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Ukuran Pemusatan dan Lokasi Pertemuan 03

Ukuran Pemusatan dan Lokasi Pertemuan 03. Matakuliah : L0104 / Statistika Psikologi Tahun : 2008. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu :

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Ukuran Pemusatan dan Lokasi Pertemuan 03

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  1. Ukuran Pemusatan dan LokasiPertemuan 03 Matakuliah : L0104 / Statistika Psikologi Tahun : 2008

  2. Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : • Mahasiswa akan dapat menghitung ukuran-ukuran pemusatan dan lokasi, Untuk data berkelompol (tersaji dalam tabel distribusi frekuensi dan data tidak berkelompok (ungrouping data). 3

  3. Outline Materi • Rata-rata (Hitung, Ukur dan Harmonis) • Modus • Median • Kuartil • Desil • Persentil 4

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

  5. Arithmetic Mean or Average • The 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 If we were able to enumerate the whole population, the population mean would be called m(the Greek letter “mu”).

  7. .5(n + 1) Median • The median of a set of measurements is the middle measurement when the measurements are ranked from smallest to largest. • The position of the medianis • once the measurements have been ordered.

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

  9. Mode • The mode is the measurement which occurs most frequently. • The set: 2, 4, 9, 8, 8, 5, 3 • The mode is 8, which occurs twice • The set: 2, 2, 9, 8, 8, 5, 3 • There are two modes—8 and 2 (bimodal) • The set: 2, 4, 9, 8, 5, 3 • There is no mode (each value is unique).

  10. Example The number of quarts of milk purchased by 25 households: 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 5 • Mean? • Median? • Mode? (Highest peak)

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

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

  13. Key Concepts I. Measures of Center 1. Arithmetic mean (mean) or average a. Population: m b. Sample of size n: 2. Median: position of the median = .5(n +1) 3. Mode 4. The median may preferred to the mean if the data are highly skewed.

  14. Rumus-rumus (Formula) di atas untuk menentukan rata-rata dan ukuran lainnya untuk data yang tidak berkelompok, sedangkan untuk data berkelompok (dalam tabel dist frekuensi) dapat digunakan Rumus di atas dengan mengganti Xi dengan fiXi (lihat referensi)

  15. Selamat Belajar Semoga Sukses.

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