contoh statistika lanjutan
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contoh statistika lanjutan
- 1. DAFTAR NILAI MATEMATIKA KELAS 8E, 8F, 8G, 8H di SMP N 5 JAMBI T.A 2013/2014 no kelompok kelas 8 e 8 f 8 g 8 h 1 90 90 86 88 2 89 91 81 86 3 91 78 81 84 4 88 82 75 80 5 86 82 84 86 6 77 75 76 83 7 77 81 77 83 8 81 77 76 76 9 77 76 76 76 10 82 75 78 77 11 80 75 75 84 12 84 77 75 80 13 76 75 78 85 14 75 76 80 81 15 83 75 80 79 16 75 75 82 75 17 75 76 78 75 18 82 75 75 78 19 77 77 75 75 20 77 76 75 77 21 75 78 75 82 22 84 79 81 75 23 77 75 75 75 24 75 79 77 75 25 75 75 75 75 26 75 77 75 81 27 75 75 75 76 28 75 75 80 75 29 77 76 79 75 30 75 75 75 75 31 75 75 75 75 32 76 75 75 75 33 75 75 75 75 34 75 75 75 75 35 76 76 75 75 36 75 75 75 75 37 75 75 75 38 75 39 75 jumlah 2912 3004 2780 2897 rata -rata 78.7027 77.02564 77.22222 78.2973 n 37 39 36 37
- 2. MENENTUKAN VARIANSI TIAP TABEL no kelompok nilai X1 X2 X3 X4 1 90 90 86 88 2 89 91 81 86 3 91 78 81 84 4 88 82 75 80 5 86 82 84 86 6 77 75 76 83 7 77 81 77 83 8 81 77 76 76 9 77 76 76 76 10 82 75 78 77 11 80 75 75 84 12 84 77 75 80 13 76 75 78 85 14 75 76 80 81 15 83 75 80 79 16 75 75 82 75 17 75 76 78 75 18 82 75 75 78 19 77 77 75 75 20 77 76 75 77 21 75 78 75 82 22 84 79 81 75 23 77 75 75 75 24 75 79 77 75 25 75 75 75 75 26 75 77 75 81 27 75 75 75 76 28 75 75 80 75 29 77 76 79 75 30 75 75 75 75 31 75 75 75 75 32 76 75 75 75 33 75 75 75 75 34 75 75 75 75 35 76 76 75 75 36 75 75 75 75 37 75 75 75 38 75 39 75 jumlah 2912 3004 2780 2897 rata -rata 78.7027 77.02564 77.22222 78.2973 N 37 39 36 37
- 3. No (Xi X) (Xi X) (Xi X) (Xi X) 1 11.2972973 12.97435897 8.777778 9.702703 2 10.2972973 13.97435897 3.777778 7.702703 3 12.2972973 0.974358974 3.777778 5.702703 4 9.297297297 4.974358974 -2.22222 1.702703 5 7.297297297 4.974358974 6.777778 7.702703 6 -1.7027027 -2.025641026 -1.22222 4.702703 7 -1.7027027 3.974358974 -0.22222 4.702703 8 2.297297297 -0.025641026 -1.22222 -2.2973 9 -1.7027027 -1.025641026 -1.22222 -2.2973 10 3.297297297 -2.025641026 0.777778 -1.2973 11 1.297297297 -2.025641026 -2.22222 5.702703 12 5.297297297 -0.025641026 -2.22222 1.702703 13 -2.7027027 -2.025641026 0.777778 6.702703 14 -3.7027027 -1.025641026 2.777778 2.702703 15 4.297297297 -2.025641026 2.777778 0.702703 16 -3.7027027 -2.025641026 4.777778 -3.2973 17 -3.7027027 -1.025641026 0.777778 -3.2973 18 3.297297297 -2.025641026 -2.22222 -0.2973 19 -1.7027027 -0.025641026 -2.22222 -3.2973 20 -1.7027027 -1.025641026 -2.22222 -1.2973 21 -3.7027027 0.974358974 -2.22222 3.702703 22 5.297297297 1.974358974 3.777778 -3.2973 23 -1.7027027 -2.025641026 -2.22222 -3.2973 24 -3.7027027 1.974358974 -0.22222 -3.2973 25 -3.7027027 -2.025641026 -2.22222 -3.2973 26 -3.7027027 -0.025641026 -2.22222 2.702703 27 -3.7027027 -2.025641026 -2.22222 -2.2973 28 -3.7027027 -2.025641026 2.777778 -3.2973 29 -1.7027027 -1.025641026 1.777778 -3.2973 30 -3.7027027 -2.025641026 -2.22222 -3.2973 31 -3.7027027 -2.025641026 -2.22222 -3.2973 32 -2.7027027 -2.025641026 -2.22222 -3.2973 33 -3.7027027 -2.025641026 -2.22222 -3.2973 34 -3.7027027 -2.025641026 -2.22222 -3.2973 35 -2.7027027 -1.025641026 -2.22222 -3.2973 36 -3.7027027 -2.025641026 -2.22222 -3.2973 37 -3.7027027 -2.025641026 -3.2973 38 -2.025641026 39 -2.025641026
- 4. No (X1 -X)2 (X2 -X)2 (X3 -X)2 (X4 -X)2 1 127.6289262 168.3339908 77.04938 94.14244 2 106.0343316 195.2827087 14.2716 59.33163 3 151.2235208 0.949375411 14.2716 32.52082 4 86.43973703 24.74424721 4.938272 2.899196 5 53.25054785 24.74424721 45.93827 59.33163 6 2.899196494 4.103221565 1.493827 22.11541 7 2.899196494 15.79552926 0.049383 22.11541 8 5.277574872 0.000657462 1.493827 5.277575 9 2.899196494 1.051939513 1.493827 5.277575 10 10.87216947 4.103221565 0.604938 1.68298 11 1.682980278 4.103221565 4.938272 32.52082 12 28.06135866 0.000657462 4.938272 2.899196 13 7.304601899 4.103221565 0.604938 44.92622 14 13.7100073 1.051939513 7.716049 7.304602 15 18.46676406 4.103221565 7.716049 0.493791 16 13.7100073 4.103221565 22.82716 10.87217 17 13.7100073 1.051939513 0.604938 10.87217 18 10.87216947 4.103221565 4.938272 0.088386 19 2.899196494 0.000657462 4.938272 10.87217 20 2.899196494 1.051939513 4.938272 1.68298 21 13.7100073 0.949375411 4.938272 13.71001 22 28.06135866 3.89809336 14.2716 10.87217 23 2.899196494 4.103221565 4.938272 10.87217 24 13.7100073 3.89809336 0.049383 10.87217 25 13.7100073 4.103221565 4.938272 10.87217 26 13.7100073 0.000657462 4.938272 7.304602 27 13.7100073 4.103221565 4.938272 5.277575 28 13.7100073 4.103221565 7.716049 10.87217 29 2.899196494 1.051939513 3.160494 10.87217 30 13.7100073 4.103221565 4.938272 10.87217 31 13.7100073 4.103221565 4.938272 10.87217 32 7.304601899 4.103221565 4.938272 10.87217 33 13.7100073 4.103221565 4.938272 10.87217 34 13.7100073 4.103221565 4.938272 10.87217 35 7.304601899 1.051939513 4.938272 10.87217 36 13.7100073 4.103221565 4.938272 10.87217 37 13.7100073 4.103221565 0 10.87217 38 4.103221565 39 4.103221565 Jumlah 875.7297297 526.974359 310.2222 605.7297
- 5. HARGA-HARGA YANG PERLU UNTUK UJI BARTLETT Sampel Dk 咋 Log 咋 Dk log咋 1 36 0,02777 24,32 1,38 49,8 2 38 0,02631 13,86 1,14 43,38 3 35 0,0285 8,86 0,94 33,1 4 36 0,02777 16,82 1,22 44 Jumlah 145 170,28 UJI BARLET 1.HIPOTESIS: H0 = 1 = 2 = 3 = 4 2. NILAI = 0,05 3. KRITERIA PENGUJIAN :TOLAK H0 JIKA X2 X2 (1 ) (K 1 ) 4. VARIASI S1 2 = (Xi X)2 n1 = 875,7297297 36 = 24,32 S2 2 = (Xi X)2 n1 = 526,974359 38 = 13,86 S3 2 = (Xi X)2 n1 = 310,2222 35 = 8,86 S4 2 = (Xi X)2 n1 = 605,7297 36 = 16,82 5. VARIANSIGABUNGAN S2 = ( (n1 1) S1 2 (n1 1) ) S2 = 36 (24,32)+ 38 (13,86)+ 35 (8,86)+ 36 (16,82) 36+38+35+36 S2 = 15,99 6. harga satuanB = logs2 B = log15,99 B = 1,203
- 6. 7. B = (logS2 ) . (n1 1) B = 1,203 x 144 B = 173,232 8. uji barlet( digunakanchi kuadrat) X2 = (ln10) (B (n1 1 ) logsi 2) X2 = (2,3026) ( 173,232 - 170,28) X2 = 6,7972 Kesimpulan:留 = 0,05, dari daftardistribusi chi kuadratdegandk= 3 di dapatX2 0,95(3) = 7,81. TernyataX2 = 6,7972 < 7,81 sehinggaHIPOTESIS:H0 = 1 = 2 = 3 = 4 diterimadalamtaraf nyata 0,05
- 7. no (x1 ) (x2) (x3) (x4) 1 8100 8100 7396 7744 2 7921 8281 6561 7396 3 8281 6084 6561 7056 4 7744 6724 5625 6400 5 7396 6724 7056 7396 6 5929 5625 5776 6889 7 5929 6561 5929 6889 8 6561 5929 5776 5776 9 5929 5776 5776 5776 10 6724 5625 6084 5929 11 6400 5625 5625 7056 12 7056 5929 5625 6400 13 5776 5625 6084 7225 14 5625 5776 6400 6561 15 6889 5625 6400 6241 16 5625 5625 6724 5625 17 5625 5776 6084 5625 18 6724 5625 5625 6084 19 5929 5929 5625 5625 20 5929 5776 5625 5929 21 5625 6084 5625 6724 22 7056 6241 6561 5625 23 5929 5625 5625 5625 24 5625 6241 5929 5625 25 5625 5625 5625 5625 26 5625 5929 5625 6561 27 5625 5625 5625 5776 28 5625 5625 6400 5625 29 5929 5776 6241 5625 30 5625 5625 5625 5625 31 5625 5625 5625 5625 32 5776 5625 5625 5625 33 5625 5625 5625 5625 34 5625 5625 5625 5625 35 5776 5776 5625 5625 36 5625 5625 5625 5625 37 5625 5625 5625 38 5625 39 5625 Jumlah 230058 231912 214988 227433 Rata rata 6217.784 5946.462 5971.889 6146.838
- 8. Uji anava satu arah Hipotesis:Ho : 1 = 2 = 3 = 4 留 = 0,05 kriteriapengujian,tolakH0 jikaf.hitung F(1 留) (v1 . v2) untukmemperolehdaftaranalisisvariansi di perlukanharga harga berikut: RY = J1+ J2+ J3+ J4 n1 = (2912+3004+2780+2897) 37+39+36+37 = (11588)2 149 = 134281744 149 = 901.219,7583 AY = ( i 2 ni ) - RY = ( 29122 37 + 30042 39 + 27802 36 + 28922 37 ) 901.219,7583 = 901290,0464 901219,7583 = 70,2881 Y2 = X1 2 + X2 2 +X3 2 + X4 2 = 230058 + 231912 + 214988 + 227433 = 904391 DY = Y2- RY AY = 904391 901219,7583-70,2881 = 3100,9536 DENGAN : K = 4 n1 = 149
- 9. (n1 1) = 145 Berdasarkantabel tabel daftaranava, ujistatistikdiperolehsebagaiberikut: f.tabel = (k1) ( n1 1) = 3 145 f.hitung= AY (K1) DY (n1 1) = 70,2881 41 3100,9536 145 = 23,42 21,38 = 1,09 * kriteriapengujian tolakH0 jikaf.hitung f(1-留) (v1 , v 2) f(1-0,05)(3 . 145)sehinggapeluang0,95 didapatf = 2,67 *kesimpulan: Ternyataf.hitung< f.tabel,jadi hipotesisH0 : 1 = 2 = 3 = 4 diterimadalamtaraf nyata0,05
- 10. 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