PENGELOLAAN STATISTIK YANG MENYENANGKAN, oleh Muhammad Rusli Hak Cipta © 2014 pada penulis GRAHA ILMU Ruko Jambusari 7A Yogyakarta 55283 Telp: 0274-889398; Fax: 0274-889057; E-mail:
[email protected] Hak Cipta dilindungi undang-undang. Dilarang memperbanyak atau memindahkan sebagian atau seluruh isi buku ini dalam bentuk apa pun, secara elektronis maupun mekanis, termasuk memfotokopi, merekam, atau dengan teknik perekaman lainnya, tanpa izin tertulis dari penerbit. ISBN: 978-602-262-183-6 Cetakan ke I, tahun 2014
Statistical Package for the Social Scences
151
KATA PENGANTAR
P
uji dan Syukur Penulis Panjatkan ke Hadirat Tuhan Yang Maha Esa karena berkat limpahan Rahmat dan Karunia-Nya sehingga penulis dapat menyusun Pengelolaan Statistik Yang Menyenangkan ini tepat pada waktunya. Dalam penyusunan Pengelolaan Statistik Yang Menyenangkan ini, penulis banyak mendapat tantangan dan hambatan akan tetapi dengan bantuan dari berbagai pihak tantangan itu bisa teratasi. Olehnya itu, penulis mengucapkan terima kasih yang sebesar-besarnya kepada semua pihak yang telah membantu dalam penyusunan Pengelolaan Statistik Yang Menyenangkan ini, semoga bantuannya mendapat balasan yang setimpal dari Tuhan Yang Maha Esa. Penulis menyadari bahwa Pengelolaan Statistik Yang Menyenangkan ini masih jauh dari kesempurnaan baik dari bentuk penyusunan maupun materinya. Kritik konstruktif dari pembaca sangat penulis harapkan untuk penyempurnaan materi selanjutnya. Akhir kata semoga Pengelolaan Statistik Yang Menyenangkan ini dapat memberikan manfaat kepada kita sekalian.
Jakarta,
Penulis
152
Pengelolaan Statistik yang Menyenangkan
DAFTAR ISI
DAFTAR PENGANTAR ...................................................................................................................................
v
DAFTAR ISI .....................................................................................................................................................
vii
BAB 1. PENDAHULUAN .................................................................................................................................
1
A. B. C. D. E. F. G. H. I.
Pengertian Statistik dan Statistika ......................................................................................................... Statistika deskriptif................................................................................................................................ Statistika inferensi ................................................................................................................................. Mengapa statistik dibutuhkan dibanyak bidang .................................................................................... Jenis-jenis Variabel................................................................................................................................ Skala Pengukuran .................................................................................................................................. Tingkat Kepercayaan (Confidence Interval).......................................................................................... Signifikansi / Probabilitas (Significance Level) .................................................................................... Soal Latihan...........................................................................................................................................
1 2 2 2 3 5 7 7 7
BAB 2. MENGGAMBARKAN DATA ............................................................................................................
9
A. B. C. D. E. F. G. H. I.
Jenis Data .............................................................................................................................................. Membuat table frekuensi ....................................................................................................................... Frekuensi kelas relative ......................................................................................................................... Persentase grafik data kualitatif............................................................................................................. Membuat distribusi frekuensi : Data kuantitatif .................................................................................... Interval kelas dan titik tengah kelas ...................................................................................................... Distribusi frekuensi relative .................................................................................................................. Distribusi frekuensi kumulatif............................................................................................................... Soal Latihan...........................................................................................................................................
9 10 11 11 12 14 14 15 16
viii
Pengelolaan Statistik yang Menyenangkan
BAB 3. PENGUKURAN NILAI PUSAT .........................................................................................................
19
A. Pengertian Rata-rata .............................................................................................................................. B. Rata-rata populasi.................................................................................................................................. C. Rata-rata sampel .................................................................................................................................... D. Median................................................................................................................................................... E. Modus.................................................................................................................................................... F. Rata-rata geometris................................................................................................................................ G. Dispersi.................................................................................................................................................. H. Jangkauan .............................................................................................................................................. I. Deviasi Rata-rata ................................................................................................................................... J. Varians dan Standar Deviasi .................................................................................................................. K. Standar Deviasi Populasi....................................................................................................................... L. Varians Sampel ...................................................................................................................................... M. Standar Deviasi Sampel......................................................................................................................... N. Teorema Chebyshev .............................................................................................................................. O. Rata-rata dan standar deviasi dari data yang dikelompokkan................................................................ P. Rata-rata hitung ..................................................................................................................................... Q. Standar Deviasi...................................................................................................................................... R. Soal-soal untuk latihan ..........................................................................................................................
19 19 21 22 22 22 23 23 23 24 25 25 26 27 27 27 28 29
BAB 4. PENGUKURAN DISPERSI ................................................................................................................
33
A. B. C. D. E. F.
Pengertian Dispersi................................................................................................................................ Rentang (range) : ................................................................................................................................... Kuartil, Desil, Persentil ......................................................................................................................... Skewedness ........................................................................................................................................... Peakedness (kurtosis /peruncingan)....................................................................................................... Soal Latihan...........................................................................................................................................
33 33 34 35 37 38
BAB 5. ANGKA INDEKS .................................................................................................................................
43
A. B. C. D. E. F. G.
Pengertian Angka Indeks....................................................................................................................... Angka indeks sederhana ........................................................................................................................ Indeks tanpa pembobotan ...................................................................................................................... Indeks agregat sederhana....................................................................................................................... Indeks Berbobot .................................................................................................................................... Indeks Nilai ........................................................................................................................................... Soal Latihan...........................................................................................................................................
43 43 45 45 46 50 51
BAB 6. DERET WAKTU DAN PERAMALAN ..............................................................................................
55
A. Pengertian Deret Waktu......................................................................................................................... B. Komponen-komponen Deret Waktu ......................................................................................................
55 55
Daftar Isi
C. D. E. F.
ix
Tren Linier............................................................................................................................................. Tren Kuadrat.......................................................................................................................................... Trend eksponensial................................................................................................................................ Soal Latihan...........................................................................................................................................
56 58 59 61
BAB 7. REGRESI DAN KORELASI...............................................................................................................
65
A. B. C. D. E. F. G.
Pengertian Regresi dan korelasi ............................................................................................................ Koefisien Korelasi................................................................................................................................. Koefisien Determinan............................................................................................................................ Analisis Regresi..................................................................................................................................... Regresi dan Korelasi Berganda ............................................................................................................. Koefisien Korelasi Parsial ..................................................................................................................... Soal Latihan...........................................................................................................................................
65 65 66 66 68 71 72
BAB 8. TEORI PROBABILITAS ....................................................................................................................
75
A. B. C. D. E. F. G.
Pengertian Probabilitas.......................................................................................................................... Ruang sampel ....................................................................................................................................... Probabilitas Klasik ................................................................................................................................ Peristiwa (event).................................................................................................................................... Peristiwa yang tidak saling lepas........................................................................................................... Teorema BAYES ................................................................................................................................... Soal Latihan...........................................................................................................................................
75 75 76 76 78 79 80
BAB 9. PERMUTASI DAN KOMBINASI ......................................................................................................
81
A. B. C. D. E.
Pengertian Permutasi dan kombinasi..................................................................................................... Faktorial ................................................................................................................................................ Permutasi............................................................................................................................................... Kombinasi ............................................................................................................................................. Soal Latihan...........................................................................................................................................
81 81 83 85 86
BAB 10. DISTRIBUSI BINOMIAL .................................................................................................................
87
A. B. C. D. E. F. G. H.
Pengertian Distribusi Binomial ............................................................................................................. Eksperimen Binomial dan Percobaan Bernaulli .................................................................................... Distribusi binomial ................................................................................................................................ Rata – rata distribusi binomial............................................................................................................... Varians dan standar deviasi ................................................................................................................... Distribusi Poisson.................................................................................................................................. Distribusi Hipergeomatrik ..................................................................................................................... Soal Latihan...........................................................................................................................................
87 87 88 88 89 90 91 92
x
Pengelolaan Statistik yang Menyenangkan
BAB 11. DISTRIBUSI NORMAL ....................................................................................................................
93
A. Pengertian Distribusi Normal ................................................................................................................ B. Hubungan antara distribusi normal dengan binomial ............................................................................ C. Soal Latihan...........................................................................................................................................
93 95 96
BAB 12. DISTRIBUSI SAMPEL .....................................................................................................................
99
A. B. C. D. E. F.
Pengertian Distribusi Sampel ................................................................................................................ Populasi dengan ditribusi sampling rata-rata......................................................................................... Populasi dengan distribusi sampling Proporsi....................................................................................... Distribusi sampling selisih rata-rata ...................................................................................................... Distribusi sampling selisih proporsi ...................................................................................................... Soal Latihan...........................................................................................................................................
99 100 101 102 103 104
BAB 13. PENDUGAAN SECARA STATISTIK..............................................................................................
105
A. B. C. D.
Pengertian Pendugaan Secara Statistik.................................................................................................. Pendugaan parameter dengan sampel besar .......................................................................................... Pendugaan parameter dengan sampel kecil ........................................................................................... Soal Latihan...........................................................................................................................................
105 105 107 109
BAB 14. PENGUJIAN HIPOTESIS ................................................................................................................
111
A. B. C. D. E.
Pengertian Pengujian Hipotesis ............................................................................................................. Prosedur pengujian statistik................................................................................................................... Pengujian dengan sampel besar............................................................................................................. Pengujian hipotesa dengan sampel kecil ............................................................................................... Soal Latihan...........................................................................................................................................
111 111 112 116 117
BAB 15. ANALYSIS OF VARIANS..................................................................................................................
119
A. Pengertian Analysis of Varians .............................................................................................................. B. Analysis Of Varians Satu Jalur .............................................................................................................. C. Analisa varians dua jalur .......................................................................................................................
119 119 123
BAB 16. CHI KUADRAT..................................................................................................................................
131
A. Pengertian Chi Kuadrat ......................................................................................................................... B. Chi – Kuadrat sebagai uji Independensi ................................................................................................ C. Soal Latihan...........................................................................................................................................
131 131 134
BAB 17. STATISTIK NON PARAMETRIK ...................................................................................................
135
A. B. C. D.
Pengertian Statistik Non Parametrik...................................................................................................... Uji Tanda ............................................................................................................................................... Menggunakan perkiraan normal pada Binomial.................................................................................... Menguji Hipotesis Tentang median .......................................................................................................
135 135 137 138
