1 Pertemuan 02 Ukuran Pemusatan dan Lokasi Matakuliah: I Statistika Tahun: 2008 Versi: Revisi

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

3 Outline Materi Rata-rata Median Modus Kuartil Desil persentil

4 Measures of Center centerA measure along the horizontal axis of the data distribution that locates the center of the distribution.

5 1. Arithmetic Mean or Average meanThe mean of a set of measurements is the sum of the measurements divided by the total number of measurements. where n = number of measurements

6 Example The set: 2, 9, 1, 5, 6 population mean  If we were able to enumerate the whole population, the population mean would be called  (the Greek letter “mu”).

7 Approximating the Arithmetic Mean –Used when raw data are not available – Mean (Arithmetic Mean)

8 medianThe median of a set of measurements is the middle measurement when the measurements are ranked from smallest to largest. position of the medianThe position of the median is 2. Median.5(n + 1) once the measurements have been ordered. a. Md = X (n+1)/2

9 Example The set: 2, 4, 9, 8, 6, 5, 3n = 7 Sort:2, 3, 4, 5, 6, 8, 9 Position:.5(n + 1) =.5(7 + 1) = 4 th Median = 4 th largest measurement The set: 2, 4, 9, 8, 6, 5n = 6 Sort:2, 4, 5, 6, 8, 9 Position:.5(n + 1) =.5(6 + 1) = 3.5 th Median = (5 + 6)/2 = 5.5 — average of the 3 rd and 4 th measurements

b. Median Data Berkelompok 10

11 3. Mode Untuk menyatakan fenomena yang paling banyak terjadi, juga untuk menentukan “rata- rata” dari data kualitatif. a. Data tak berkelompok : Modus (Mo) dilihat dari data yang memiliki frekuensi terbanyak The set: 2, 4, 9, 8, 8, 5, 3 8 –The mode is 8, which occurs twice The set: 2, 2, 9, 8, 8, 5, 3 82bimodal –There are two modes — 8 and 2 (bimodal) The set: 2, 4, 9, 8, 5, 3 no mode –There is no mode (each value is unique).

b. Modus Data Berkelompok Kuartil (Q i ) Membagi kelompok data yang telah terurut menjadi 4 bagian yang sama besar. a. Data tak berkelompok

b. Kuartil Data Berkelompok 13

14 Example Mean? Median? Mode? (Highest peak) The number of quarts of milk purchased by 25 households:

15 The mean is more easily affected by extremely large or small values than the median. Extreme Values Applet The median is often used as a measure of center when the distribution is skewed.

16 Extreme Values Skewed left: Mean < Median Skewed right: Mean > Median Symmetric: Mean = Median

5. Desil Membagi kelompok data yang telah terurut menjadi 10 bagian yang sama besar. a. Data tak berkelompok b. Data berkelompok 17

6. Persentil (Pi) Membagi kelompok data yang telah terurut menjadi 100 bagian yang sama besar. a. Data tak berkelompok b. Data berkelompok 18

19 Selamat Belajar Semoga Sukses.