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

2. 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. 3 Outline Materi Ukuran Kemiringan (Skewness) dan Kerruncingan (Kurtosis) Data Metode-metode Penyajian Data

4. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-4 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

5. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-5 Skewed to left Skewness

6. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-6 Skewness Symmetric

7. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-7 Skewness Skewed to right

8. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-8 Kurtosis Platykurtic - flat distribution

9. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-9 Kurtosis Mesokurtic - not too flat and not too peaked

10. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-10 Kurtosis Leptokurtic - peaked distribution

11. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-11 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

12. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-12 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 234234 Chebyshev’s Theorem

13. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-13 l For roughly mound-shaped and symmetric distributions, approximately: Empirical Rule

14. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-14 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

15. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-15 Pie Chart

16. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-16 Bar Chart Average Revenues Average Expenses Fig. 1-11 Airline Operating Expenses and Revenues 12 10 8 6 4 2 0 Airline AmericanContinentalDeltaNorthwestSouthwestUnitedUSAir

17. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-17 Relative Frequency Polygon Ogive Frequency Polygon and Ogive 50403020100 0.3 0.2 0.1 0.0 Relative Frequency Sales 50403020100 1.0 0.5 0.0 Cumulative Relative Frequency Sales

18. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-18 Time Plot

19. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-19 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

20. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-20 1 122355567 2 0111222346777899 3 012457 4 11257 5 0236 6 02 1 122355567 2 0111222346777899 3 012457 4 11257 5 0236 6 02 Example 1-8: Stem-and-Leaf Display

21. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-21 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 1 -1.5(IQR)Q 3 +1.5(IQR) Q 3 +3(IQR) Elements of a Box Plot Box Plot

22. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-22 Example: Box Plot

23. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-23 1-10 Using the Computer – The Template Output

24. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-24 Using the Computer – Template Output for the Histogram

25. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-25 Using the Computer – Template Output for Histograms for Grouped Data

26. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-26 Using the Computer – Template Output for Frequency Polygons & the Ogive for Grouped Data

27. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-27 Using the Computer – Template Output for Two Frequency Polygons for Grouped Data

28. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-28 Using the Computer – Pie Chart Template Output

29. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-29 Using the Computer – Bar Chart Template Output

30. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-30 Using the Computer – Box Plot Template Output

31. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-31 Using the Computer – Box Plot Template to Compare Two Data Sets

32. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-32 Using the Computer – Time Plot Template

33. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-33 Using the Computer – Time Plot Comparison Template

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