Pertemuan 05 Ukuran Deskriptif Lain

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1 Pertemuan 05 Ukuran Deskriptif Lain
Matakuliah : I0134 – Metoda Statistika Tahun : 2005 Versi : Revisi Pertemuan 05 Ukuran Deskriptif Lain

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa dapat memberikan contoh tentang penggunaan ukuran deskriptif lain.

3 Outline Materi Koefisien variasi Skor Z Skewness Kurtosis

4 Skewness and Kurtosis Skewness Kurtosis
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)

5 Mean < median < mode
Skewness Skewed to left 6 5 4 3 2 1 x F r e q u n c y Mean < median < mode

6 Skewness Symmetric Mean = median = mode 6 5 4 3 2 1 x F r e q u n c y

7 Skewness Skewed to right Mode > median > mean y c n u q e r F x
6 5 4 3 2 1 x F r e q u n c y

8 Kurtosis Platykurtic - flat distribution y c n u q e r F X 3 . 7 2 9 1
5 - 6 4 X F r e q u n c y

9 Kurtosis Mesokurtic - not too flat and not too peaked y c n u q e r F
4 3 2 1 - 5 X F r e q u n c y

10 Kurtosis Leptokurtic - peaked distribution 1 - 2 Y F r e q u n c y

11 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

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

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

14 Selamat Belajar Semoga Sukses.