DAFTAR NILAI MATEMATIKA KELAS 8E, 8F, 8G, 8H di SMP N 5 JAMBI T.A 2013/2014

nokelompok kelas

8 e 8 f 8 g 8 h1 90 90 86 882 89 91 81 863 91 78 81 844 88 82 75 805 86 82 84 866 77 75 76 837 77 81 77 838 81 77 76 769 77 76 76 7610 82 75 78 7711 80 75 75 8412 84 77 75 8013 76 75 78 8514 75 76 80 8115 83 75 80 7916 75 75 82 7517 75 76 78 7518 82 75 75 7819 77 77 75 7520 77 76 75 7721 75 78 75 8222 84 79 81 7523 77 75 75 7524 75 79 77 7525 75 75 75 7526 75 77 75 8127 75 75 75 7628 75 75 80 7529 77 76 79 7530 75 75 75 7531 75 75 75 7532 76 75 75 7533 75 75 75 7534 75 75 75 7535 76 76 75 7536 75 75 75 7537 75 75 7538 7539 75

jumlah 2912 3004 2780 2897rata -rata 78.7027 77.02564 77.22222 78.2973

n 37 39 36 37

MENENTUKAN VARIANSI TIAP TABEL

nokelompok nilai

X1 X2 X3 X4

1 90 90 86 882 89 91 81 863 91 78 81 844 88 82 75 805 86 82 84 866 77 75 76 837 77 81 77 838 81 77 76 769 77 76 76 7610 82 75 78 7711 80 75 75 8412 84 77 75 8013 76 75 78 8514 75 76 80 8115 83 75 80 7916 75 75 82 7517 75 76 78 7518 82 75 75 7819 77 77 75 7520 77 76 75 7721 75 78 75 8222 84 79 81 7523 77 75 75 7524 75 79 77 7525 75 75 75 7526 75 77 75 8127 75 75 75 7628 75 75 80 7529 77 76 79 7530 75 75 75 7531 75 75 75 7532 76 75 75 7533 75 75 75 7534 75 75 75 7535 76 76 75 7536 75 75 75 7537 75 75 7538 7539 75

jumlah 2912 3004 2780 2897rata -rata 78.7027 77.02564 77.22222 78.2973

N 37 39 36 37

No(Xi –X) (Xi – X) (Xi – X) (Xi – X)

1 11.2972973 12.97435897 8.777778 9.7027032 10.2972973 13.97435897 3.777778 7.7027033 12.2972973 0.974358974 3.777778 5.7027034 9.297297297 4.974358974 -2.22222 1.7027035 7.297297297 4.974358974 6.777778 7.7027036 -1.7027027 -2.025641026 -1.22222 4.7027037 -1.7027027 3.974358974 -0.22222 4.7027038 2.297297297 -0.025641026 -1.22222 -2.29739 -1.7027027 -1.025641026 -1.22222 -2.2973

10 3.297297297 -2.025641026 0.777778 -1.297311 1.297297297 -2.025641026 -2.22222 5.70270312 5.297297297 -0.025641026 -2.22222 1.70270313 -2.7027027 -2.025641026 0.777778 6.70270314 -3.7027027 -1.025641026 2.777778 2.70270315 4.297297297 -2.025641026 2.777778 0.70270316 -3.7027027 -2.025641026 4.777778 -3.297317 -3.7027027 -1.025641026 0.777778 -3.297318 3.297297297 -2.025641026 -2.22222 -0.297319 -1.7027027 -0.025641026 -2.22222 -3.297320 -1.7027027 -1.025641026 -2.22222 -1.297321 -3.7027027 0.974358974 -2.22222 3.70270322 5.297297297 1.974358974 3.777778 -3.297323 -1.7027027 -2.025641026 -2.22222 -3.297324 -3.7027027 1.974358974 -0.22222 -3.297325 -3.7027027 -2.025641026 -2.22222 -3.297326 -3.7027027 -0.025641026 -2.22222 2.70270327 -3.7027027 -2.025641026 -2.22222 -2.297328 -3.7027027 -2.025641026 2.777778 -3.297329 -1.7027027 -1.025641026 1.777778 -3.297330 -3.7027027 -2.025641026 -2.22222 -3.297331 -3.7027027 -2.025641026 -2.22222 -3.297332 -2.7027027 -2.025641026 -2.22222 -3.297333 -3.7027027 -2.025641026 -2.22222 -3.297334 -3.7027027 -2.025641026 -2.22222 -3.297335 -2.7027027 -1.025641026 -2.22222 -3.297336 -3.7027027 -2.025641026 -2.22222 -3.297337 -3.7027027 -2.025641026   -3.297338   -2.025641026    39   -2.025641026    

No(X1 -X)2  (X2 -X)2  (X3 -X)2  (X4 -X)2

1 127.6289262 168.3339908 77.04938 94.142442 106.0343316 195.2827087 14.2716 59.331633 151.2235208 0.949375411 14.2716 32.520824 86.43973703 24.74424721 4.938272 2.8991965 53.25054785 24.74424721 45.93827 59.331636 2.899196494 4.103221565 1.493827 22.115417 2.899196494 15.79552926 0.049383 22.115418 5.277574872 0.000657462 1.493827 5.2775759 2.899196494 1.051939513 1.493827 5.27757510 10.87216947 4.103221565 0.604938 1.6829811 1.682980278 4.103221565 4.938272 32.5208212 28.06135866 0.000657462 4.938272 2.89919613 7.304601899 4.103221565 0.604938 44.9262214 13.7100073 1.051939513 7.716049 7.30460215 18.46676406 4.103221565 7.716049 0.49379116 13.7100073 4.103221565 22.82716 10.8721717 13.7100073 1.051939513 0.604938 10.8721718 10.87216947 4.103221565 4.938272 0.08838619 2.899196494 0.000657462 4.938272 10.8721720 2.899196494 1.051939513 4.938272 1.6829821 13.7100073 0.949375411 4.938272 13.7100122 28.06135866 3.89809336 14.2716 10.8721723 2.899196494 4.103221565 4.938272 10.8721724 13.7100073 3.89809336 0.049383 10.8721725 13.7100073 4.103221565 4.938272 10.8721726 13.7100073 0.000657462 4.938272 7.30460227 13.7100073 4.103221565 4.938272 5.27757528 13.7100073 4.103221565 7.716049 10.8721729 2.899196494 1.051939513 3.160494 10.8721730 13.7100073 4.103221565 4.938272 10.8721731 13.7100073 4.103221565 4.938272 10.8721732 7.304601899 4.103221565 4.938272 10.8721733 13.7100073 4.103221565 4.938272 10.8721734 13.7100073 4.103221565 4.938272 10.8721735 7.304601899 1.051939513 4.938272 10.8721736 13.7100073 4.103221565 4.938272 10.8721737 13.7100073 4.103221565 0 10.8721738   4.103221565    39   4.103221565    

Jumlah 875.7297297 526.974359 310.2222 605.7297

HARGA-HARGA YANG PERLU UNTUK UJI BARTLETT

Sampel Dk 1dk

S I2 Log S I

2 Dk logS I2

1 36 0,02777 24,32 1,38 49,82 38 0,02631 13,86 1,14 43,383 35 0,0285 8,86 0,94 33,14 36 0,02777 16,82 1,22 44

Jumlah 145 170,28

UJI BARLET

1.HIPOTESIS : H0 = σ 1=σ2=σ3=σ4

2. NILAI α = 0,05

3. KRITERIA PENGUJIAN : TOLAK H0 JIKA X2 ≥ X2 (1 – α ) (K – 1 )

4. VARIASI

S12 = ∑ (X i−X )2

n−1=875,7297297

36=24,32

S22 = ∑ (X i−X )2

n−1=526,974359

38=13,86

S32 = ∑ (X i−X )2

n−1=310,222235

=8,86

S42 = ∑ (X i−X )2

n−1=605,729736

=16,82

5. VARIANSI GABUNGAN

S2 = ¿

S2 = 36 (24,32 )+38 (13,86 )+35 (8,86 )+36 (16,82)

36+38+35+36

S2 = 15,99

6. harga satuan B = log s2

B = log 15,99

B = 1,203

7. B = (log S2 ) . ∑ (n1−1 )

B = 1,203 x 144

B = 173,232

8. uji barlet ( digunakan chi kuadrat)

X2 = (ln 10) (B – ∑ (n1−1 ) log si2)

X2 = (2,3026) ( 173,232 - 170,28)

X2 = 6,7972

Kesimpulan : α = 0,05, dari daftar distribusi chi kuadrat degan dk = 3 di dapat X20,95(3) = 7,81.

Ternyata X2 = 6,7972 < 7,81 sehingga HIPOTESIS : H0 = σ 1=σ2=σ3=σ4 diterima dalam taraf nyata 0,05

no (x1 ) (x2) (x3) (x4)1 8100 8100 7396 77442 7921 8281 6561 73963 8281 6084 6561 70564 7744 6724 5625 64005 7396 6724 7056 73966 5929 5625 5776 68897 5929 6561 5929 68898 6561 5929 5776 57769 5929 5776 5776 5776

10 6724 5625 6084 592911 6400 5625 5625 705612 7056 5929 5625 640013 5776 5625 6084 722514 5625 5776 6400 656115 6889 5625 6400 624116 5625 5625 6724 562517 5625 5776 6084 562518 6724 5625 5625 608419 5929 5929 5625 562520 5929 5776 5625 592921 5625 6084 5625 672422 7056 6241 6561 562523 5929 5625 5625 562524 5625 6241 5929 562525 5625 5625 5625 562526 5625 5929 5625 656127 5625 5625 5625 577628 5625 5625 6400 562529 5929 5776 6241 562530 5625 5625 5625 562531 5625 5625 5625 562532 5776 5625 5625 562533 5625 5625 5625 562534 5625 5625 5625 562535 5776 5776 5625 562536 5625 5625 5625 562537 5625 5625 562538 562539 5625

Jumlah 230058 231912 214988 227433Rata – rata 6217.784 5946.462 5971.889 6146.838

Uji anava satu arah

Hipotesis :Ho : μ1=μ2=μ3=μ4

α = 0,05

kriteria pengujian, tolak H0 jika f.hitung ≥ F(1 – α) (v1 . v2)

untuk memperoleh daftar analisis variansi di perlukan harga – harga berikut:

RY = J 1+J 2+J3+J 4

∑ n1 =

(2912+3004+2780+2897)37+39+36+37

= (11588)2

149

= 134281744149

= 901.219,7583

AY = ( σ i2

∑ ni ) - RY

¿( 2912237+ 3004

2

39+ 2780

2

36+ 2892

2

37 )−901.219,7583= 901290,0464 – 901219,7583

= 70,2881

∑Y 2=∑ X12+∑ X2

2+¿∑ X 32+∑ X4

2 ¿

= 230058 + 231912 + 214988 + 227433

= 904391

DY = ∑Y 2- RY – AY

= 904391 – 901219,7583-70,2881

= 3100,9536

DENGAN :

K = 4

∑ n1=149

∑ (n1−1 )=145

Berdasarkan tabel – tabel daftar anava, ujistatistik diperoleh sebagai berikut:

f.tabel = (k−1)

(∑ n1−1) = 3145

f.hitung =

AY(K−1 )DY

(∑ n1−1) =

70,28814−1

3100,9536145

= 23,4221,38

=1,09

* kriteria pengujian

tolak H0 jika f.hitung ≥f(1-α) (v1 , v 2)

f(1-0,05)(3 . 145)sehingga peluang 0,95 didapat f = 2,67

*kesimpulan:

Ternyata f.hitung < f.tabel, jadi hipotesis H0 : μ1=μ2=μ3=μ4 diterima dalam taraf nyata 0,05

STATISTIKA LANJUTAN

Disusun oleh : AYU FEBRIYANTI MANALU

NPM:1200884202002

DOSEN PENGAMPU : Dra.risma simamora M.Pd

FAKULTAS KEGURUAN ILMU PENDIDIKAN

UNIVERSITAS BATANGHARI JAMBI

T.A 2014/2015