Modul Statistik Deskriptif 1 Revisi

8/2/2019 Modul Statistik Deskriptif 1 Revisi

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IV.1 Pengumpulan data

No Data Acak Copy Data Acak

1 0.629863827 0.49885358

2 0.705214891 0.564183923

3 0.114142574 0.88398198

4 0.121280154 0.553265959

5 0.326574319 0.904510182

6 0.65488703 0.435459356

7 0.7223497140.011172671

8 0.687392389 0.61731309

9 0.991344966 0.938172572

10 0.463196204 0.60569092

11 0.720071649 0.066737823

12 0.251480522 0.909574363

13 0.869568777 0.68203027

14 0.500666403 0.364792124

15 0.213835375 0.720031893

16 0.25772226 0.314048847

17 0.368078676 0.254391154

18 0.643446722 0.96960407919 0.866769693 0.894744566

20 0.926352063 0.152656428

21 0.620575644 0.059721541

22 0.050241627 0.16815938

23 0.704957154 0.996372063

24 0.591633533 0.319596356

25 0.58403562 0.111537889

26 0.385085992 0.295427826

27 0.182141453 0.170468128

28 0.251492983 0.00781719

29 0.114704339 0.9125301330 0.023178842 0.882140146

31 0.849379717 0.453746772

32 0.69867702 0.894709881

33 0.163539987 0.203778318

34 0.322096425 0.274381612

35 0.760650235 0.1077527

Bab IV

Pengumpulan & Pengolahan Data


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22 0.16815938 81.6815938 81.682 83.140

23 0.996372063 89.96372063 89.964 83.196

24 0.319596356 83.19596356 83.196 83.636

25 0.111537889 81.11537889 81.115 83.648

26 0.295427826 82.95427826 82.954 83.944

27 0.170468128 81.70468128 81.705 84.355

28 0.00781719 80.0781719 80.078 84.537

29 0.91253013 89.1253013 89.125 84.98930 0.882140146 88.82140146 88.821 85.196

31 0.453746772 84.53746772 84.537 85.533

32 0.894709881 88.94709881 88.947 85.642

33 0.203778318 82.03778318 82.038 86.057

34 0.274381612 82.74381612 82.744 86.173

35 0.1077527 81.077527 81.078 86.820

36 0.009351811 80.09351811 80.094 87.109

37 0.217778335 82.17778335 82.178 87.200

38 0.394386718 83.94386718 83.944 87.315

39 0.096346263 80.96346263 80.963 87.564

40 0.001919127 80.01919127 80.019 88.82141 0.0839754 80.839754 80.840 88.835

42 0.73149613 87.3149613 87.315 88.840

43 0.204518115 82.04518115 82.045 88.947

44 0.519559907 85.19559907 85.196 88.947

45 0.710918109 87.10918109 87.109 89.045

46 0.109278088 81.09278088 81.093 89.096

47 0.305821156 83.05821156 83.058 89.125

48 0.363579939 83.63579939 83.636 89.382

49 0.883507243 88.83507243 88.835 89.696

50 0.756352968 87.56352968 87.564 89.964

4225.88145 4225.881 4225.881


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IV.2 Pengolahan data

No Data Acak Data acak80-90

X Data Urut X

1 0.498854 84.988536 84.989 80.019 1

2 0.564184 85.641839 85.642 80.078 1

3 0.883982 88.83982 88.840 80.094 1

4 0.553266 85.53266 85.533 80.112 1

5 0.90451 89.045102 89.045 80.597 1

6 0.435459 84.354594 84.355 80.667 1

7 0.011173 80.111727 80.112 80.840 1

8 0.617313 86.173131 86.173 80.963 1

9 0.938173 89.381726 89.382 81.078 110 0.605691 86.056909 86.057 81.093 1

11 0.066738 80.667378 80.667 81.115 1

12 0.909574 89.095744 89.096 81.527 1

13 0.68203 86.820303 86.820 81.682 1

14 0.364792 83.647921 83.648 81.705 1

15 0.720032 87.200319 87.200 82.038 1

16 0.314049 83.140488 83.140 82.045 1

17 0.254391 82.543912 82.544 82.178 1 80.0192 -

18 0.969604 89.696041 89.696 82.544 1 81.4398 -

19 0.894745 88.947446 88.947 82.744 1 82.8605 -20 0.152656 81.526564 81.527 82.954 1 84.2811 -

21 0.059722 80.597215 80.597 83.058 1 85.7018 -

22 0.168159 81.681594 81.682 83.140 1 87.1224 -

23 0.996372 89.963721 89.964 83.196 1 88.5431 -

24 0.319596 83.195964 83.196 83.636 1

25 0.111538 81.115379 81.115 83.648 1 11

26 0.295428 82.954278 82.954 83.944 1 8

27 0.170468 81.704681 81.705 84.355 1 7

28 0.007817 80.078172 80.078 84.537 1 6

29 0.91253 89.125301 89.125 84.989 1 430 0.88214 88.821401 88.821 85.196 1 3

31 0.453747 84.537468 84.537 85.533 1 11

32 0.89471 88.947099 88.947 85.642 1

33 0.203778 82.037783 82.038 86.057 1

34 0.274382 82.743816 82.744 86.173 1

35 0.107753 81.077527 81.078 86.820 1

36 0.009352 80.093518 80.094 87.109 1


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37 0.217778 82.177783 82.178 87.200 1

38 0.394387 83.943867 83.944 87.315 1

39 0.096346 80.963463 80.963 87.564 1

40 0.001919 80.019191 80.019 88.821 1

41 0.083975 80.839754 80.840 88.835 1

42 0.731496 87.314961 87.315 88.840 1

43 0.204518 82.045181 82.045 88.947 144 0.51956 85.195599 85.196 88.947 1

45 0.710918 87.109181 87.109 89.045 1

46 0.109278 81.092781 81.093 89.096 1

47 0.305821 83.058212 83.058 89.125 1

48 0.36358 83.635799 83.636 89.382 1

49 0.883507 88.835072 88.835 89.696 1

50 0.756353 87.56353 87.564 89.964 1

4225.8815 4225.881 4225.881


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81.4388

82.8595

84.280185.7008

87.1214

88.5421

89.9637


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IV.2.1 Pengolahan Data Tunggal

NoX

1 80.019 -4.498 20.236 -91.030 409.493

2 80.078 -4.439 19.709 -87.496 388.436

3 80.094 -4.424 19.573 -86.592 383.093

4 80.112 -4.406 19.412 -85.527 376.825

5 80.597 -3.920 15.370 -60.255 236.226

6 80.667 -3.850 14.824 -57.078 219.764

7 80.840 -3.678 13.527 -49.750 182.973

8 80.963 -3.554 12.632 -44.897 159.570

9 81.078 -3.440 11.834 -40.711 140.051

10 81.093 -3.425 11.730 -40.172 137.583

11 81.115 -3.402 11.575 -39.382 133.988

12 81.527 -2.991 8.946 -26.759 80.039

13 81.682 -2.836 8.043 -22.811 64.691

14 81.705 -2.813 7.913 -22.258 62.610

15 82.038 -2.480 6.150 -15.250 37.818

16 82.045 -2.472 6.113 -15.114 37.369

17 82.178 -2.340 5.475 -12.810 29.974

18 82.544 -1.974 3.896 -7.689 15.175

19 82.744 -1.774 3.146 -5.581 9.900

20 82.954 -1.563 2.444 -3.821 5.973

21 83.058 -1.459 2.130 -3.108 4.536

22 83.140 -1.377 1.897 -2.612 3.597

23 83.196 -1.322 1.747 -2.309 3.051

24 83.636 -0.882 0.778 -0.686 0.605

25 83.648 -0.870 0.756 -0.658 0.572

26 83.944 -0.574 0.329 -0.189 0.108

27 84.355 -0.163 0.027 -0.004 0.001

28 84.537 0.020 0.000 0.000 0.000

29 84.989 0.471 0.222 0.104 0.049

30 85.196 0.678 0.460 0.312 0.211

31 85.533 1.015 1.030 1.046 1.061

32 85.642 1.124 1.264 1.421 1.597

33 86.057 1.539 2.369 3.647 5.614

4)( XX)( XX

2)( XX 3)( XX


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34 86.173 1.656 2.741 4.537 7.511

35 86.820 2.303 5.302 12.209 28.114

36 87.109 2.592 6.716 17.405 45.10737 87.200 2.683 7.197 19.307 51.794

38 87.315 2.797 7.825 21.889 61.232

39 87.564 3.046 9.278 28.258 86.072

40 88.821 4.304 18.522 79.716 343.081

41 88.835 4.317 18.640 80.479 347.461

42 88.840 4.322 18.681 80.744 348.992

43 88.947 4.429 19.620 86.907 384.952

44 88.947 4.430 19.623 86.928 385.073

45 89.045 4.527 20.498 92.804 420.168

46 89.096 4.578 20.959 95.953 439.28547 89.125 4.608 21.231 97.824 450.740

48 89.382 4.864 23.659 115.082 559.769

49 89.696 5.178 26.816 138.864 719.095

50 89.964 5.446 29.660 161.531 879.710

4225.881 0 512.525 402.4184 8690.715

Mean

Median

k = 1/2 n

1/2 n = 25 banyaknya jumlah data /2 (nilai Tengah)

Xk 83.648 (nilai tengah)

Xk+1 = 83.944 (nilai tengah+1)

Median = 1/2* (Xk+Xk+1)

= 1/2*(83,648+83,944)

Median = 83.796

84.518=


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A. Quartil

*berdasarkan letak *Berdasarkan nilai :

Q1 = 81,527+0,75*(81,682-81,527)

81.643

Q2 = 83,648+0,5*(83,944-83,648)

83.796

Q3 = 87,314+0,25*(87,563-87,314)87.377

B. Persentil


Qi = Pi = X(j) + P Pi = X(j) + P[X(j + 1)-X(j)]

P5 = 80,078+0,55*(80,094-80,078)

Q1 = 2.55 80.087

= P50 = 83,648+0,5*(83,944-83,648)

25.5 83.796

P95 = 89,382+0,45*(89,696-89,382)

48.45 89.382

C. Desil


Qi = Di = X(j) + P[X(j + 1)-X(j)]

D1 = 80,597+0,1*(80,667- 80,597)

=

25.5

12.75

38.25

=

=


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80.604

D5 = 83,648+0,5*(83,944-83,648)83.796

D9 = 89,045+0,9*(89,096-89,045)

45.9 89.091

D. Variance

10.460

E. STDV

3.234

3,234^4 109.405

3,234^3 33.828

F. Kurtoisis

1.589

25.5

5.1

10

)150(11

D

10

)150(99

D

10

)150(55

D


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S.E Kurtoisis

S.E Kurtoisis 0.491

Kurva :

Ket :

Kurva yang terbentuk dari nilai < 3 adalah kurva platykurtic

G. Skewness

=

= 0.238

S.E Skewness

=

S.E Skewness = 0.074

Kurva Platykurtic


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Kurva :

Ket:

Kurva condong ke kanan (+) karena bernilai positif


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IV.2.2 Pengolahan Data Bergolong (Kelompok)

Max = a 89.964

Min = b 80.019

Range = a-b 9.945

kelas = 6.658 7

Interval Range/kelas 1.421

1 80.019 - 81.439 11

2 81.440 - 82.859 83 82.860 - 84.280 7

4 84.281 - 85.701 6

5 85.702 - 87.121 4

6 87.122 - 88.542 2

7 88.543 - 89.964 12

50

Mean Dimana :

fi*Xi = Hasil jumlah dari kolom fi*Xi =

fi = Hasil jumlah dari kolom frekuensi (fi) =

=4232,506/5084.650

Median

Dimana :

fm = frekuensi dari kelas yan menggandung median=7

n = jumlah semua frekuensi = 50

c = besarnya interval = 1,421

(fi )o = jumlah frekuensi semua kelas di bawahyang mengandung median = 19

Median =82,86+(1,421*((50/2)-19)/7)

median 84.078

Modus

Interval data Fi

=1+3,33*LOG(n)

Kelas

fi

Xi

fiX

*

_

m

i

n

O

f

fc

L

0

2


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Lo= kelas yang mempunyai jumlah frekuensi terbanyak=88,543-0,0005=

b1= Selisih frekuensi kelas modus dengan kelas sebelumnya = 11-3 =b2= Selisih frekuensi kelas modus dengan kelas sesudahnya = 11-0 =

c= Interval

Modus = 89.182

A. Quartil

*berdasarkan Letak *berdasarkan nilai

,Dimana

b = nilai batas bawah dari kelas yang menggand

p = interval

F = jumlah frekuensi kelas di bawah kelas yangf = frekuensi dari kelas yang mengandung kuartil

Q1 =1*50/4 : 12.5 81,44-0,0005+1,421*(12,5-11)/8

Q2 =2*50/4 : 25 82,860-0,0005+1,421*(25-19)/7

Q3 =3*50/4 : 37.5 87,122-0,0005+1,421*(37,5-36)/3

B. Persentil

*berdasarkan letak *berdasarkan nilai

b = nilai batas bawah bawah dari kelas yang me

p = interval

F = jumlah frekuensi dari semua kelas sebelum k

f = frekuensi dari kelas yang mengandung kuartil

P5 =5*50/100 2.5 80,019-0,0005+1,421*(2,5-0)/11

P50 =50*50/100 25 82,86-0,0005+1,421*(25-19)/7

P95 =95*50/100 47.5 88,543-0,0005+1,421*(47,5-38)/11

C. Desil

*berdasarkan letak *berdasarkan nilai

b = nilai batas bawah bawah dari kelas yang me

F = jumlah frekuensi dari semua kelas sebelum k

f = frekuensi dari kelas yang mengandung kuartil

,Dimana :

p = interval

3

,

2

,

1

,

4

.

i

n

i

Qi

f

FipbQi

n

4*

f

FipbPi

n100

*99,..3,2,1,

100

* i

niPi

10*niDi

fFipbDi

n

10*

)119

9(421,1543,88


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D1=1*50/10 5 80,019-0,0005+1,421*(5-0)/11

D5=5*50/10 25 82,860-0,0005+1,421*(25-19)/7D9=9*50/10 45 88,543-0,0005+1,421*(25-38)/12

D.Variance

n= jumlah semua frekuensi

S= 10.509

E. STDV

S = =10,509*0,5 = 3.242 3.234144705

S4 = S^4 =5,255^4 = 110.442

S3 =5,255^3 = 34.068

F. Kurtosis

dimana

adalah hasil ju

kolom

=1/50*8554,499/762,342 1.549

S.E Kurtosis

=0,224/5,255 = 0.47787

Kurva

Dari hasil < 3 maka kurva yang terbentuk adalah kurva platykurtic

G. Skewness Dimana

adalah hasil ju

kolom

=1/50*460,031/145,082 0.2701

Jumlah dari kolom)

(

_

2

X

X

fi

i

)

(

_

2

X

X

fi*

i

2S

(*fi

(*fi

1

)(_

2

2

n

XXfiS

i

150

948,5142

S


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S.E Kweness

=0,634/5,255 0.083

Kurva Dari hasil yang mengindikasikan nilai positif maka

kurva yang ter bentuk akan miring ke kanan


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11 80.729 888.019 -3.921 15.375

19 82.150 657.197 -2.500 6.25226 83.570 584.992 -1.080 1.166

32 84.991 509.946 0.341 0.116

36 86.412 345.646 1.761 3.103

38 87.832 175.665 3.182 10.126

50 89.253 1071.041 4.603 21.190

594.937 4232.506 2.386 57.328

4232.506

50

F. Kumulatif X-X'Xi Fi*Xi )( XX2)( XX


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88.543

911

1.421

ng kuartil

meggandung kuartilke-i

81.706

84.078

88.187

uat kuartil ke-i

elas yang mengandung kuartil ke i

ke-i

80.337

84.078

89.667

uat kuartil ke-i

elas yang mengandung kuartil ke i

ke-i )

(

_

2

X

X

fi

i


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80.665

84.07889.372

lah dari

lah dari

4)X

3)XX


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169.126 -60.287 -663.160 236.393 2600.321

50.018 -15.634 -125.069 39.091 312.7298.162 -1.259 -8.813 1.360 9.517

0.697 0.040 0.238 0.013 0.081

12.411 5.466 21.862 9.627 38.510

20.252 32.222 64.444 102.535 205.070

254.282 97.544 1170.530 449.023 5388.272

514.948 58.091 460.031 838.042 8554.499

(X-X')4 fi*(X-X')4fi*(X-X')2 (X-X')3 fi*(X-X')32)(* XXfi

3)( XX

4)( XX

4)(* XXfi 3)(* XXfi


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Parameter Data Tuggal Data berkelompok Spss

Mean 84.518 84.650 84.517

Modus 89.182 88.947

Median 83.796 84.078 83.796

Q1 81.643 81.706

Q2 83.796 84.078Q3 87.377 79.308

P5 80.087 80.337 80.094

P50 83.796 84.078 83.796

P95 89.261 89.667 89.382

D1 80.604 80.665

D5 83.796 84.078

D9 89.091 89.372

S 3.234 3.242 3.234

10.460 10.509

1.589 0.224 -1.36

S.E Kurtoisis 0.491 0.043 0.662

0.238 0.063 0.253

S.E Kewness 0.074 0.012 0.337

Date post:	05-Apr-2018
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Modul Statistik Deskriptif 1 Revisi

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