Download - PENGUJIAN DISTRIBUSI
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 1/35
PENGUJIAN DISTRIBUSI
1. Data Distribusi Binomial
Adapun untuk langkah-langkah untuk membangkitkan data distribusi
binomial terdapat pada flowchart berikut. Adapun ketentuan-ketentuan yang
diberikan pada data distribusi binomial adalah:
1. Jumlah data (generate) = 150
2. Banyak percobaan (number of trials) = 30
3. Peluang kejadian (event probability) = 0,5
Mulai
1. Klik Calc padaMenu Bar
2. Pilih Random3. Klik Binomial
Input:Generate : 150
Number of Trials : 30Event Probability : 0.5
Proses Random
Print :150
Selesai
Gambar 1. Flowchart Pembangkitan Bilangan Random Distribusi Binomial
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 2/35
Tabel 1. Data Bilangan Random Distribusi Binomial
No Hasil No Hasil No Hasil No Hasil No Hasil1 6 16 11 31 13 46 14 61 15
2 9 17 11 32 13 47 14 62 15
3 9 18 11 33 13 48 14 63 15
4 10 19 12 34 13 49 14 64 15
5 10 20 12 35 13 50 14 65 15
6 10 21 12 36 13 51 14 66 15
7 10 22 12 37 13 52 14 67 15
8 10 23 12 38 13 53 14 68 15
9 10 24 12 39 13 54 14 69 1510 10 25 12 40 14 55 14 70 15
11 10 26 12 41 14 56 15 71 15
12 10 27 12 42 14 57 15 72 15
13 11 28 12 43 14 58 15 73 15
14 11 29 13 44 14 59 15 74 15
15 11 30 13 45 14 60 15 75 15
76 15 91 16 106 17 121 17 136 19
77 15 92 16 107 17 122 17 137 19
78 15 93 16 108 17 123 17 138 19
79 15 94 16 109 17 124 17 139 19
80 16 95 16 110 17 125 18 140 19
81 16 96 16 111 17 126 18 141 19
82 16 97 16 112 17 127 18 142 19
83 16 98 16 113 17 128 18 143 20
84 16 99 16 114 17 129 18 144 20
85 16 100 16 115 17 130 18 145 20
86 16 101 17 116 17 131 18 146 21
87 16 102 17 117 17 132 18 147 21
88 16 103 17 118 17 133 18 148 21
89 16 104 17 119 17 134 18 149 21
90 16 105 17 120 17 135 19 150 22
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 3/35
1.1. Pengujian Distribusi Binomial
Adapun data bilangan random data distribusi binomial dapat dilihat pada
Tabel 2.
Tabel 2. Bilangan Random Data Distribusi Binomial
Bilangan Random Data Distribusi Binomial
6 11 13 14 15 15 16 17 17 19
9 11 13 14 15 15 16 17 17 19
9 11 13 14 15 15 16 17 17 19
10 12 13 14 15 15 16 17 17 19
10 12 13 14 15 16 16 17 18 1910 12 13 14 15 16 16 17 18 19
10 12 13 14 15 16 16 17 18 19
10 12 13 14 15 16 16 17 18 20
10 12 13 14 15 16 16 17 18 20
10 12 14 14 15 16 16 17 18 20
10 12 14 15 15 16 17 17 18 21
10 12 14 15 15 16 17 17 18 21
11 12 14 15 15 16 17 17 18 21
11 13 14 15 15 16 17 17 18 21
Langkah-langkah pengujian yang dilakukan adalah sebagai berikut:
1. Rumusan Hipotesis
Ho : data berdistribusi binomial
Hi : data tidak berdistribusi binomial
2. Asumsikan α = 0,05
3. Tentukan nilai max, min, range, banyak kelas, dan panjang kelas
Data maksimum = 22
Data minimum = 6
Setelah didapat nilai dari Max dan Min maka data tersebut dirangkum di
dalam sebuah tabel frekuensi. Tabel frekuensi dapat dilhat seperti Tabel 3 berikut
:
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 4/35
Tabel 3. Tabel Frekuensi Data Pengujian Distribusi Binomial
No. Kelas Frekuensi (Oi) Xi Xi.Oi
1 6 1 6 6
2 9 2 9 18
3 10 9 10 90
4 11 6 11 66
5 12 10 12 120
6 13 11 13 143
7 14 16 14 224
8 15 24 15 360
9 16 21 16 336
10 17 24 17 408
11 18 10 18 180
12 19 8 19 152
13 20 3 20 60
14 21 4 21 84
15 22 1 22 22
Jumlah 150 2263
4. Menghitung peluang (P) dari masing-masing kelas dengan menggunakan
software Minitab agar lebih mudah, sehingga akan didapatlkan hasil seperti
Tabel 4.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 5/35
Tabel 4. Perhitungan Frekuensi Peluang Data Distribusi Binomial
No X Frekuensi (Oi) Xi.Oi Luas Kurva
1 6 1 6 0.000552996
2 9 2 18 0.013324572
3 10 9 90 0.027981601
4 11 6 66 0.050875638
5 12 10 120 0.080553093
6 13 11 143 0.111535052
7 14 16 224 0.13543542
8 15 24 360 0.144464448
9 16 21 336 0.13543542
10 17 24 408 0.111535052
11 18 10 180 0.080553093
12 19 8 152 0.050875638
13 20 3 60 0.027981601
14 21 4 84 0.013324572
15 22 1 22 0.005450961
Jumlah 150 2269 1,0000
5. Hitung nilai ekspektasinya (ei) untuk setiap interval.
ei = luas ke-i x n
misalnya: e1 = 0,000552996 x 150 = 0,082949409
Sehingga akan didapatkan hasil dalam tabel berikut ini.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 6/35
Tabel 5. Perhitungan Nilai Ekspektasi (ei) Binomial
No X Frekuensi (Oi) Xi.Oi Luas Kurva Ei
1 6 1 6 0.000552996 0.082949409
3 9 2 18 0.013324572 1.998685766
4 10 9 90 0.027981601 4.197240109
5 11 6 66 0.050875638 7.631345652
6 12 10 120 0.080553093 12.08296395
7 13 11 143 0.111535052 16.73025778
8 14 16 224 0.13543542 20.31531301
9 15 24 360 0.144464448 21.66966721
10 16 21 336 0.13543542 20.31531301
11 17 24 408 0.111535052 16.73025778
12 18 10 180 0.080553093 12.08296395
13 19 8 152 0.050875638 7.631345652
14 20 3 60 0.027981601 4.197240109
15 21 4 84 0.013324572 1.998685766
16 22 1 22 0.005450961 0.817644177
Jumlah 150 2269 1 150
6. Setelah didapatkan nilai ei dan Oi maka dapat dihitung nilai χ 2
hitung
χ 2
hitung
Nilai dari χ 2
hitung untuk masing-masing kelas dapat dilihat pada Tabel 6.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 7/35
Tabel 6. Tabel Nilai χ 2
hitung Data Pengujian Distribusi Binomial
Kelas Frekuensi (Oi) Xi Xi.Oi Luas Kurva Ei χ 2
6 1 6 6 0.000552996 0.082949409 10.13849036
9 2 9 18 0.013324572 1.998685766 8.64173E-07
10 9 10 90 0.027981601 4.197240109 5.495635698
11 6 11 66 0.050875638 7.631345652 0.348731241
12 10 12 120 0.080553093 12.08296395 0.359079017
13 11 13 143 0.111535052 16.73025778 1.962662776
14 16 14 224 0.13543542 20.31531301 0.916644818
15 24 15 360 0.144464448 21.66966721 0.25060149
16 21 16 336 0.13543542 20.31531301 0.023076005
17 24 17 408 0.111535052 16.73025778 3.158896457
18 10 18 180 0.080553093 12.08296395 0.359079017
19 8 19 152 0.050875638 7.631345652 0.017808921
20 3 20 60 0.027981601 4.197240109 0.341506285
21 4 21 84 0.013324572 1.998685766 2.003946159
22 1 22 22 0.005450961 0.817644177 0.04067007
Jumlah 150 2269 1 150 25.41682918
7. Hitung χ 2
tabel
Jumlah kelas (k) = 15
V (derajat bebas) = 15 – 3 = 12
α = 0,05
Sehingga nilai χ 2
tabel yang diperoleh = 21.02607
8. Kesimpulan: Ho ditolak (χ 2
hitung = 25,416829 > χ 2
tabel = 21.02607) atau dapat
disimpulkan bahwa data tersebut tidak berdistribusi binomial.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 8/35
Adapun gambar kurva distribusi binomial adalah sebagai berikut :
Gambar 2. Kurva Distribusi Binomial
9. Kurtosis dan Skewness
Adapun data yang digunakan dalam perhitungan Kurtosis dan skewness dapat
dilihat pada tabel berikut :
Tabel 7. Data Perhitungan Kurtosis dan Skewness
No Xi X Xi-X S ((Xi-X)/S)3
((Xi-X)/S)4
1 6 15.1267 -9.1267 2.8668 -32.264737 102.715861
2 9 15.1267 -6.1267 2.8668 -9.760326 20.858629
3 9 15.1267 -6.1267 2.8668 -9.760326 20.858629
4 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
5 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
6 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
7 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
8 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
9 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
F r e k u e n s i
Xi
Oi
ei
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 9/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
10 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
11 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
12 10 15.1267 -5.1267 2.8668 -5.718693 10.226548
13 11 15.1267 -4.1267 2.8668 -2.982564 4.293251
14 11 15.1267 -4.1267 2.8668 -2.982564 4.293251
15 11 15.1267 -4.1267 2.8668 -2.982564 4.293251
16 11 15.1267 -4.1267 2.8668 -2.982564 4.293251
17 11 15.1267 -4.1267 2.8668 -2.982564 4.293251
18 11 15.1267 -4.1267 2.8668 -2.982564 4.293251
19 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
20 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
21 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
22 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
23 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
24 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
25 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
26 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
27 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
28 12 15.1267 -3.1267 2.8668 -1.297288 1.414865
29 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
30 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
31 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
32 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 10/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
33 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
34 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
35 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
36 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
37 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
38 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
39 13 15.1267 -2.1267 2.8668 -0.408216 0.302821
40 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
41 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
42 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
43 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
44 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
45 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
46 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
47 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
48 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
49 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
50 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
51 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
52 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
53 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
54 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
55 14 15.1267 -1.1267 2.8668 -0.060698 0.023855
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 11/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
56 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
57 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
58 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
59 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
60 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
61 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
62 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
63 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
64 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
65 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
66 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
67 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
68 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
69 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
70 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
71 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
72 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
73 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
74 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
75 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
76 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
77 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
78 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 12/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
79 15 15.1267 -0.1267 2.8668 -0.000086 0.000004
80 16 15.1267 0.8733 2.8668 0.028270 0.008612
81 16 15.1267 0.8733 2.8668 0.028270 0.008612
82 16 15.1267 0.8733 2.8668 0.028270 0.008612
83 16 15.1267 0.8733 2.8668 0.028270 0.008612
84 16 15.1267 0.8733 2.8668 0.028270 0.008612
85 16 15.1267 0.8733 2.8668 0.028270 0.008612
86 16 15.1267 0.8733 2.8668 0.028270 0.008612
87 16 15.1267 0.8733 2.8668 0.028270 0.008612
88 16 15.1267 0.8733 2.8668 0.028270 0.008612
89 16 15.1267 0.8733 2.8668 0.028270 0.008612
90 16 15.1267 0.8733 2.8668 0.028270 0.008612
91 16 15.1267 0.8733 2.8668 0.028270 0.008612
92 16 15.1267 0.8733 2.8668 0.028270 0.008612
93 16 15.1267 0.8733 2.8668 0.028270 0.008612
94 16 15.1267 0.8733 2.8668 0.028270 0.008612
95 16 15.1267 0.8733 2.8668 0.028270 0.008612
96 16 15.1267 0.8733 2.8668 0.028270 0.008612
97 16 15.1267 0.8733 2.8668 0.028270 0.008612
98 16 15.1267 0.8733 2.8668 0.028270 0.008612
99 16 15.1267 0.8733 2.8668 0.028270 0.008612
100 16 15.1267 0.8733 2.8668 0.028270 0.008612
101 17 15.1267 1.8733 2.8668 0.279021 0.182326
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 13/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
102 17 15.1267 1.8733 2.8668 0.279021 0.182326
103 17 15.1267 1.8733 2.8668 0.279021 0.182326
104 17 15.1267 1.8733 2.8668 0.279021 0.182326
105 17 15.1267 1.8733 2.8668 0.279021 0.182326
106 17 15.1267 1.8733 2.8668 0.279021 0.182326
107 17 15.1267 1.8733 2.8668 0.279021 0.182326
108 17 15.1267 1.8733 2.8668 0.279021 0.182326
109 17 15.1267 1.8733 2.8668 0.279021 0.182326
110 17 15.1267 1.8733 2.8668 0.279021 0.182326
111 17 15.1267 1.8733 2.8668 0.279021 0.182326
112 17 15.1267 1.8733 2.8668 0.279021 0.182326
113 17 15.1267 1.8733 2.8668 0.279021 0.182326
114 17 15.1267 1.8733 2.8668 0.279021 0.182326
115 17 15.1267 1.8733 2.8668 0.279021 0.182326
116 17 15.1267 1.8733 2.8668 0.279021 0.182326
117 17 15.1267 1.8733 2.8668 0.279021 0.182326
118 17 15.1267 1.8733 2.8668 0.279021 0.182326
119 17 15.1267 1.8733 2.8668 0.279021 0.182326
120 17 15.1267 1.8733 2.8668 0.279021 0.182326
121 17 15.1267 1.8733 2.8668 0.279021 0.182326
122 17 15.1267 1.8733 2.8668 0.279021 0.182326
123 17 15.1267 1.8733 2.8668 0.279021 0.182326
124 17 15.1267 1.8733 2.8668 0.279021 0.182326
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 14/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
125 18 15.1267 2.8733 2.8668 1.006815 1.009097
126 18 15.1267 2.8733 2.8668 1.006815 1.009097
127 18 15.1267 2.8733 2.8668 1.006815 1.009097
128 18 15.1267 2.8733 2.8668 1.006815 1.009097
129 18 15.1267 2.8733 2.8668 1.006815 1.009097
130 18 15.1267 2.8733 2.8668 1.006815 1.009097
131 18 15.1267 2.8733 2.8668 1.006815 1.009097
132 18 15.1267 2.8733 2.8668 1.006815 1.009097
133 18 15.1267 2.8733 2.8668 1.006815 1.009097
134 18 15.1267 2.8733 2.8668 1.006815 1.009097
135 19 15.1267 3.8733 2.8668 2.466302 3.332178
136 19 15.1267 3.8733 2.8668 2.466302 3.332178
137 19 15.1267 3.8733 2.8668 2.466302 3.332178
138 19 15.1267 3.8733 2.8668 2.466302 3.332178
139 19 15.1267 3.8733 2.8668 2.466302 3.332178
140 19 15.1267 3.8733 2.8668 2.466302 3.332178
141 19 15.1267 3.8733 2.8668 2.466302 3.332178
142 19 15.1267 3.8733 2.8668 2.466302 3.332178
143 20 15.1267 4.8733 2.8668 4.912131 8.350130
144 20 15.1267 4.8733 2.8668 4.912131 8.350130
145 20 15.1267 4.8733 2.8668 4.912131 8.350130
146 21 15.1267 5.8733 2.8668 8.598952 17.616813
147 21 15.1267 5.8733 2.8668 8.598952 17.616813
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 15/35
Tabel 7. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
148 21 15.1267 5.8733 2.8668 8.598952 17.616813
149 21 15.1267 5.8733 2.8668 8.598952 17.616813
150 22 15.1267 6.8733 2.8668 13.781414 33.041395
Jumlah -39.583155 449.957129
)583155,39()148)(149(
150
)2)(1(
3
Skewness
s
X Xi
nn
nSkewness
= -0.269249
√
SES = 0.19803837
Rasio Skewness = iai
Rasio Skewness =0,0
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 16/35
Rasio Skewness = -1,359578
Karena nilai rasio skewness -1,359578 dan berada diantara -1.96 dan 1.96,
berarti kurva distribusi binomial tersebut normal berdasarkan kemencengan
kurvanya.
)147)(148(
)149(3
)957129,449()147)(148)(149(
)151(150
)3)(2(
)1(3
)3)(2)(1(
)1(
2
24
Kurtosis
nn
n
s
X Xi
nnn
nnKurtosis
= 0.082576
√
SEK = 0,393583
Rasio Kurtosis = iai
Rasio Kurtosis =0,5
Rasio Kurtosis = 0,2098057
Karena nilai rasio kurtosis 0,2098057 dan berada diantara -1.96 dan 1.96, berarti
kurva distribusi binomial tersebut normal berdasarkan kecondongan kurvanya.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 17/35
Berdasarkan perhitungan dengan menggunakan software Minitab 16, maka
dapat dilihat gambar grafik beserta hasil perhitungannya di bawah ini:
2118151296
Median
Mean
16.0015.7515.5015.2515.0014.7514.50
1st Quartile 13.000
M edian 15.0003rd Quartile 17.000
Maximum 22.000
14.664 15.589
15.000 16.000
2.575 3.234
A -Squared 1.30
P -V alue < 0.005
Mean 15.127
StDev 2.867
V ariance 8.219
Skewness -0.269249
Kurtosis 0.082576
N 150
M inimum 6.000
A nderson-Darling N ormality Test
95% C onfidence Interv al for Mean
95% C onfidence Interval for Median
95% C onfidence Interv al for StDev95 % Confidence Intervals
Summary for Binomial
Gambar 3. Kurva Skewness dan Kurtosis Distribusi Binomial
Keterangan: karena nilai skewness dan kurtosis di antara ± 1.96, maka
bentuk grafik normalitasnya mengumpul di tengah (berbentuk seperti lonceng).
2. Distribusi Gamma
Adapun untuk langkah-langkah untuk membangkitkan data distribusi
gamma terdapat pada flowchart berikut. Ketentuan-ketentuan yang diberikan
pada data distribusi gamma adalah:
1. Jumlah data (generate) = 150
2. Shape parameter = 7
3. Scale parameter = 5
4. Threshold parameter = 0,0
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 18/35
Mulai
1. Klik Calc padaMenu Bar
2. Pilih Random3. Klik Gamma
Input:
Generate : 150 Shape Parameter: 7
Scale Parameter: 5 Threshold
Parameter : 0,0
Proses Random
Print :150
Selesai
Gambar 4. Flowchart Pembangkitan Data Distribusi Gamma
Tabel 8. Data Bilangan Random Distribusi Gamma
No Hasil No Hasil No Hasil No Hasil No Hasil
1 10.9062 16 19.2220 31 23.3011 46 27.4442 61 30.5599
2 11.9965 17 19.9879 32 23.5032 47 27.6178 62 30.9813
3 12.2602 18 20.3335 33 23.6701 48 27.7520 63 31.1297
4 12.6182 19 20.4310 34 23.6773 49 28.1644 64 31.2004
5 15.1994 20 20.6145 35 23.9103 50 28.4409 65 31.3167
6 15.9978 21 21.2667 36 24.3371 51 28.7590 66 31.4351
7 16.0645 22 21.9321 37 24.3732 52 28.9346 67 31.5616
8 16.9282 23 22.1904 38 24.8321 53 29.4972 68 31.7142
9 16.9821 24 22.6218 39 24.9279 54 29.5745 69 31.8096
10 17.2982 25 22.6561 40 26.1507 55 29.7250 70 31.9729
11 17.4798 26 22.7865 41 26.2277 56 29.7989 71 32.1008
12 17.5922 27 22.9607 42 26.3328 57 29.9159 72 32.1543
13 17.7966 28 22.9789 43 27.0954 58 30.1183 73 32.4062
14 17.9416 29 23.2518 44 27.2112 59 30.1642 74 32.4369
15 19.1903 30 23.2825 45 27.3194 60 30.4446 75 32.5840
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 19/35
Tabel 8. Data Bilangan Random Distribusi Gamma (Lanjutan)
No Hasil No Hasil No Hasil No Hasil No Hasil76 33.0821 91 35.8414 106 40.2899 121 45.4045 136 53.6507
77 33.1069 92 36.6770 107 40.4862 122 45.7913 137 54.0913
78 33.7099 93 37.0458 108 41.5977 123 45.9445 138 54.1004
79 33.8580 94 37.5532 109 42.0100 124 46.3361 139 54.4601
80 33.9151 95 37.8077 110 42.4898 125 46.5509 140 54.7571
81 34.2309 96 38.3755 111 42.8176 126 47.1999 141 56.7374
82 34.3364 97 38.3774 112 43.9733 127 47.3150 142 57.2407
83 34.4234 98 38.4222 113 44.0152 128 47.7343 143 57.5343
84 34.5519 99 38.6773 114 44.3554 129 48.2174 144 58.204685 34.8480 100 38.7437 115 44.3898 130 48.8687 145 59.0535
86 35.0600 101 38.8017 116 44.5588 131 50.2410 146 59.4449
87 35.0999 102 39.5681 117 44.6934 132 50.4061 147 63.3753
88 35.3198 103 39.5773 118 44.8671 133 51.0824 148 63.3902
89 35.8126 104 39.9896 119 45.0164 134 52.5999 149 67.1089
90 35.8377 105 40.0168 120 45.3419 135 53.2459 150 78.0758
2.1. Pengujian Distribusi Gamma
Adapun data bilangan bilangan random data distribusi gamma dapat
dilihat pada Tabel 9.
Tabel 9. Bilangan Random Data Distribusi Gamma
Data Distribusi Gamma
10.9062 19.2220 23.3011 27.4442 30.5599 33.0821 35.8414 40.2899 45.4045 53.6507
11.9965 19.9879 23.5032 27.6178 30.9813 33.1069 36.6770 40.4862 45.7913 54.0913
12.2602 20.3335 23.6701 27.7520 31.1297 33.7099 37.0458 41.5977 45.9445 54.1004
12.6182 20.4310 23.6773 28.1644 31.2004 33.8580 37.5532 42.0100 46.3361 54.4601
15.1994 20.6145 23.9103 28.4409 31.3167 33.9151 37.8077 42.4898 46.5509 54.7571
15.9978 21.2667 24.3371 28.7590 31.4351 34.2309 38.3755 42.8176 47.1999 56.7374
16.0645 21.9321 24.3732 28.9346 31.5616 34.3364 38.3774 43.9733 47.3150 57.2407
16.9282 22.1904 24.8321 29.4972 31.7142 34.4234 38.4222 44.0152 47.7343 57.5343
16.9821 22.6218 24.9279 29.5745 31.8096 34.5519 38.6773 44.3554 48.2174 58.2046
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 20/35
Tabel 9. Bilangan Random Data Distribusi Gamma (Lanjutan)
Data Distribusi Gamma
17.2982 22.6561 26.1507 29.7250 31.9729 34.8480 38.7437 44.3898 48.8687 59.0535
17.4798 22.7865 26.2277 29.7989 32.1008 35.0600 38.8017 44.5588 50.2410 59.4449
17.5922 22.9607 26.3328 29.9159 32.1543 35.0999 39.5681 44.6934 50.4061 63.3753
17.7966 22.9789 27.0954 30.1183 32.4062 35.3198 39.5773 44.8671 51.0824 63.3902
17.9416 23.2518 27.2112 30.1642 32.4369 35.8126 39.9896 45.0164 52.5999 67.1089
19.1903 23.2825 27.3194 30.4446 32.5840 35.8377 40.0168 45.3419 53.2459 78.0758
Langkah-langkah pengujian yang dilakukan adalah sebagai berikut:
1. Rumusan Normal
Ho : data berdistribusi gamma
Hi : data tidak berdistribusi gamma
2. Asumsikan α = 0,05
3. Tentukan nilai max, min, range, banyak kelas, dan panjang kelas
Data maksimum = 78,0758
Data minimum = 10,9062
R = Data max – Data min = 78,0758 – 10,9062 = 67,1696
K = 1 + 3,3 log (N)
K = 1 + 3,3 log 150 = 8,1811 9
2103,8
1811,8
0758,78
I
K
R I
Setelah didapat nilai dari Max, Min, Range, jumlah kelas dan panjang
kelas maka data tersebut dirangkum di dalam sebuah tabel frekuensi. Tabel
frekuensi dapat dilhat seperti Tabel 10.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 21/35
Tabel 10. Tabel Frekuensi Data Pengujian Distribusi Gamma
Interval BKB BKA Xi Frekuensi (Oi) Xi.Oi
10.9062 - 19.1164 -∞ 19.11645 15.0113 14 210.1582
19.1165 - 27.3267 19.11645 27.32675 23.2216 31 719.8696
27.3268 - 35.5370 27.32675 35.53705 31.4319 43 1351.5717
35.5371 - 43.7473 35.53705 43.74735 39.6422 23 911.7706
43.7474 - 51.9576 43.74735 51.95765 47.8525 22 1052.7550
51.9577 - 60.1679 51.95765 60.16795 56.0628 13 728.8164
60.1680 - 68.3782 60.16795 68.37825 64.2731 3 192.8193
68.3783 - 76.5885 68.37825 76.58855 72.4834 0 0.0000
76.5886 - 84.7988 76.58855 ∞ 80.6937 1 80.6937
Jumlah 150 5248.4545
4. Hitung nilai rata-rata dari tabel distribusi frekuensi.
io
Xioi
.
98969,34
150
4545,5248
5. Menghitung peluang (P) dari masing-masing kelas dengan menggunakan
software Minitab agar lebih mudah, sehingga akan didapatlkan hasil seperti
Tabel 11.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 22/35
Tabel 11. Perhitungan Frekuensi Peluang Data Distribusi Gamma
Interval BKB BKA Oi P(X<BKB) P(X<BKA)Luas
Kurva
10.9062 - 19.1165 -∞ 19.11645 14 0 0.093086 0.093086
19.1166 - 27.3268 19.11645 27.32675 31 0.093086 0.308529 0.215443
27.3269 - 35.5372 27.32675 35.53705 43 0.308529 0.566167 0.257639
35.5373 - 43.7475 35.53705 43.74735 23 0.566167 0.769437 0.203270
43.7476 - 51.9578 43.74735 51.95765 22 0.769437 0.892678 0.123240
51.9579 - 60.1682 51.95765 60.16795 13 0.892678 0.955026 0.062349
60.1683 - 68.3785 60.16795 68.37825 3 0.955026 0.982675 0.027649
68.3786 - 76.5888 68.37825 76.58855 0 0.982675 0.993767 0.011092
76.5889 - 84.7992 76.58855 ∞ 1 0.993767 1 0.006233
Jumlah 150 1.0000
6. Hitung nilai ekspektasinya (ei) untuk setiap interval.
ei = luas ke-i x n
misalnya: e1 = 0,093087 x 150 = 13,96310
Sehingga akan didapatkan hasil dalam tabel berikut ini.
Tabel 12. Perhitungan Nilai Ekspektasi (ei) Gamma
Interval Oi ei
10.9062 - 19.1164 14 13.96288
19.1165 - 27.3267 31 32.31642
27.3268 - 35.5370 43 38.64582
35.5371 - 43.7473 23 30.49049
43.7474 - 51.9576 22 18.48602
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 23/35
Tabel 12. Perhitungan Nilai Ekspektasi (ei) Gamma (Lanjutan)
Interval Oi ei
51.9577 - 60.1679 13 9.35233
60.1680 - 68.3782 3 4.14729
68.3783 - 76.5885 0 1.66385
76.5886 - 84.7988 1 0.93489
Jumlah 150 150
Karena terdapat nilai ei < 5 maka akan dilakukan penggabungan kelas ke
interval terdekat dengan nilai ei tersebut. Maka tabel nilai ei menjadi:
Tabel 13. Penggabungan Nilai Ekspektasi (ei) Gamma
Interval Oi ei
10.9062 - 19.1165 14 13.96288
19.1166 - 27.3268 31 32.31642
27.3269 - 35.5372 43 38.64582
35.5373 - 43.7475 23 30.49049
43.7476 - 51.9578 22 18.48602
51.9579 - 60.1682 13 9.35233
60.1683 - 68.3785 3 4.14729
68.3786 - 76.5888 0 1.66385
76.5889 - 84.7992 1 0.93489
7. Setelah didapatkan nilai ei dan Oi maka dapat dihitung nilai χ 2
hitung
χ 2
hitung
Nilai dari χ 2hitung untuk masing-masing kelas dapat dilihat pada Tabel 14.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 24/35
Tabel 14. Tabel Nilai χ 2
hitungData Pengujian Distribusi Gamma
Interval Oi Ei χ
10.9062 - 19.1165 14 13.96288 0.000099
19.1166 - 27.3268 31 32.31642 0.053624721
27.3269 - 35.5372 43 38.64582 0.49058021
35.5373 - 43.7475 23 30.49049 1.840162271
43.7476 - 51.9578 22 18.48602 0.667966133
51.9579 - 60.1682 13 9.35233 1.422689643
60.1683 - 84.7992 4 6.74603 1.117796443
Jumlah 5.5929
8. Hitung χ 2
tabel
Jumlah kelas (k) = 7
V (derajat bebas) = 7 – 4 = 3
α = 0,05
Sehingga nilai χ 2
tabel yang diperoleh = 7,81473
9. Kesimpulan: Ho diterima (χ 2
hitung = 5,5929 < χ 2
tabel = 7,81473) atau dapat
disimpulkan bahwa data tersebut berdistribusi gamma.
Adapun gambar kurva distribusi gamma adalah sebagai berikut :
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 25/35
Gambar 5. Kurva Distribusi Gamma
10. Kurtosis dan Skewness
Adapun data yang digunakan dalam perhitungan Kurtosis dan skewness dapat
dilihat pada tabel berikut :
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness
No Xi X Xi-X S ((Xi-X)/S)
((Xi-X)/S)
1 10.9062 34.753908 -23.8477 12.726871 -6.579196 12.328126
2 11.9965 34.753908 -22.7574 12.726871 -5.717448 10.223579
3 12.2602 34.753908 -22.4937 12.726871 -5.521036 9.758000
4 12.6182 34.753908 -22.1357 12.726871 -5.261563 9.151376
5 15.1994 34.753908 -19.5545 12.726871 -3.627231 5.573144
6 15.9978 34.753908 -18.7561 12.726871 -3.200830 4.717191
7 16.0645 34.753908 -18.6894 12.726871 -3.166829 4.650497
8 16.9282 34.753908 -17.8257 12.726871 -2.747745 3.848592
9 16.9821 34.753908 -17.7718 12.726871 -2.722897 3.802259
0
5
10
15
20
25
30
35
40
45
50
1 2 3 4 5 6 7
F r e k u e n s i
Kelas
Oi
ei
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 26/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
10 17.2982 34.753908 -17.4557 12.726871 -2.580183 3.538892
11 17.4798 34.753908 -17.2741 12.726871 -2.500467 3.393866
12 17.5922 34.753908 -17.1617 12.726871 -2.451962 3.306371
13 17.7966 34.753908 -16.9573 12.726871 -2.365420 3.151697
14 17.9416 34.753908 -16.8123 12.726871 -2.305237 3.045235
15 19.1903 34.753908 -15.5636 12.726871 -1.828796 2.236422
16 19.2220 34.753908 -15.5319 12.726871 -1.817647 2.218261
17 19.9879 34.753908 -14.7660 12.726871 -1.561798 1.812034
18 20.3335 34.753908 -14.4205 12.726871 -1.454696 1.648274
19 20.4310 34.753908 -14.3229 12.726871 -1.425382 1.604138
20 20.6145 34.753908 -14.1394 12.726871 -1.371292 1.523491
21 21.2667 34.753908 -13.4872 12.726871 -1.190147 1.261248
22 21.9321 34.753908 -12.8218 12.726871 -1.022555 1.030186
23 22.1904 34.753908 -12.5635 12.726871 -0.961984 0.949637
24 22.6218 34.753908 -12.1321 12.726871 -0.866260 0.825780
25 22.6561 34.753908 -12.0978 12.726871 -0.858923 0.816467
26 22.7865 34.753908 -11.9674 12.726871 -0.831448 0.781832
27 22.9607 34.753908 -11.7932 12.726871 -0.795658 0.737285
28 22.9789 34.753908 -11.7750 12.726871 -0.791978 0.732742
29 23.2518 34.753908 -11.5021 12.726871 -0.738185 0.667145
30 23.2825 34.753908 -11.4714 12.726871 -0.732301 0.660064
31 23.3011 34.753908 -11.4528 12.726871 -0.728735 0.655783
32 23.5032 34.753908 -11.2507 12.726871 -0.690843 0.610716
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 27/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
33 23.6701 34.753908 -11.0838 12.726871 -0.660546 0.575269
34 23.6773 34.753908 -11.0766 12.726871 -0.659265 0.573782
35 23.9103 34.753908 -10.8436 12.726871 -0.618521 0.526995
36 24.3371 34.753908 -10.4168 12.726871 -0.548319 0.448791
37 24.3732 34.753908 -10.3807 12.726871 -0.542641 0.442605
38 24.8321 34.753908 -9.9218 12.726871 -0.473810 0.369379
39 24.9279 34.753908 -9.8260 12.726871 -0.460220 0.355321
40 26.1507 34.753908 -8.6032 12.726871 -0.308902 0.208815
41 26.2277 34.753908 -8.5262 12.726871 -0.300674 0.201432
42 26.3328 34.753908 -8.4211 12.726871 -0.289692 0.191682
43 27.0954 34.753908 -7.6585 12.726871 -0.217902 0.131124
44 27.2112 34.753908 -7.5427 12.726871 -0.208172 0.123376
45 27.3194 34.753908 -7.4345 12.726871 -0.199336 0.116443
46 27.4442 34.753908 -7.3097 12.726871 -0.189467 0.108820
47 27.6178 34.753908 -7.1361 12.726871 -0.176287 0.098846
48 27.7520 34.753908 -7.0019 12.726871 -0.166525 0.091616
49 28.1644 34.753908 -6.5896 12.726871 -0.138805 0.071868
50 28.4409 34.753908 -6.3130 12.726871 -0.122049 0.060540
51 28.7590 34.753908 -5.9949 12.726871 -0.104514 0.049230
52 28.9346 34.753908 -5.8194 12.726871 -0.095600 0.043713
53 29.4972 34.753908 -5.2567 12.726871 -0.070464 0.029104
54 29.5745 34.753908 -5.1794 12.726871 -0.067402 0.027430
55 29.7250 34.753908 -5.0289 12.726871 -0.061694 0.024378
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 28/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
56 29.7989 34.753908 -4.9550 12.726871 -0.059015 0.022976
57 29.9159 34.753908 -4.8380 12.726871 -0.054934 0.020883
58 30.1183 34.753908 -4.6356 12.726871 -0.048323 0.017601
59 30.1642 34.753908 -4.5897 12.726871 -0.046902 0.016914
60 30.4446 34.753908 -4.3094 12.726871 -0.038821 0.013145
61 30.5599 34.753908 -4.1941 12.726871 -0.035788 0.011794
62 30.9813 34.753908 -3.7726 12.726871 -0.026046 0.007721
63 31.1297 34.753908 -3.6242 12.726871 -0.023093 0.006576
64 31.2004 34.753908 -3.5535 12.726871 -0.021767 0.006077
65 31.3167 34.753908 -3.4372 12.726871 -0.019699 0.005320
66 31.4351 34.753908 -3.3188 12.726871 -0.017733 0.004624
67 31.5616 34.753908 -3.1923 12.726871 -0.015781 0.003958
68 31.7142 34.753908 -3.0397 12.726871 -0.013624 0.003254
69 31.8096 34.753908 -2.9443 12.726871 -0.012382 0.002864
70 31.9729 34.753908 -2.7810 12.726871 -0.010434 0.002280
71 32.1008 34.753908 -2.6531 12.726871 -0.009059 0.001888
72 32.1543 34.753908 -2.5997 12.726871 -0.008523 0.001741
73 32.4062 34.753908 -2.3477 12.726871 -0.006277 0.001158
74 32.4369 34.753908 -2.3170 12.726871 -0.006034 0.001099
75 32.5840 34.753908 -2.1699 12.726871 -0.004956 0.000845
76 33.0821 34.753908 -1.6718 12.726871 -0.002267 0.000298
77 33.1069 34.753908 -1.6470 12.726871 -0.002167 0.000280
78 33.7099 34.753908 -1.0440 12.726871 -0.000552 0.000045
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 29/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
79 33.8580 34.753908 -0.8959 12.726871 -0.000349 0.000025
80 33.9151 34.753908 -0.8388 12.726871 -0.000286 0.000019
81 34.2309 34.753908 -0.5230 12.726871 -0.000069 0.000003
82 34.3364 34.753908 -0.4175 12.726871 -0.000035 0.000001
83 34.4234 34.753908 -0.3305 12.726871 -0.000018 0.000000
84 34.5519 34.753908 -0.2020 12.726871 -0.000004 0.000000
85 34.8480 34.753908 0.0941 12.726871 0.000000 0.000000
86 35.0600 34.753908 0.3061 12.726871 0.000014 0.000000
87 35.0999 34.753908 0.3460 12.726871 0.000020 0.000001
88 35.3198 34.753908 0.5659 12.726871 0.000088 0.000004
89 35.8126 34.753908 1.0587 12.726871 0.000576 0.000048
90 35.8377 34.753908 1.0838 12.726871 0.000618 0.000053
91 35.8414 34.753908 1.0875 12.726871 0.000624 0.000053
92 36.6770 34.753908 1.9231 12.726871 0.003450 0.000521
93 37.0458 34.753908 2.2919 12.726871 0.005840 0.001052
94 37.5532 34.753908 2.7993 12.726871 0.010641 0.002341
95 37.8077 34.753908 3.0538 12.726871 0.013815 0.003315
96 38.3755 34.753908 3.6216 12.726871 0.023043 0.006557
97 38.3774 34.753908 3.6235 12.726871 0.023080 0.006571
98 38.4222 34.753908 3.6683 12.726871 0.023946 0.006902
99 38.6773 34.753908 3.9234 12.726871 0.029297 0.009032
100 38.7437 34.753908 3.9898 12.726871 0.030810 0.009659
101 38.8017 34.753908 4.0478 12.726871 0.032172 0.010232
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 30/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
102 39.5681 34.753908 4.8142 12.726871 0.054127 0.020475
103 39.5773 34.753908 4.8234 12.726871 0.054437 0.020631
104 39.9896 34.753908 5.2357 12.726871 0.069624 0.028643
105 40.0168 34.753908 5.2629 12.726871 0.070716 0.029243
106 40.2899 34.753908 5.5359 12.726871 0.082302 0.035800
107 40.4862 34.753908 5.7323 12.726871 0.091373 0.041155
108 41.5977 34.753908 6.8438 12.726871 0.155496 0.083617
109 42.0100 34.753908 7.2561 12.726871 0.185332 0.105666
110 42.4898 34.753908 7.7359 12.726871 0.224577 0.136507
111 42.8176 34.753908 8.0637 12.726871 0.254351 0.161155
112 43.9733 34.753908 9.2194 12.726871 0.380142 0.275377
113 44.0152 34.753908 9.2613 12.726871 0.385347 0.280416
114 44.3554 34.753908 9.6015 12.726871 0.429395 0.323948
115 44.3898 34.753908 9.6359 12.726871 0.434016 0.328605
116 44.5588 34.753908 9.8049 12.726871 0.457260 0.352277
117 44.6934 34.753908 9.9395 12.726871 0.476357 0.372029
118 44.8671 34.753908 10.1132 12.726871 0.501766 0.398720
119 45.0164 34.753908 10.2625 12.726871 0.524311 0.422784
120 45.3419 34.753908 10.5880 12.726871 0.575808 0.479038
121 45.4045 34.753908 10.6506 12.726871 0.586083 0.490470
122 45.7913 34.753908 11.0374 12.726871 0.652288 0.565700
123 45.9445 34.753908 11.1906 12.726871 0.679823 0.597761
124 46.3361 34.753908 11.5822 12.726871 0.753717 0.685927
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 31/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
125 46.5509 34.753908 11.7970 12.726871 0.796438 0.738249
126 47.1999 34.753908 12.4460 12.726871 0.935241 0.914601
127 47.3150 34.753908 12.5611 12.726871 0.961420 0.948894
128 47.7343 34.753908 12.9803 12.726871 1.060948 1.082079
129 48.2174 34.753908 13.4635 12.726871 1.183875 1.252394
130 48.8687 34.753908 14.1148 12.726871 1.364138 1.512903
131 50.2410 34.753908 15.4871 12.726871 1.801952 2.192759
132 50.4061 34.753908 15.6522 12.726871 1.860209 2.287787
133 51.0824 34.753908 16.3285 12.726871 2.111902 2.709558
134 52.5999 34.753908 17.8460 12.726871 2.757150 3.866165
135 53.2459 34.753908 18.4920 12.726871 3.067534 4.457102
136 53.6507 34.753908 18.8968 12.726871 3.273417 4.860360
137 54.0913 34.753908 19.3374 12.726871 3.507751 5.329728
138 54.1004 34.753908 19.3465 12.726871 3.512703 5.339761
139 54.4601 34.753908 19.7062 12.726871 3.712306 5.748109
140 54.7571 34.753908 20.0032 12.726871 3.882671 6.102496
141 56.7374 34.753908 21.9835 12.726871 5.153780 8.902279
142 57.2407 34.753908 22.4868 12.726871 5.515909 9.745918
143 57.5343 34.753908 22.7804 12.726871 5.734826 10.265032
144 58.2046 34.753908 23.4507 12.726871 6.256046 11.527449
145 59.0535 34.753908 24.2995 12.726871 6.960323 13.289416
146 59.4449 34.753908 24.6910 12.726871 7.302179 14.166742
147 63.3753 34.753908 28.6214 12.726871 11.373846 25.578582
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 32/35
Tabel 4.15. Data Perhitungan Kurtosis dan Skewness (Lanjutan)
No Xi X Xi-X S ((Xi-X)/S)3 ((Xi-X)/S)4
148 63.3902 34.753908 28.6363 12.726871 11.391622 25.631896
149 67.1089 34.753908 32.3550 12.726871 16.430830 41.771429
150 78.0758 34.753908 43.3219 12.726871 39.441966 134.259413
Jumlah 82.0452 457.0577
)0452,82()148)(149(
150
)2)(1(
3
Skewness
s
X Xi
nn
nSkewness
= 0,558080
√
SES = 0.19803837
Rasio Skewness = iai
Rasio Skewness =0,0
Rasio Skewness = 2,8180413
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 33/35
Karena nilai rasio skewness 2,8180413 dan tidak berada diantara -1,96
dan 1,96, berarti kurva distribusi gamma tersebut tidak normal berdasarkan
kemencengan kurvanya.
)147)(148(
)149(3)0577,457(
)147)(148)(149(
)151(150
)3)(2(
)1(3
)3)(2)(1(
)1(
2
24
Kurtosis
nn
n
s
X Xi
nnn
nnKurtosis
= 0,132189
√
SEK = 0,393583
Rasio Kurtosis = iai
Rasio Kurtosis =0,5
Rasio Kurtosis = 0,3358601
Karena nilai rasio kurtosis 0,3358601 dan berada diantara -1,96 dan 1,96,
berarti kurva distribusi gamma tersebut normal berdasarkan kecondongan
kurvanya.
Berdasarkan perhitungan dengan menggunakan software Minitab 16, maka
dapat dilihat gambar grafik beserta hasil perhitungannya di bawah ini:
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 34/35
7560453015
Median
Mean
37363534333231
1st Quartile 24.717
M edian 32.833
3rd Q uartile 44.100
Maximum 78.076
32.701 36.807
31.168 35.201
11.431 14.356
A -Squared 0.88
P -V alue 0.024
Mean 34.754
StDev 12.727
V ariance 161.973
Skewness 0.558080
Kurtosis 0.132189
N 150
M inimum 10.906
A nderson-Darling N ormality Test
95% C onfidence Interval for Mean
95% C onfidence Interval for Median
95% C onfidence Interv al for StD ev95 % Confidence Intervals
Summary for Gamma
Gambar 6. Kurva Skewness dan Kurtosis Distribusi Gamma
Keterangan: karena nilai skewness dan kurtosis di antara ± 1,96, maka
bentuk grafik normalitasnya mengumpul di tengah.
5/10/2018 PENGUJIAN DISTRIBUSI - slidepdf.com
http://slidepdf.com/reader/full/pengujian-distribusi 35/35
TUGAS
PENGUJIAN DISTRIBUSI
Oleh:
PERLIN MARTUA
(090403097)
L A B O R A T O R I U M P E N G U K U R A N D A N S T A T I S T I KP R O G R A M S T U D I R E G U L E R
D E P A R T E M E N T E K N I K I N D U S T R I
F A K U L T A S T E K N I K
UNIVERSITAS SUMATERA UTARA
M E D A N
2 0 1 1