# 1 Pertemuan 04 Ukuran Pemusatan dan Penyebaran Matakuliah: I0134 – Metoda Statistika Tahun: 2005 Versi: Revisi.

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1 Pertemuan 04 Ukuran Pemusatan dan Penyebaran Matakuliah: I0134 – Metoda Statistika Tahun: 2005 Versi: Revisi

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa dapat menghitung, mengidentifikasi penggunaan ukuran pemusatan dan penyebaran.

3 Outline Materi Rata-rata Median Modus Kuartil Desil Persentil Varians dan Simpangan baku

4  Medianâ Middle value when sorted in order of magnitude â 50th percentile  Modeâ Most frequently- occurring value  Meanâ Average Ukuran Pemusatan dan Penyebaran

5 SalesSorted Sales 9 6 6 9 12 10 10 12 13 15 14 16 14 14 15 14 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24 Median 50th Percentile (20+1)50/100=10.516 + (.5)(0) = 16 The median is the middle value of data sorted in order of magnitude. It is the fiftieth percentile. Contoh Soal - Median

6...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24 Mode = 16 The mode is the most frequently occurring value. It is the value with the highest frequency. Contoh Soal - Mode

7 The mean of a set of observations is their average - the sum of the observed values divided by the number of observations. Population Mean Sample Mean    x N i N 1 x x n i n    1 Arithmetic Mean or Average

8 x x n i n    1 317 20 1585. Sale s 9 6 12 10 13 15 16 14 16 17 16 24 21 22 18 19 18 20 17 317 Contoh Soal - (Mean)

9...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24 Median and Mode = 16 Mean = 15.85 Contoh Soal - Mode

10 l Range –Difference between maximum and minimum values l Interquartile Range –Difference between third and first quartile (Q 3 - Q 1 ) l Variance –Mean * squared deviation from the mean l Standard Deviation –Square root of the variance   Definitions of population variance and sample variance differ slightly. Ukuran Penyebaran

11 Sorted SalesSalesRank 9 6 1 6 9 2 1210 3 1012 4 1313 5 1514 6 1614 7 1415 8 1416 9 161610 171611 161712 241713 211814 221815 181916 192017 182118 202219 172420 First Quartile Third Quartile Q 1 = 13 + (.25)(1) = 13.25 Q 3 = 18+ (.75)(1) = 18.75 Minimum Maximum Range Maximum - Minimum = 24 - 6 = 18 Interquartile Range Q3 - Q1 = 18.75 - 13.25 = 5.5 Contoh. Range and Interquartile Range

12 ( )     2 2 1 2 1 2 2 1            ()x N x N N i N i N x i N Population Variance     s xx n x x n n s s i n i n i n 2 2 1 2 1 2 2 1 1 1              () Sample Variance Variance and Standard Deviation ( )

13 6-9.85 97.0225 36 9-6.85 46.9225 81 10-5.85 34.2225 100 12-3.85 14.8225 144 13-2.85 8.1225 169 14-1.85 3.4225 196 15-0.85 0.7225 225 16 0.15 0.0225 256 17 1.15 1.3225 289 18 2.15 4.6225 324 19 3.15 9.9225 361 20 4.15 17.2225 400 21 5.15 26.5225 441 22 6.15 37.8225 484 24 8.15 66.4225 576 317 0 378.5500 5403 Calculation of Sample Variance

14 l Dividing data into groups or classes or intervals l Groups should be: –Mutually exclusive Not overlapping - every observation is assigned to only one group –Exhaustive Every observation is assigned to a group –Equal-width (if possible) First or last group may be open-ended Group Data and the Histogram

15 Selamat Belajar Semoga Sukses.

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