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Pertemuan 4 Statistik Deskriptif-2

Pertemuan 4 Statistik Deskriptif-2. Matakuliah : A0064 / Statistik Ekonomi Tahun : 2005 Versi : 1/1. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu :

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Pertemuan 4 Statistik Deskriptif-2

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  1. Pertemuan 4Statistik 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

  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

  5. Skewness Skewed to left

  6. Skewness Symmetric

  7. Skewness Skewed to right

  8. Kurtosis Platykurtic - flat distribution

  9. Kurtosis Mesokurtic - not too flat and not too peaked

  10. Kurtosis Leptokurtic- peaked distribution

  11. Chebyshev’s Theorem Applies to anydistribution, 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 1-7 Relations between the Mean and Standard Deviation

  12. At least of the elements of anydistribution lie within k standard deviations of the mean Chebyshev’s Theorem 2 3 4 Standard deviations of the mean At least Lie within

  13. Empirical Rule • For roughly mound-shaped and symmetric distributions, approximately:

  14. 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 1-8 Methods of Displaying Data

  15. Pie Chart

  16. Bar Chart Fig. 1-11 Airline Operating Expenses and Revenues 1 2 Average Revenues Average Expenses 1 0 8 6 4 2 0 American Continental Delta Northwest Southwest United USAir A i r l i n e

  17. 0 . 3 1 . 0 0 . 2 0 . 5 Cumulative Relative Frequency Relative Frequency 0 . 1 0 . 0 0 . 0 0 1 0 2 0 3 0 4 0 5 0 0 1 0 2 0 3 0 4 0 5 0 Sales Sales Frequency Polygon and Ogive Relative Frequency Polygon Ogive

  18. M o n t h l y S t e e l P r o d u c t i o n ( P r o b l e m 1 - 4 6 ) 8 . 5 s 7 . 5 n o T f o s n o i l l i 6 . 5 M 5 . 5 M o n t h J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O Time Plot

  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 1-9 Exploratory Data Analysis - EDA Techniques to determine relationships and trends, identify outliers and influential observations, and quickly describe or summarize data sets.

  20. Example 1-8: Stem-and-Leaf Display 1 122355567 2 0111222346777899 3 012457 4 11257 5 0236 6 02

  21. Smallest data point not below inner fence Largest data point not exceeding inner fence Suspected outlier Outlier o * X X Q1 Median Q3 Inner Fence Outer Fence Inner Fence Outer Fence Q1-1.5(IQR) Q3+1.5(IQR) Interquartile Range Q1-3(IQR) Q3+3(IQR) Box Plot Elements of a Box Plot

  22. Example: Box Plot

  23. 1-10 Using the Computer – The Template Output

  24. Using the Computer – Template Output for the Histogram

  25. Using the Computer – Template Output for Histograms for Grouped Data

  26. Using the Computer – Template Output for Frequency Polygons & the Ogive for Grouped Data

  27. Using the Computer – Template Output for Two Frequency Polygons for Grouped Data

  28. Using the Computer – Pie Chart Template Output

  29. Using the Computer – Bar Chart Template Output

  30. Using the Computer – Box Plot Template Output

  31. Using the Computer – Box Plot Template to Compare Two Data Sets

  32. Using the Computer – Time Plot Template

  33. 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

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