Inner Fence Inner Fence Outer Fence Outer Fence Interquartile Range Smallest data point not below inner fence Largest data point not exceeding inner fence Suspected outlier Outlier Q 1 -3(IQR) Q (IQR)Q (IQR) Q 3 +3(IQR) Elements of a Box Plot Box Plot

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Example: Box Plot

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – The Template Output

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Template Output for the Histogram

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Template Output for Histograms for Grouped Data

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Template Output for Frequency Polygons & the Ogive for Grouped Data

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Template Output for Two Frequency Polygons for Grouped Data

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Pie Chart Template Output

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Bar Chart Template Output

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Box Plot Template Output

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Box Plot Template to Compare Two Data Sets

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Time Plot Template

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Using the Computer – Time Plot Comparison Template

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