bab 1 statistika

Kunci Penyelesaian Matematika SMA Jl.2A- Sukino Bab 1 | page 1

Latihan Kompetensi Siswa 1

A. Evaluasi Pengertian atau Ingatan

1. C. Data kualitatif2. D. Statistik3. E. Membuat tabel frekuensi4. A. Datum5. C. 67,666. B. 126,687. D. Sampling8. E. Sampel9. B. Data kuantitatif10. A. Statistika deskriptif

B. Evaluasi Pemahaman dan PenguasaanMateri

1. - Karena statistika mempunyai peran atautugas untuk menyediakan bahan-bahanketerangan mengenai beberapa hal untukdiolah ataupun ditafsirkan, dan juga untukmenyediakan berbagai alat atau cara untukmenemukan kembali keterangan-keteranganyang seolah-olah tersembunyi didalam angka-angka statistik.- Cabang ilmu seperti ekonometri,pcychometri, sosiometri dan sebagainya.

2. - Statistika adalah cabang ilmu matematikayang mempelajari metode pengumpulan,pengolahan, penafsiran dan penarikankesimpulan dari data yang berupa angka-angka.- Statistika deskriptif dan statistika induktif /inferensi.

3. - Memberikan keterangan (informasi)mengenai satu hal.- Data kualitatif : berbentuk bilangan.

Data kuantitatif : tidak berbentuk bilangan.

4. Dapat dilakukan dengan beberapa cara :1. Penelusuran Literatur

Menggunakan sebagian atau seluruh datayang telah dicatat atau laporan data daripeneliti sebelumnya.

2. Angket (kuesioner)Menggunakan daftar isian atau daftarpertanyaan yang sebelumnya harusdisusun dan disiapkan oleh peneliti sesuaidengan hal yang sedang ditelitinya.

3. WawancaraPelaksanaannya langsung mengadakantanya jawab kepada responden (objek)

atau kepada perantara yang mengetahuipersoalan objek yang sedang dteliti.

4. Pengamatan (observasi)Mengamati objek.

5. * Populasi : keseluruhan objek yang akanditeliti.

* Sampel : populasi yang benar-benar diamati.

6. a. Rp3.436 e. 24 kmb. 27 meter f. 28 yardc. 2 ton g. 138°d. 66 ton h. 169 Newton

7. a. sampel : 10 siswa yang diamatipopulasi : seluruh siswa kelas XII-A

SMU ‘Erlangga’.b. data kualitatif : makanan favorit

data kuantitatif : banyak teman akrab, beratbadan, tinggi badan



1.D. 6-4 -2 3 5 | 7 8 9 10

62

75 me

2.B. 7

3 4 4 5 6 | 7 7 7 8 9

Q1 2

762

Q Q

3

5,6

3.B. 52Q

5,31Q 7

3Q

1min

x 7xmaks

Data: 1 2 3 | 4 4 5 | 5 6 7 | 7 7 7

5,31Q 5

2Q 7

3Q

xmin xmaks

BAB 1STATISTIKA


4. C. 54321 481 xxxxx

data : 1x 2x 3x 4x 5x

221

1

xxQ Q2 2

54

3

xxQ

RT = QQQ321

241

=

2

224

1 543

21 xxxxx

= 54321 481 xxxxx

5. B. Rk = 2RT - Q2

Rk = QQ312

1

=

QQ

3141

2

=

QRT

221

2

= QRT2

2

6. C. 163,25Data : 157 159 160 162 163 | 164 165 166 167 170

Q1

5,1632Q Q

3

RT = QQQ321

241

= 1665,163.216041

= 163,25

7. D. 35

Rk = 60 = 12021

3121 QQQQ

RT = QQQ321

241

= 10.212041

= 35

8. A. Q2

2RT – Rk

Dari jawaban no.5 diperoleh :Rk = 2RT - Q

2

Q2

2RT – Rk

9. C. 1313103

minxx maks

10. D. 32

Data : 2 3 4 4 5 | 6 6 8 9 10

41Q 5,5

2Q 8

3Q

328.431

QQ


1. a. Data : 2 3 5 | 5 7 8

31Q 5

2Q 7

3Q

b. Data : 7 8 9 10 10 11 13 13 15 16 16

91Q 11

2Q 15

3Q

c. Data : 28 28 29 | 31 32 32 | 34 35 37 | 37 37 39

301Q 11

2Q 37

3Q

d.101 104 106 107 | 109 109 111 113 113 115 116 118 118| 118 120 121 125

1081Q 113

2Q 118

3Q

e. 48,7 | 48,9 49,5 50,3 | 51,6

8,481Q Q

295,50

3Q

2. a. (i) 52Q

31Q 7

3Q

2min

x 8xmaks

(ii) Rk = 57321

(iii) RT = 5710341

b. (i) 112Q9

1Q 15

3Q

7min

x 16xmaks

(ii) Rk = 1215921

(iii) RT = 5,111522941

c. (i) 332Q

301Q 37

3Q

28min

x 39xmaks

(ii) Rk = 5,33373021

(iii) RT = 25,3337663041


d. (i) 1132Q

1081Q 118

3Q

101min

x 125xmaks

(ii) Rk = 11311810821

(iii) RT = 11311822610841

e. (i) 5,492Q

8,481Q 95,50

3Q

7,48min

x 6,51xmaks

(ii) Rk = 875,4995,508,4821

(iii) RT = 6875,4995,50998,4841

3. Data :60 65 70 70 70 100 120 180 240 300 300

701Q 100

2Q 240

3Q

a. 1002Q

701Q 240

3Q

60min

x 300xmaks

b. Rk = 1552407021

c. RT = 5,1022401007041

4. a. 51,02Q

5,01Q 53,0

3Q

49,0min

x 54,0xmaks

b. Rk = 515,053,05,021

c. RT = 5125,053,051,0.25,041

5. 5,62

761

Q10

2Q

143Q

6. RT = 40 = QQQ321

241

160 = 30 + 2Q2

130 = 2Q2

a. Rk = 15 = 3021

3131 QQQQ

b. 652Q

c. Q2- RT = 25

7. Data tekstil :499 500 501 504 507 507 508 513 517 520 521

Data batik :731 732 734 734 734 737 737 750 758 761 763

a. (i) tekstil :507

2Q

5011Q 517

3Q

499min

x 521xmaks

(ii) batik :737

2Q

7341Q 758

3Q

731min

x 763xmaks

b. tekstil : RT = 508517507.250141

batik : RT = 5,741758737.273441

c. tekstil : RK = 50951750121

batik : RK = 74675873421

8. RT = 5 = QQQ321

241 ; 16

32xQ

20 = QQQ321

2

QQ31

= 20 - Q2

2 = -12

225421 xxxx

= -12

a. xxxx 5421 = -24

b. ( xxxx 5421 ) – ( QQ

31 )

= -24 – (-12)= -12

c. Rk = QQ312

1

= 61221




1. A.xxxx

15

15

2. B. xx 2622

Data : x1 x2 x3 x4 x5 x6 x7

Q1

Q2

Q3

H = xxxxQQ 262613 22

3. C. xx 2523

Data : x1 x2 x3| x4 x5 x6

Q1

Q2

Q3

L = xxQQ 2513 23

23

4. E. ca 3521

L = acQQ 23

23

13

PD = Q1

L

= aca 23

= ca23

25

= ca 3521

5. D. 4 QQ31

PD – PL = Q1- L – (Q

3+L)

= QQ31

2L

= QQQQ1331 2

3.2

= QQ31

+ 3 QQ31

= 4 QQ31

6. C. 7

Rk = 4 = QQQQ3131

821

Qd

= 3 = QQQQ1313

621

+14 = 2Q

3

Q3= 7

7. A.52

Rk = 5 = 1021

3131 QQQQ

Qd

= 2 = 421

1313 QQQQ

koef. Qd

=52

104

13

13

QQQQ

8. C. 6Data : 2 4 5 | 6 6 8

Q1

5,52Q Q

3

2L = QQ132

3.2

= 3 (6 – 4)= 6

9. C.177

Data : 2 4 | 6 8 | 9 11 | 13 16

51Q 5,8

2Q 12

3Q

koef. Qd

=177

512512

13

13

QQQQ

10. D. 20PL – PD = Q

3L – (Q

1- L)

= QQ13

+ 2L

= QQ13

+ 2. QQ132

3

= 4 QQ13

= 4 (7 – 2 )= 20

11. A. 9Data: 2 3 | 5 6 | 8 9 | 11 14

41Q 7

2Q 10

3Q

L = 941023

23

13QQ


12. E. -5Data: 2 3 | 5 6 | 8 9 | 11 14

41Q 7

2Q 10

3Q

PD = Q1

L

= QQQ131 2

3

= QQ31 2

325

= 10.34.521

= -5

13. B. 19Data: 2 3 | 5 6 | 8 9 | 11 14

41Q 7

2Q 10

3Q

PL = Q3

L

= QQQ133 2

3

= QQ13 2

325

= 4.310.521

= 19

14. A. 20Data :20 36 46 50 50 51 52 54 60 65 66 68 77 80 94

PD = Q1- L

= QQ31

3521

= 68.350.521

= 23PL = Q

3- L

= QQ13

3521

= 50.368.521

= 95

20 < PD=23; jadi 20 adalah peneilan

15. D. 3Data : 2 3 4 6 8 9 11

Qd

= 33921


1. a. Data :3 5 13 14 18 | 27 29 30 48 49

Q1

5,222Q Q

3

range = 46349min

xxmaks

H = 17133013

QQL = 5,25

25117.

23

23

13QQ

b. Data :2 3 3 5 8 | 8 9 9 9 25

Q1

82Q Q

3

range = 25 – 2 = 23H = 9 – 3 = 6

L = 93923

c. Data :-8 -7 | -6 -5 -4 -3 -2 | -1 3

5,61

Q 42

Q 5,13

Qrange = 3 – (-8) = 11H = -1,5 – (-6,5) = 5

L = 5,75.23

2. a. Data :3 5 | 6 7 | 10 12 | 15 18

5,51Q 5,8

2Q 5,13

3Q

range = 15318min

xxmaks

Qd

= 45,55,1321

21

13QQ

PD = Q1- L

= QQQ131 2

3

= 8.235,5

= -6,5PL = Q

3+ L

= Q3

+ QQ132

3

= 13,5


b. Data :3 8 | 8 8 | 9 9 | 9 18

81Q 5,8

2Q 9

3Q

range = 18 – 3 = 15

Qd

= 2189

21

PD = 8 - 8923

= 8 -23 = 6,5

PL= 9 + 8923

= 9 +23 = 10,5

c. Data :3 3 4 5 6 7 12

Q1

Q2

Q3

range = 12 – 3 = 9

Qd

= 23721

PD = 3 - 3723

= -3

PL = 7 + 3723

= 13

d. Data :6,351 6,453 8,628 | 8,772 9,434 10,624

Q1

Q2

Q3

range = 10,624 – 6,351 = 4,273

Qd

= 4905,1453,6434,921

PD = 6,435 - 453,6434,923 = 1,9815

PL = 9,434 + 453,6434,923 = 13,9055

3. Data :4 5 5 5 6 6 7 7 7 7 8 8 9 9 10

Q1

Q2

Q3

a. Range = 10 – 4 = 6b. 7

2Q

51Q 8

3Q

4min

x 10xmaks

c. Qd

= 5,15821

21

13QQ

d. L = 5,45823

23

13QQ

e. PD = Q1- L = 5 – 4,5 = 0,5

PL = Q3+ L = 8 + 4,5 = 12,5

f. koef. Qd

=133

5858

13

13

QQQQ

nilai data normal.

4. Rk = 100 = 20021

3131 QQQQ

Qd

= 1005021

1313 QQQQ

-

2 1001Q

501Q

a. koef. Qd

=21

200100

13

13

QQQQ

b. Q1= 50 ; Q

3= 150

c. QQ31

= 50 x 150 = 7500

d. L = 1505015023

23

13QQ

e. PD = Q1- L = 50 – 150 = -100

PL = Q3+ L = 150 + 150 = 300

5. PD + PL = 100

Q1- L + Q

3+ L = 100

Q1+Q

3= 100

Qd

= 502521

1313 QQQQ

10031QQ

+2 150

3Q

753Q ; 25

1Q

a. koef. Qd

=21

10050

13

13

QQQQ

b.31

7525

3

1 QQ

c. L = 755023

23

13QQ

d. PD = Q1- L = 25 – 75 = -50

PL = Q3+ L = 75 + 75 = 150



1. 1984/1985

1985/1986

1986/1987

2. ternak dan populasi :

sapi/perah kerbau kuda babi kambing domba

9.738.400 3.493.000 715.100 6.215.900 10.737.800 5.318.000

3. a.

Negara1983 1987

ASEAN 23,7 30,6

Jepang 23,9 11,8AS 23,2 27,9MEE 13,7 19,3

lainnya 15,5 10,4

Tahun

Nilai impor (dalam persen)

b. Jepang, negara lainnya, ASEAN dan AS- Jepang turun :

5,326.12

1008,11

8,351.16100

9,23

= 3.908,0802 – 1.454,527= 2.453,5532 juta/million US$

- negara lainnya turun :

6,326.12

1004,108,351.16

1005,15

= 2.534,529 – 1.281,9664= 1.252,5626 juta/million US$

- ASEAN turun :

8,351.16

1007,23

6,326.12100

6,30

= 3.771,9396 + 3.875,3766= 103,437 juta/million US$

- AS turun :

8,351.16

1002,236,326.12

1009,27

= 3.439,1214 + 3.793,6176= 354,4962 juta/million US$

c. MEE naik :

8,351.16

1007,136,326.12

1003,19

= 2.379,0338 – 2.240,1966= 138,8372 juta/million US$

4. a.


b.

5.

6. a.

b. pada hari ke – 5.

7. a.

b. (i) minggu 14 dan minggu 16(ii) minggu 4 dan minggu 6

c. minggu 15


A. Evaluasi Pemahaman dan PenguasaanMateri

1. Data :5 5 7 8 17 18 19 21 22 | 22 28 28 29 31 32 34 37 39

222Q

a.

Batang Daun0 55781 7892 1228893 12479

b. PD = Q1- L

= Q1- QQ

1323

= 17 - 173123

= -4PL = Q

3+ L

= 31 + 21= 51

Ternyata setiap data x, memenuhiPD x PL. Jadi tidak ada pencilan.


2. a.Kedalaman Batang Daun

11 6 4 5 6 6 6 7 7 8 8 8 913 7 0 0 1 2 2 2 3 3 3 4 4 5 5

b.

PD = Q1- L

= Q1- QQ

1323

= 67 - 677323

= 58

PL = Q3+ L

= 73 + 9= 82

Tidak ada pencilan.

3. Data :10 12 15 19 23 24 26 28 32 34 36 38 40 41 46


15 15 4 4 5 5 5 6 6 6 6 7 7 7 8 8 915 16 0 0 0 0 1 1 1 1 2 2 2 2 2 3 3

b. 5,1592Q

1561Q 161

3Q

154min

x 163xmaks

5. a. Data :8 8 9 9 9 9 11 12 14 21 31 32 34 34 38 40 43

Kedalaman Batang Daun5 0 8 8 9 9 93 1 1 2 41 2 15 3 1 2 4 4 82 4 0 3

b. Rk = 5,1293421

21

13QQ

RT = QQQ321

241

= 345,17.2941

= 7841

= 19,5

B. Evaluasi Kemampuan Analisis

1. a.

b. 62Q

51Q 5,6

3Q

xmin10xmaks

c. koef. range :

137

310310

min

min

xxxx

maks

maks

koef. Qd

=233

5,115,1

55,655,6

13

13

QQQQ

d. Ya.


1 11 93 12 5 6 87 13 2 5 5 5 6 8 8

14 14 0 0 2 2 4 4 5 5 6 6 7 7 8 98 15 0 0 2 3 4 6 7 85 16 1 3 4 8 82 17 3 6

b. 1462Q

1381Q 155

3Q

119min

x 176xmaks

c. PD = Q1- L

= Q1- QQ

1323

= 138 - 13815523

= 112,5PL = Q

3+ L

= 155 + 25,5= 180,5

d. Qd

= 5,813815521

21

13QQ


3.Kedalaman Batang Daun

1 3 83 5 0 2 61 6 46 7 0 0 0 2 6 66 8 0 0 4 4 8 88 9 0 0 2 2 4 4 6 85 10 0 0 4 6 83 11 2 4 63 12 2 6 82 13 6 61 14 61 15 2

a.

b. 922Q

761Q 110

3Q

38min

x 152xmaks

c. koef. Qd

=9317

18634

7611076110

13

13

QQQQ



1. B. 152. D. 1623. B. 5

panjang kelas : 154,5 – 149,5 = 54. B. 70

selisih nilai tengah terbesar dan terkecil :95,5 – 25,5 = 70

5. D. %100

fi

6. A. Nk 3,3.10log

7. E. 42 – 438. E. 42,59. C. 30

selisih : 50,5 – 20,5 = 3010. E. 50 - 60


1.Interval Kelas Frekuensi Tepi int. Kelas Nilai Tengah

8,5 – 8,9 2 8,0 – 8,4 8,79,0 – 9,4 8 8,5 – 8,9 9,29,5 – 9,9 10 9,0 – 9,4 9,7

10,0 – 10,4 22 9,5 – 9,9 10,210,5 – 10,9 28 10,0 – 10,4 10,711,0 – 11,4 9 10,5 – 10,9 11,211,5 – 11,9 7 11,0 – 11,4 11,712,0 – 12,4 2 11,5 – 11,9 12,2

a. Histogram

b. 46

2. a. 39,5b. 60,49c. 15,49d. 69,5e. 80,49f. 10

g.100

1

h. 1i. 60,00 – 69,99

3. a. 99,5b. 90,49c. 75,49d. 89,5e. 100,49f. 10g. 16

h.6516

i. 70 – 79,99


4. a.Interval Kelas Frekuensi

115 – 119 1120 – 124 0125 - 129 3130 – 134 1135 – 139 6140 – 144 6145 – 149 8150 – 154 5155 – 159 3160 – 164 3165 – 169 2170 – 174 1175 – 179 1

b. Distribusi frekuensi kumulatif kurang dari

Panjang (mm) Frekuensikumulatif

<115 0<120 1<125 1<130 4<135 5<140 11<145 17<150 25<155 30<160 33<165 36<170 38<175 39<180 40

c. Histogram

5. a.b.Interval Kelas Frekuensi Frekuensi Relatif (%)

10 – 19 3 320 – 29 19 1930 – 39 21 2140 – 49 34 3450 – 59 16 1660 – 69 7 7

c.Kurang dari Lebih dari

<10 0 >10 100<20 3 >20 97<30 22 >30 78<40 43 >40 57<50 77 >50 23<60 93 >60 7<70 100 >70 0

d.




1. B.nnn

xnxnxn321

332211

2. D. 1632

30

17.2016.10x 16

32

3. B. 11

13,4 =15

6.158.5,12 x

100 + 90 + x = 201x = 11

4. A.10

15 =12

.220.610.4 x

40 + 120 + 2 x = 1802 x = 20

x = 10

5. E. 8

nx = 11 x = 11n

13129

nx

11n + 29 = 13n + 13

16 = 2nn = 8

6. D. 6,8

8,65

6.38.2

x

7. C. Rp1.925

192540

17.100010.20008.20005.4000

x

8. D. 16

105

91357

xx

5034 x16x

9. A. 9

115

8642

xxxxxx

115

205

x

55205 x355 x7x

x3pertama = 9

31197

10. C. – 8

x1= 20

4

dcba

a+b+c+d = 80

x2= 12

44 xdcba

80 + 4x = 484x = -32

x = -8

11. A. 4939 x 75 x > 39

3114

37539 xxx

jika xx 11414749x = 33

(tidak mungkin) sebab x > 39

12. C. 2

126621

xx

1241262,620

y

yx

y = 2

13. B. 13 tahun

165

23242

xxxxxx

7x + 3 = 807x = 77

x = 11anak ke-2 = x + 2 + 13 tahun


14. E. 1:2

40.50.35

yx

yxx

35x + 50y = 40x + 40y10y = 5x

21

105

xy

15. E. 100

1010

191715131197531

x

16.

17.

18. B. 6

* nn xx

ii 1212

range = 6min

xxmaks

* 22....

bnna

nb

a

b

ax

xxi

ni

212

bn

an

22

12

a

412 aa = 8

3min

b

a

b

a xxmaks

63min

bxxmaks

b = 2a – b = 8 – 2 = 6

19. E. 5,31

nxn

x66

25,618625,6

1

8

nn

n

x

25,625,686 nn1,75 = 0,25n

n = 7

9

425845438

n

xxbaru

31,516

4342

20. A. 50

20405140

xxi

i

5039

90204039

90

xx i

baru


1. a. mean = 45

65432

me= 4

Qd

= 25,15,521

21

13QQ

b. mean = 64

me= 6

Qd

= 50,45821

c. mean = 106,17

me= 103

Qd

= 110310521

d. mean = 0,24

me= 0,20

Qd

= 06,081

41

21

e. mean = 20,36

me= 20

Qd

= 50,2182321

f. mean = 49,80

me= 49,50

Qd

= 82,08,4845,5021

g. mean = 13,54

me= 13

Qd

= 50,1121521

h. mean = 12,50

me= 11

Qd

= 50,391621

i. mean = 4,80

me= 5

Qd

= 75,045,521

j. mean = 5,10

me= 5

Qd

= 5,13621

2. 3,5100

10.730.640.520.4

x

3. 5,163

40,1.1853,1.1048,1.2062,1.15

x

4. 61,7874

82.3274.2579.17

x


5. 7,6750

7.475,6.46 x

6. 1656

160.5 xx

800 + x = 990x = 190 cm

7. 02,1750

24.2013.720.108.510.4 x

8. 67,1630

17.2016.10 x

9. 2041,540

xx

539

920439

0,9

x

x

10. 000.25010.000.210.000.260

wp

px

10.000 p = 40.000 w

14

wp

p : w = 4 : 1

11. 8008010

xx

99628008312

.2

xxx

2 196x98x

12. nxn

x1111

13132911131

29

nnn

x

162 n8n

13. nxn

x55

1,51,5751,51

7

nnn

x

9,11,0 n19n

14. 15025,624

xx

x

1551502,625

xx

enieni

x

5xeni

15. 720809

xx

8207208210

xx

jj

x

100x j

16. 252642

xx

2362529,540

yx

yxx

16yx

17.15

15.65,12.84,13 15xx

100 + 90 + x15= 201

x15= 11

18.yx

yxonsx

000.9000.12

/000.10

1000 y = 2000 x

yx

20001000

x : y = 1 : 2

19. a. x = 2 + (-5) + 4 + (-8) = -7

b. y = 5

c. xy = -6 + 40 + 40 + (-48) = 24

d. 2x = 4 + 25 + 16 + 64 = 109

e. 2y = 9 + 64 + 100 + 36 = 209

f. yx = (-7).(5) = -35

g.2

xy = 2.9 + (-5).64 + 4.100 + (-8).36

= -190h. yxyx = 2x - 2y

= (4 - 9)+(25 – 64)+(16 – 100)+(64 – 36)= -5 + (-39) + (-84) + 28= -100

C. Evaluasi Kemampuan Analisis

1. a.

6

1

32j

jx = 2

6

1jjx +18

= 2. (-4) + 18 = 10

b.

6

1

1j

jj xx =

6

1

2

jjx -

6

1jjx

= 10 – (-4) = 14

c. 26

1

5

j

jx =

6

1

2 2510j

jj xx

= 10 -10.(-4) + 150 = 200


2. xx j = xx j

= n

xx j

j

=n

xnx j

j

= 0

3. 1 + 8 + 27 + …. + n 3 =

n

i

i1

3

n

ix

n

i 1

3

4.yx

yxx .71.738,71

0,8 y = 1,2 x

yx

2,18,0

x : y = 2 : 3

5. 15815,4634

xx

x

164515814735

xx

waliwali

x

kgxwali56



1. D. 20

6140

10.10870.640.520.4

a

ax

800 + 8a = 840 + 6a2a = 40

a = 20

2. B. 40

06,660

3.96.814.717.612.55.43.3

x

lulus jika x i > 5,06maka, banyak siswa yang lulus :17 + 14 + 6 + 3 = 40

3. E. 2,93

93,230

6.54.47.38.25.1

x

4. E. A,B dan C benar

5. D. 67,45 kg

Berat Badan(kg)

Nilai Tengahx

Jumlah karyawan(f)

fx

60 – 62 61 5 30563 – 65 64 18 115266 – 68 67 42 281469 – 71 70 27 189072 – 74 73 8 584

45,671006745

f

fxx

6. D. 55,5

Interval Nilai Tengahx

Frekuensi(f)

fx

20 – 29 24,5 3 73,530 – 39 34,5 7 241,540 – 49 44,5 8 35650 – 59 54,5 12 65460 – 69 64,5 9 580,570 – 79 74,5 6 44780 – 89 84,5 5 422,5

5,5550

2775

f

fxx

7. B. 24,12

Interval Nilai Tengahx

Frekuensi(f)

fx

10 – 15 12 5 6015 – 20 17 6 10220 – 25 22 8 17625 – 30 27 12 32430 – 35 32 6 19235 – 40 37 3 111

125,2440965

f

fxx

8. C. 30

5,3060

7.5015.40.2010.208.10 ax

1230 + 20a = 183020a = 600

a = 30

9. B. 632

326

36060.960.860.790.660.530.4 x

10. D. Rp110.000

30.000.5090.000.4545.000.3045.000.20000.60 x

36090.30.000.7030.000.60 x

21.600.000 = 11.700.000 + 90 x90 x = 9.900.000

x = 110.000



1. A = 74,5

Nilai x f d=x-A fd50 – 59 54,5 3 -20 -6060 – 69 64,5 21 -10 -21070 – 79 74,5 33 0 080 – 89 84,5 15 10 15090 – 99 94,5 8 20 160

7580405,74

ffd

Ax

2. A = 39,5 ; C = 10

Interval x f d=x-AcAxu Fu

10 – 19 14,5 3 -25 -2,5 -7,520 – 29 24,5 20 -15 -1,5 -3030 – 39 34,5 21 -5 -0,5 -10,540 – 49 44,5 34 5 0,5 1750 – 59 54,5 15 15 1,5 22,560 – 69 64,5 7 25 2,5 17,5

a. x = A + C.f

fu

= 39,5 + 10.10036

= 43,1b. 41 keluarga.

3. A = 49,5 ; C = 10

Interval x f d u fx fd fu

0 – 9 4,5 3 -45 -4,5 13,5 -135 -13,510 – 19 14,5 5 -35 -3,5 72,5 -175 -17,520 – 29 24,5 7 -25 -2,5 171,5 -175 -17,530 – 39 34,5 10 -15 -1,5 345 -150 -15,040 – 49 44,5 12 -5 -0,5 534 -6 -6,050 – 59 54,5 15 5 0,5 817,5 75 7,560 – 69 64,5 12 15 1,5 774 180 1870 – 79 74,5 6 25 2,5 447 150 1580 – 89 84,5 2 35 3,5 169 70 790 – 99 94,5 8 45 4,5 756 360 36

a. cara biasa :

25,5180

4100

ffx

x

b. cara deviasi :

25,5180

1405,49

f

fdAx

c. cara coding :

x = A + C.f

fu

= 49,5 + 10.8014

= 51,25

4. a.

b.Uang Saku

(ribu rupiah)Nilai Tengah

(x)Frekuensi

(f)fx

60 – 69,9 65,4 3 196,270 – 79,9 75,4 16 1206,480 – 89,9 85,4 25 213590 – 99,9 95,4 46 4388,4

100 – 109,9 105,4 35 3689110 – 119,9 115,4 13 1500,2120 – 129,9 125,4 2 205,8

47,95140

366.13

f

fxx

5.Interval Nilai Tengah

(x)Frekuensi

(f)fx

10 – 20 15 5 7520 – 30 25 3 7530 – 40 35 4 14040 – 50 45 x 45x50 – 60 55 2 11060 – 70 65 6 39070 – 80 75 13 975

xx

ffx

x

33451765

52

1716 + 52x = 1765 + 45x7x = 49

x = 7



1. B. 3,12

H =77240

6012152030

4

51

41

31

21

4

= 3,12

2. A. x HG


3. C. 7,55

k = 577

144100493636259

= 7,55

4. A. 11,25

25,114

1512810 x

5. E. 5,87

H = 87,5

121

101

71

61

61

51

31

7

6. C. 10G = 2050.16.3 x

800x = 8000x = 10

7. C. 16 dan 4

20102 21

21 xxxxx

G = 8.221 xx

21 .xx = 64

2x =1

64x

21 xx = 20

11

64x

x = 20

0642012

xx 0416 11 xx

161 x ; 42 x

8. C. 80

802

60100 x km/jam

9. C. 2,668

G = 668,2000.10

15.1500.23.154

10. A.7

2

G = 3 8.4.2 4643

K = 72283

64164

7

2

72

4

KG


1. G = antilog

8122log116log126log130log110log120log132log107log

= antilog (1,0795) = 12

2. a. G = antilog

532log

16log8log4log2log

= antilog (0,9031) = 8

4,125

3216842

x

b. G = antilog

62log7log

3log8log5log3log

= antilog (0,6171) = 4,14

67,46

273853

x

c. G = antilog

58,64log5,31log

2,47log6,73log5,28log

= antilog (1,6611) = 45,35

12,495

8,645,312,476,735,28 x

d. G = 2300600.3002

4502

600300 x

3. a. H = 3

663

61

31

21

3

323

3632 x

b. H = 22,018340

10183

4

1042

1061

1048

1032

4

575,44

2,41,68,42,3 x

c. Rataan harmonis tidak ada (tidak terdefinisi)karena ada data 0.

34

6420 x

d. H = 82,2080430993,0

9

2239

20079

xx


4. a. k = 25625352311 222

b. k = 615,124

3,42,38,37,2 2222

5. 53754

500.2000.5000.4000.10

x

jadi, rataan harga kain per helai : Rp5.375

6.

1892

yxyx

22 2,72,7 xyxy

x

y22,7

18

2,7 2

x

x

02,718 22 xx

7. G = antilog

405,94log.3

5,84log.75,74log.85,64log75,54log.65,44log.45,34log.5

8. H =

171.2

161.9

151.5

141.6

131.8

121.4

34

9. G = antilog

30350log.10040log92

30log.7220log.2710log.12

10. k =34

12108642 248301410


1.

3000.320000.80000.100 100

5100

31002

x

= Rp6.800

2.31

93

6148

x bulan

3. H = 89,881808000.2

1001

801

2

4. a. G = antilog

8032log.2

27log.922log.1217log2512log.157log.122log.5

b. k = 4182450302410 322722171272

5. b.250500

4001200

500250050012002500

v

104200

v

v = 420

7. b. H =

45,3135.1229.1035.291210



1. C. 12

2. E.

11

1

2 fffffL

o

oo .c

3. D. 5 dan 84. C. 145. E. 55,21

21,5510.9812.2

8125,49

om

6. A. 50 - 597. B. 468. B. 27,80

80,275.161830.2

18305,25

om

9. C. 53,7

75,5315.201825.2

182545

om

10. C. 12

124.102123.2

21235,11

om


1. 59,5010.133247263.2

2472635,49

om

2. a. om = 12b. om = 2,3,7c. om = 21,22,23,26,27d. tidak ada moduse. om = 5f. om = 9


3. em = 6 ; om = 9

5,72

96 x

4.Interval Frekuensi

(f)x fx

20 – 29 5 24,5 122,530 – 39 10 34,5 34540 – 49 5 44,5 222,550 – 59 22 54,5 119960 – 69 11 64,5 709,570 – 79 7 74,5 521,5

a. 36,5510.11522.2

5225,49

om

b. 5260

3120

f

fxx


(f)x fx

10 – 25 6 17,5 10525 – 40 20 32,5 65040 – 55 44 47,5 209055 – 70 26 62,5 162570 – 85 3 77,5 232,585 – 100 1 92,5 92,5

95,471004795

f

fxx

36,4715.262044.2

20445,39

om



1. C. Rp138.750

Q2=

12

17440.2

5,136 .9

= 138,75 (ribu rupiah)

2. B. 2,53. B. 57

Q2=

20

20450.2

5,54 .10 = 57

4. D. ogif5. D. median, rataan hitung, dan modus A adalah

sama.6. B. 66,6

Q1=

21

154120.1

5,59 .10 = 66,6

7. E. 70,95

Q1=

27

304140.1

9,70 . 0.3 = 70,95

8. B. 46,5

Q3=

120

5504799.3

5,44 . 5 = 46,5

9. C. 5,5

Q1=

18

164112.1

5,11 . 4 = 14,7

Q3=

12

794112.3

5,23 . 4 = 25,17

Qd

= 5,517,1417,2521

21

13QQ

10. B. 0,273

koef. Qd

= 273,017,1417,2517,1417,25

13

13

QQQQ


1. a.Nilai Frekuensi Nilai Frekuensi

<20,5 0 >20,5 100<30,5 5 >30,5 95<40,5 13 >40,5 87<50,5 25 >50,5 75<60,5 40 >60,5 60<70,5 60 >70,5 40<80,5 76 >80,5 24<90,5 90 >90,5 10<100,5 100 >100,5 0

b.


c. Q1=

12

134100.1

5,40 . 10 = 50,5

Q2=

20

404100.2

5,60 . 10 = 65,5

Q3

=

16

604100.3

5,70 . 10 = 79,875

d. Qd

= 6875,1421

13QQ

koef. Qd

= 225,0375,130375,29

13

13

QQQQ

2. a. Q1=

8

6430.1

5,50 . 10 = 52,375

Q2=

7

14430.2

5,60 . 10 = 61,93

Q3

=

6

21430.3

5,70 . 10 = 73

b. 50,5 +

86x .10 = 55 x = 9,6

jadi, siswa yang lulus sebanyak :30 – 9,6 = 20,4 20 orang.

c. 50,5 +

8610 .10 = 55,5

jadi, batas nilai lulusnya adalah 55,5.

3. a. Q1=

36

344216.1

1,17 . 0,3 = 17,267

Q2=

53

704216.2

4,17 . 0,3 = 17,615

Q3

=

46

1234216.3

7,17 . 0,3 = 17,954

b. 17,4 +

5370100 .0,2 = 17,5

jadi, umur yang termasuk adalah yangkurang dari 17,5 tahun.

4. Ulangan INilai Frekuensi Nilai Frekuensi

<30,5 0 >30,5 25<40,5 2 >40,5 23<50,5 8 >50,5 17<60,5 16 >60,5 9<70,5 20 >70,5 5<80,5 23 >80,5 2<90,5 25 >90,5 0

a.


b. Q1=

8

2425.1

5,40 . 10 = 45,81

Q2=

8

8425.2

5,50 . 10 = 56,125

Q3

=

4

16425.3

5,60 . 10 = 67,375

c. Banyak siswa yang harus lulus :

10055

x 25 = 13,75

Berarti yang tidak lulus : 25 – 13,75 = 11,25

50,5 +

8825,11 .10 = 54,5625

jadi, agar 55% siswa lulus maka nilai bataslulusnya adalah 54,5625.

Ulangan IINilai Frekuensi Nilai Frekuensi

<30,5 0 >30,5 25<40,5 1 >40,5 24<50,5 3 >50,5 22<60,5 6 >60,5 19<70,5 16 >70,5 9<80,5 23 >80,5 2<90,5 25 >90,5 0

b. Q1=

10

6425.1

5,60 . 10 = 60,75

Q2=

10

6425.2

5,60 . 10 = 67

Q3

=

7

16425.3

5,70 . 10 = 73,25

c. 60,5 +

10625,11 .10 = 65,75

jadi, agar 55% siswa lulus maka batasnilai lulusnya adalah 65,75.

5. a. Q1=

45,10

3,74

72,43.1

5,34 . 10 = 37,97

Q2=

47,9

75,174

72,43.2

5,44 . 10 = 48,84

Q3

=

63,6

22,274

72,43.3

5,54 . 10 = 62,9

b. Qd

= 465,1297,379,6221

21

13QQ

c. koef. Qd

= 247,087,10095,24

13

13

QQQQ

6. Q1=

30

204159.1

5,19 . 10 = 26,083

Q2=

45

504159.2

5,29 . 10 = 36,056

Q3=

35

954159.3

5,39 . 10 = 46,43

7. a. Q1= 50 ; Q

2= 70 ; Q

3= 80

b. Qd

= 15508021

21

13QQ

c. koef. Qd

=133

13030

50805080

13

13

QQQQ


8. Q2= 399,5 +

326

1024

1000.2a

. 25 = 413,11

326398 a . 25 = 13,61

398 – a = 177,4744a = 220,5256 220

f = 525 + a + b = 1000

525 + 220 + b = 1000b = 255



1. C. 47D 4 = 4x + 0,6 45 xx

= 45 + 0,6 (50 – 45)= 47

10

113410

1

ni= 5,6

2. B. 20,4

101131

101

ni= 1,4

jadi, D 1 = 121 4,0 xxx = 20 + 0,4 (21 – 20)= 20,4

3. D. 64

101137

101

ni= 9,8

jadi, D 7 = 787 8,0 xxx = 60 + 0,8 (65 - 60)= 64

4. E. 29

101135

101

ni= 7

D 5 = 7x = 29

5. B. 3

101275

101

ni= 14

D 5 = 14x = 3

6. C. 28

D 5 =

11

141050.5

5,20 . 7 = 27,5 28

7. D. 17,22

D 1=

18

210159.1

5,9 . 10 = 17,22

8. E. 50,5

D 2 =

5

31040.2

5,40 . 10 = 50,5


1.Nilai Frekuensi

110 – 120 6120 – 130 25130 – 140 48140 – 150 72150 – 160 116160 – 170 60170 – 180 38180 – 190 22190 – 200 3

a. D 1 =

48

3110390.1

5,129 . 10 = 131,17

b. D 3 =

72

7910390.3

5,139 . 10 = 144,78

c. D 5 =

116

15110390.5

5,149 . 10 = 153,29

d. D 7 =

60

26710390.7

5,159 . 10 = 160,5

e. D 9 =

38

32710390.9

5,169 . 10 = 175,815

2. a.

101142

101

ni= 3

D 2 = 3x = 22

b. 10

114410

1 ni = 6

D 4 = 6x = 26

c. 10

114610

1 ni = 8

D 6 = 8x = 29


d. 10

114810

1 ni = 12

D 8 = 12x = 34

3. a. D 3 =

8

101050.3

5,39 . 10 = 45,75

D 6 =

12

181050.6

5,49 . 10 = 59,5

D 3 + D 6 = 45,75 + 59,5 = 105,25

b. D 8 =

6

391050.8

5,69 . 10 = 71,17

D 5 =

12

181050.5

5,49 . 10 = 55,33

D 8 - D 5 = 71,17 – 55,33 = 15,84

4. D 2 =

9

121077.2

5,7 . 4 = 9,01

D 3 =

17

211077.3

5,11 . 4 = 11,99

D 4 =

17

211077.4

5,11 . 4 = 13,8

D 5 =

15

381077.5

5,15 . 4 = 15.63

D 6 =

15

381077.6

5,15 . 4 = 17,68

D 7 =

14

531077.7

5,19 . 4 = 19,75

D 8 =

14

531077.8

5,19 . 4 = 21,95

D 9 =

6

671077.9

5,23 . 4 = 25,03

a. (D 7 + D 5 + D 3 ) – (D 6 + D 4 + D 2 )= 47,37 – 40,49 = 6,88

b. (D 8 + D 6 + D 4 + D 2 ) – (D 9 + D 7 + D 5 + D 3 )= 62,44 – 72,4 = -9,96

5. D 5 =

30

3510100.5

5,29a

. 10 = 30

1,5 = 50 – (35 + a)a = 15 – 1,5

= 13,5n = 100 = 75 + a + b b = 100 – 75 – 13,5 = 11,5



1. C. 2,75

88

14111087653 x

MD =81 75,263201235

2. E. 2,8

115

15913117 x

S = 8,2228164401651

3. D. 634

76

12810354

x

S = 6346

6825191649

61

4. E. 8

105

12146810

x

S 2 =51 84161640

5. E. 14

106

141595116 x

S = 14162512511661


6. E. 200

505

5070604030

x

S 2 =51 2000400100100400

7. C. 13,72ix if ii xf

114 3 342123 5 615132 9 1188141 12 1692150 5 750159 4 636168 2 336

975,13840

5559

i

ii

f

xfx

S =

2

2

2

2

975,138168.2

975,138159.4975,138150.5

975,138141.12975,138132.9

975,138123.5975,138114.3

401

= 13,72

8. A. 47,69

ix if ii xf37 4 14842 5 21047 9 42352 15 78057 12 68462 5 310

1,5150

2555

i

ii

f

xfx

S 2 =501

22

22

22

5,5162.55,5157.12

5,5152.155,5147.9

5,5142.55,5137.4

= 47,69


1. a. 6,98

518101537612

x

MD =81 5,45,85,05,55,65,25,35,2

= 4,25

b. 64

5973 x

MD =41 21313

c. 06,35

4,31,48,36,14,2 x

MD =51 848,034,004,174,046,166,0

d.6

351,6434,9628,8624,10453,6772,8

x

= 8,377

MD =61

17,13026,2057,1

251,0247,2924,1395,0

2. a. 6,45

57263

x

S = 22222 4,04,26,24,16,151

= 2,1751

44,3

S 2 = 3,44

b. 04,45

4,42,58,26,42,3 x

S = 22222 36,016,124,156,084,051

= 2464,13751 44,27

S 2 = 27,44

c. 428,07

1110000

x

S = 244,0572,0.3428,0.471 22

S 2 = 0,244

3. a. 85

14118521 x

S 21 =

51 183690936

83

14822 x

S 22 =

31 2436036

S 2gab =

3524.318.5

21

222

211

nnSnSn

= 25,208

162

b. 1x = 8

S 21 = 18

163

2216102 x

S 22 =

31 2436036

S 2gab =

3524.318.5

= 20,25


4. a. 96,95480

46064

i

ii

f

xfx

b. S = 6,109c.

S 2 =4801

2

22

22

22

22

22

22

22

96,951262

96,95122596,9511811

96,951141896,9511027

96,951063896,9510254

96,95987296.959485

96,95906696,958645

96,95822896,957816

96,9574996,95704

5.

6. A = 25

Intervalix if d fd 2fd

5 – 10 7,5 6 -17,5 -105 1837,510 – 15 12,5 5 -12,5 -62,5 781,2515 – 20 17,5 15 -7,5 -112,5 843,7520 – 25 22,5 10 -2,5 -25 62,525 – 30 27,5 5 2,5 12,5 31,2530 – 35 32,5 4 7,5 30 22535 – 40 37,5 3 12,5 37,5 468,7540 – 45 42,5 2 17,5 35 612,5

8,350190

i

ii

f

xfx

S = 23850

5,4862 = 81,82

S 2 = 82,81

7.

8. A = 20 ; C = 5

Intervalix if u fu 2fu

1 – 5 3 7 -3,4 -23,8 80,926 – 10 8 10 -2,4 -24 57,611 – 15 13 16 -1,4 -22,4 31,3616 – 20 18 32 -0,4 -12,8 5,1221 – 25 23 24 0,6 14,4 8,6426 – 30 28 18 1,6 28,8 46,0831 – 35 33 10 2,6 26 67,636 – 40 38 5 3,6 18 64,841 – 45 43 1 4,6 4,6 21,16

S =2

1238,8

12328,383

= 11,3.5

= 5 . 1,765 = 8,825S 2 = 77,88

9. S 2gab =

nn

105.2.10 = 4

n = 20

10. 12803240

xx

S = 232.401

ix = 25

232ix = 25.000

1024.40642ii xx = 25.000

1024.401280.642ix = 25.000

2ix = 65.960

a. x =

40

102 ix

=40

102 ix

=40

10.401280.2 = 54

b. S = 254102.401

ix

= 40962564.401 2

ii xx

= 4096256.4401 2

ii xx

= 4096.401280.25665960.4401

= 884.18 = 137,44


1. MD =

n

ii xx

n 1

||1

= || xx i

2. S 2 =

n

ii xx

n 1

21 = 2xxi

3. a. 505

10080402010

x

MD =51 325030103040

b. 505

7060504030

x

MD =51 12201001020

c. 85,21427212021302170

2160215021402130

x

MD =71

85,2285,12

15,2715,1715,785,285,12

=7

85,102= 14,69


d.8

71457110711571357130712571207115

x

= 7124,375

MD =81

625,20375,14375,9625,10

625,5625,0375,4375,9

=825,46

= 5,78

4.ix if fx

25 120 300035 201 703545 150 675055 75 412565 25 1625

57122535

x = 39,46

Q2= 29,5 +

201

1204571.2

. 10 = 37,73

MDx

=5711

|46,3965|25|46,3955|75|46,3945|150|46,3935|201|46,3925|120

= 9,22

MD2Q =

5711

|73,3765|25|73,3755|75|73,3745|150|73,3735|201|73,3725|120

= 9

Uji Kompetensi Akhir Bab 1

A. Pilihan Ganda

1. D. 13Data :7 8 9 10 10 10 11 11 12 12 13 14 15 18

Q1

Q2

Q3

2. C. 5,0Data :12 12 14 15 15 15 15 17 17 17 19 20 20 20

20 21 23 23 24

H = Q3-Q

1= 20 – 15 = 5

3. D. 3,5Data : 2 3 4 5 6 6 9 10

Q1=3,5 Q

2=5,5 Q

3=7,5

4. D. 3Data : 2 3 4 6 8 9 11

Q1

Q2

Q3

Qd

= 33921

21

13QQ

5. C. 13interval : 13,5 – 16,5batas bawah : 13

6. B. 37 dan 47interval : 37,5 – 47,5batas bawah : 37batas atas : 47

7. B. 3

148

910151718151117 x

MD =81 354134133

8. E. 59,25

Interval Frekuensi

41 – 45 346 – 50 651 – 55 656 – 60 461 - 65 5

Q3= 59,5 +

4

15424.3

. 5 = 59,25

9. C. 32

Interval Frekuensi

20 – 23 1424 – 27 1628 – 31 1832 – 35 1636 – 39 1440 – 43 1244 – 47 10

Q2= 31,5 +

16

484100.2

. 4 = 32


10. C. 13

Interval Frekuensi

151 – 164 7165 – 178 10179 – 192 x193 – 206 9207 - 220 6

mo= 184,5 = 178,5 +

910210

xx

. 14

19210

146

x

x

12x – 114 = 14x – 1402x = 26

x = 13

11. B. 25,62Q

9,51Q 7,6

3Q

4,5min

x 2,7xmaks

Data :

Q2= 6,25

Q1

Q3

5,4 ; 5,6 ; 5,7 ; 5,9 ; 6,0 ; 6,1 ; 6,2 ; 6,3 ; 6,5 ; 6,6 ; 6,7 ;6,9 ; 7,0 ; 7,2

12. D. median = 5 ; modus = 6Data : -6 -3 0 4 6 6 8 10

Q2= 5

mo= 6

13. C. 70,0

5077.1272.1467.1862.457.2

i

ii

f

xfx

= 70

14. D. 6,50

24x

= 5,25 x = 126

x = 3,525

susulanxx

= 126 + susulanx = 132,5

susulanx = 6,5

15. A. 13,0

Q2= 11,5 +

4

18440.2

. 3 = 13

16. C. Simpangan kuartil menjadi 80

50x

= 35 x = 1750

x =

50152

50152

xx

=50

15.501750.2

= 5550

7503500

40 = 2

.501

xxi

80.000 = 22 35.2 xxx ii

S = 2

152.501

xx

= 255152.501

x

= 2702.501

x

= 49002804.501 2

ii xx

= 4900.501750.280141250.4.501

= 6400 = 80

em = 2.40 – 15 = 65

17. C. Simpangan baku menjadi 20

10 = 2

.501

xx i

5000 = 22 2 xxxx ii

2ix = 5000 + 70.1750 – 50.35 2

= 66250

S = 2

152.501 xx

= 2702.501

ix

= 4900.501750.28066250.4.501

= 400 = 20

18. C. 10 192

G = 3 16.12.10 = 3 1920 = 10 192

19. D. 3,45

H = 45,3

21

31

41

61

51

3


20. E. 66

ix if ii xf35,5 5 177,545,5 4 18255,5 6 33365,5 7 458,575,5 8 60485,5 7 598,595,5 3 286,5

6640

2640

i

ii

fxf

x

21. C. 60,33

H =

5,953

5,857

5,758

5,657

5,556

5,454

5,355

40

= 60,33

22. A

505

4030507060 x

MDx

=51 12102002010

em = 50

x = em sehingga MDx= MD

em

23. D. 1531

86

9688710

x

S = 14001461

=6

10 = 1531

24. E. 200

505

3050706040

x

S 2 = 400040010010051

= 200

25. D

ix if ii xf114 3 342123 5 615132 9 1188141 12 1692150 5 750159 4 636168 2 336

975,13840

5559

i

ii

fxf

x

S =

2

22

22

22

975,138168.2

975,138159.4975,138150.5

975,138141.12975,138132.9

975,138123.5975,138114.3

.401

= 3791409

B. Bentuk Uraian

1.ix if ii xf

143 1 143148 4 592153 5 765158 15 2370163 7 1141168 6 1008173 2 346

a. 125,15940

6365

i

ii

fxf

x

mo= 155,5 +

7515.2515

. 5 = 158,278

b. Q1=

5

5440.1

5,150 . 5 = 155,5

Q2=

15

10440.2

5,155 . 5 = 158,83

Q3=

7

25440.3

5,160 . 5 = 164,07

c. MD x =401

875,13.2875,8.6875,3.7125,1.15

125,6.5125,11.4125,16

=40

25,216= 5,4

MDem =

401

17,14.217,9.617,4.7

83,0.1583,5.583,10.483,15

=40

3,213= 5,3325

d. 83,1582Q5,155

1Q 07,164

3Q

143min

x 173xmaks


2.ix if ii xf

71 5 35574 7 51877 10 77080 8 64083 3 249

a. 72,7633

2532

i

ii

f

xfx

MDx=

331

28,6.3

28,3.828,0.1072,2.772,5.5

=33

52,95= 2,89

b. me= Q

2= 75,5 +

10

12433.2

. 3 = 76,85

MDem =

331

15,6.615,3.8

15,0.1085,2.785,5.5

=33

8,112= 3,42

c. S 2 =331

4384,39.37584,10.8

0784,0.1039,7.77184,32.5

=334884,420

= 12,74

S = 74,12

d. Q1=

7

5433.1

5,72 . 3 = 73,89

Q3=

8

22433.3

5,78 . 3 = 79,53

RT = QQQ321

241

= 53,7985,76.289,7341

= 76,78

3. Q2=

137

2984730.2

5,59 . 10 = 64,39

mo= 79,5 +

146150.2146150 . 10 = 79,75

4.n

x = 80 x = 8n

1

n

xx= 82 80n + x = 82n + 82

x = 2n + 82


ix ii xf40,5 – 49,5 20 45 90050,5 – 59,5 30 55 165060,5 – 69,5 40 65 260070,5 – 79,5 25 75 187580,5 – 89,5 5 85 425

a. banyak kelas = 5panjang kelas = 10

b. 083,621207450

i

ii

fxf

x

c. S 2 =1201

917,22.5917,12.25

917,2.40083,7.30083,17.20

=120

34,1108= 9,236

bab 1 statistika

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