PEMBAHASAN STATISTIKA KELAS XI

1. Rata-rata = 7+5+8+6+7+8+7+7+7+9+5+8+6+8

14 = 9814 = 7

2. Median = 7+7

2 = 7

3. Modus = 7

4. Jangkauan = 9 – 5 = 4

5. Mean = 5+6+9+6+5+8+6+9+6+10

10 = 7

Median = 6

Modus = 6

6. Mean = 6+4+5+8+8+4+7+6

9 = 6

Median = 6+6

2=6

Modus = 6

7. Rata-rata = 4 (52)+6 (57)+8(62)+10(67)+8 (72)+4(77)

40 =

2.60040 = 65 kg

8. Mo = 64,5+( 22+2 )5 = 64,5 + 2,5 = 67

9. Kuartil atas = 34 x 40 = 30

Q3 = L3+( 34 ∑ f− fK3

f Q3

) i= 69,5+( 3

4.40−28

8 )5

= 69,5 + 1,25

= 70,75

10. D4=L4+( 4 xn10

−f k

f )xc = 59 ,5+( 4 x 4010

−10

8 )x 5 = 63,25

11. 6=3+7+5+a+6+4+6+9+6+410

a = 101

12.38(5)+43(x )+48(10)+53(8)+58 (4 )

27+x = 48

1.326 + 43 x = 48 ( 27 + x )

1.326 + 43 x = 1.296 + 48 x

5x = 30

x = 6

13. Data setelah diurutkan:

5 6 7 7 8 9 10 12 14

Q1 Q2 Q3

Kuartil bawah = 6+7

2 = 6,5

14. Kuartil atas = 10+12

2 = 11

15. D8=L8+( 8 xn10

− f k

f ) xc = 55 ,5+( 8 x4010

−28

8 ) x5 = 58

16. Nilai rata-rata = 6(22)+10(27)+2(32)+5(37)+4 (42)+3(47)

30 =

96030 = 32

17. Modus

Mo = L+( d1

d1+d2) i = 24,5+( 4

4+8 )5 = 24,5+( 412 )5 = 26,2

18. Media

Q2 = L2+( 12∑ f− fK2

f med ) i= 24,5+( 1

2.30−6

10 )5

= 24,5+ 910

.5

= 29

19. Kuartil atas

Q3 = L3+( 34 ∑ f− fK3

f Q3

) i2

= 34,5+( 34

.30−18

5 )5

= 34,5 + 4,5

= 39

20. Kuartil bawah

Q1 = L1+( 14∑ f− fK1

f Q1

) i= 24,5+( 1

4.30−6

10 )5

= 24,5 + 0,75

= 25,25

21. Simpangan kuartil

Qd = 12¿ Q1) =

12¿) = 6,875

22. Rata-rata data tersebut adalah 7

sehingga diperoleh ragam S2, yaitu

S2 = 16

( (4−7 )2+(8−7 )2+(5−7 )2+(9−7 )2+(10−7 )2+ (6−7 )2 )

= 16 (9 + 1 + 4 + 4 + 9 + 1)

= 4,67

S = √4,67 = 2,16

23.5(4 )+6(8)+7(5)+8 (M )+9 (2)

19+M = 7

121 + 8 M = 7 ( 19 + M)

121 + 8 M = 133 + 7M

M = 12

24.x+(x+2)+(x+7)

3 = 24

3x + 9 = 24 . 3

3x = 72 – 9

x = 21

3

25.10(7.000)+8(6.000)+12(10.000)+11(8.000)+9(5.000)

50 =

37150 = 7.420

26. x=x1. f 1+x2 . f 2

f 1+ f 2

7,5=7,8.20+x2 .12

20+12

7,5=156+x2 .12

32

240 = 156 + x2 . 12

12 x2 = 84

x2 = 7

27. x=x1. f 1+x2 . f 2

f 1+ f 2

6,6=6,5. f 1+9 .1f 1+1

6,6 f 1 + 6,6 = 6,5. f 1+9 .1

0,1 f 1 = 2,5

f 1 = 25

28. Rata-rata = x = 4 (2)+5 (5)+6(8)+7(11)+8 (4 )

30 =

8+25+48+77+3230 =

19030 = 6,3

Siswa dinyatakan lulus ujian matematika jika nilainya lebih besar dari 6,3.

Jadi, jumlah siswa yang lulus adalah 11 + 4 = 15 siswa

29. Nilai total kelompok = 50 x 64 = 3.200

Nilai rata-rata 49 siswa = 3.200−88,5

49 = 63,5

30. Misal:

Jumlah siswa laki-laki = a

Jumlah siswa perempuan = b

65a+54ba+b

=58

65a + 54 b = 58a + 58b

7a = 4b

b : a = 7 : 4

4

5