Bab 4 Statistik

8/19/2019 Bab 4 Statistik

1/69

A. PENGUMPULAN DATA

No Data Acak

1 0.66

2 0.41

3 0.20

4 0.61

5 0.89

6 0.54

7 0.018 0.33

9 0.81

10 0.35

11 0.53

12 0.88

13 0.73

14 0.99

15 0.44

16 0.83

17 0.90

18 0.64

19 0.05

20 0.53

21 0.03

22 0.00

23 0.70

24 0.26

25 0.87

26 0.45

27 0.14

28 0.22

29 0.04

30 0.81

31 0.90

32 0.31

33 0.96


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34 0.47

35 0.87

36 0.2437 0.15

38 0.13

39 0.46

40 0.00

41 0.58

42 0.92

43 0.82

44 0.05

45 0.50

46 0.2047 0.65

48 0.73

49 0.32

50 0.02

51 0.17

52 0.83

53 0.82

54 0.98

55 0.01

56 0.17

57 0.27

58 0.11

59 0.25

60 0.44

∑ 28.20

B. PENGOLAHAN DATA

IV.2.1 Pengolahan Data Acak

*Buat Data Random Sebanyak 60 Data

No DATA ACAK Data Acak 160-170


3/69

1 0.66 166.57 166.57

2 0.41 164.13 164.133 0.20 162.02 162.02

4 0.61 166.12 166.12

5 0.89 168.85 168.85

6 0.54 165.36 165.36

7 0.01 160.14 160.14

8 0.33 163.27 163.27

9 0.81 168.09 168.09

10 0.35 163.55 163.55

11 0.53 165.32 165.32

12 0.88 168.83 168.8313 0.73 167.31 167.31

14 0.99 169.89 169.89

15 0.44 164.42 164.42

16 0.83 168.30 168.30

17 0.90 168.98 168.98

18 0.64 166.44 166.44

19 0.05 160.51 160.51

20 0.53 165.28 165.28

21 0.03 160.28 160.28

22 0.00 160.00 160.00

23 0.70 166.95 166.95

24 0.26 162.62 162.62

25 0.87 168.66 168.66

26 0.45 164.50 164.50

27 0.14 161.42 161.42

28 0.22 162.25 162.25

29 0.04 160.41 160.41

30 0.81 168.08 168.08

31 0.90 168.98 168.98

32 0.31 163.11 163.11

33 0.96 169.55 169.55

34 0.47 164.75 164.75

35 0.87 168.67 168.67

36 0.24 162.45 162.45

37 0.15 161.48 161.48

38 0.13 161.30 161.30


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39 0.46 164.59 164.59

40 0.00 160.03 160.03

41 0.58 165.81 165.8142 0.92 169.23 169.23

43 0.82 168.24 168.24

44 0.05 160.47 160.47

45 0.50 164.97 164.97

46 0.20 162.00 162.00

47 0.65 166.53 166.53

48 0.73 167.29 167.29

49 0.32 163.25 163.25

50 0.02 160.23 160.23

51 0.17 161.65 161.6552 0.83 168.29 168.29

53 0.82 168.15 168.15

54 0.98 169.84 169.84

55 0.01 160.13 160.13

56 0.17 161.70 161.70

57 0.27 162.73 162.73

58 0.11 161.06 161.06

59 0.25 162.47 162.47

60 0.44 164.43 164.43

∑ 28.20 9881.96 9881.96

IV.2.2 Pengolahan Data Tunggal

No

1 160.00 -4.70 22.07

2 160.03 -4.67 21.79

3 160.13 -4.57 20.91

4 160.14 -4.55 20.75

5 160.23 -4.47 19.95

6 160.28 -4.42 19.57

7 160.41 -4.29 18.43

8 160.47 -4.23 17.88

9 160.51 -4.19 17.57

Χ ( ) Χ− Χ ( )2

Χ− Χ


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10 161.06 -3.64 13.24

11 161.30 -3.40 11.57

12 161.42 -3.28 10.7513 161.48 -3.22 10.38

14 161.65 -3.05 9.28

15 161.70 -2.99 8.97

16 162.00 -2.70 7.27

17 162.02 -2.68 7.18

18 162.25 -2.45 6.01

19 162.45 -2.25 5.06

20 162.47 -2.23 4.98

21 162.62 -2.08 4.34

22 162.73 -1.97 3.8723 163.11 -1.59 2.52

24 163.25 -1.45 2.10

25 163.27 -1.43 2.03

26 163.55 -1.15 1.33

27 164.13 -0.57 0.32

28 164.42 -0.28 0.08

29 164.43 -0.27 0.07

30 164.50 -0.20 0.04

31 164.59 -0.11 0.01

32 164.75 0.05 0.00

33 164.97 0.27 0.08

34 165.28 0.58 0.33

35 165.32 0.62 0.38

36 165.36 0.66 0.44

37 165.81 1.11 1.23

38 166.12 1.42 2.02

39 166.44 1.74 3.03

40 166.53 1.83 3.36

41 166.57 1.87 3.48

42 166.95 2.25 5.08

43 167.29 2.59 6.72

44 167.31 2.61 6.81

45 168.08 3.38 11.44

46 168.09 3.39 11.52

47 168.15 3.45 11.94

48 168.24 3.54 12.53


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49 168.29 3.59 12.92

50 168.30 3.60 12.95

51 168.66 3.96 15.7052 168.67 3.97 15.73

53 168.83 4.13 17.09

54 168.85 4.15 17.25

55 168.98 4.28 18.35

56 168.98 4.28 18.35

57 169.23 4.53 20.53

58 169.55 4.85 23.57

59 169.84 5.14 26.41

60 169.89 5.19 26.96

∑ 9881.96 0.00 596.52

Mean

9912.01/60 = 164.70

Modu

168.98

Med!an

k = 1/2 n = 60/2 = 30

Nilai m!ian

= 1/2"#$k % #$k%1&&

= 1/2"#164.50 % #164.59 %1 && = 165.04

A. "ua#t!l

*berdasarkan letak;

'1 = 1"#60 % 1&/4 = 15.25

( )

4

1+= ni

Qi

=ΣΧ

η = Χ


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'2 = 2"#60 % 1&/4 = 30.5

'3 = 3"#60 % 1&/4 = 45.75

B. Pe#ent!l

*Berdasarkan letak ;

(5 =5"#60%1&/100 = 3.05

(50 =50"#60%1&/100 = 30.50

(95 =95"#60%1&/100 = 57.95

$. De!l

*Berdasarkan letak ;

D1 =1"#60 % 1&/10 = 6.10

D5 =5"#60 % 1&/10 = 30.50

D9 =9"#60 % 1&/10 = 54.90

( )100

1+= ni Pi

( )

10

1+= ni

Di


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D. Va#!ance

=8.94

E. %TDV

)a*ian

,t!+4 =

,t!+3 =

&. 'u#to!

2.03

,.. K*toi

( ) 22

1−

−=∑

n

X Xi s

( )σ

2S =σ 2S

=4 s =

4 s

=3

s =3 s

( )

( )

4

4

4 /1

σ

α ∑ −

= X Xin

STD

4α

=

( ) 2

160

52.596

−=

=

Σ

96.79

41.9730*60/1=


9/69

ltok*tik

kt*anan

ika k*a ltok*tik #m*ncin&

k*a mok*tik #no*mal&

k*a latk*titik #mn!ata*&

Nilai kt*toi an !i !aat a!ala 2.03 3. a!i k*

G. %k(ene

0.07

,.. ,k:n

34>α

34 =α

34


10/69


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PEN


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Data @**t


13/69

160.00

160.03160.13

160.14

160.23

160.28

160.41

160.47

160.51

161.06

161.30

161.42161.48

161.65

161.70

162.00

162.02

162.25

162.45

162.47

162.62

162.73

163.11

163.25

163.27

163.55

164.13

164.42

164.43

164.50

164.59

164.75

164.97

165.28

165.32

165.36

165.81

166.12


14/69

166.44

166.53

166.57166.95

167.29

167.31

168.08

168.09

168.15

168.24

168.29

168.30

168.66168.67

168.83

168.85

168.98

168.98

169.23

169.55

169.84

169.89

9881.96

-103.67 487.04

-101.71 474.74

-95.63 437.34

-94.50 430.43

-89.12 398.07

-86.54 382.81

-79.11 339.59

-75.58 319.57

-73.63 308.59

( ) 3 Χ− Χ ( ) 4 Χ− Χ


15/69

-48.19 175.36

-39.36 133.90

-35.23 115.47-33.43 107.68

-28.26 86.09

-26.86 80.44

-19.61 52.89

-19.25 51.58

-14.74 36.15

-11.39 25.63

-11.12 24.81

-9.05 18.85

-7.62 14.99-4.00 6.34

-3.05 4.43

-2.90 4.13

-1.53 1.76

-0.18 0.10

-0.02 0.01

-0.02 0.01

-0.01 0.00

0.00 0.00

0.00 0.00

0.02 0.01

0.19 0.11

0.24 0.15

0.29 0.19

1.37 1.52

2.87 4.08

5.28 9.19

6.17 11.31

6.50 12.13

11.46 25.83

17.43 45.20

17.78 46.42

38.69 130.84

39.12 132.81

41.24 142.46

44.37 157.06


16/69


17/69

'2 = 164.50 % 0.05"#164.59 - 164.50& = 164.51

'3 = 168.09 % 0.75"#168.15 - 168.09& = 168.14

'et )

$#& = Nilai n

( =,ia !ila

$# % 1& = Nilai a!a

*Berdasarkan Nilai ;

P! * +,- / P0+,- / 1 +,-

(5 = 160.13 % 0.05"#160.14 - 160.13& = 160.13

(50 = 164.50 % 0.50"#164.59 - 164.50& = 164.54

(95 = 169.55 % 0.95"#169.84 - 169.55& = 169.82

'et )

$#& = Nilai n

( =,ia !ila

$# % 1& = Nilai a!a

*Berdasarkan Nilai ;

D! * +,- / P0+,- / 1 +,-

D1 = 160.28 % 0.10"#160.41 - 160.28& =

D5 = 164.50 % 0.50"#164.59 - 164.50& =

D9 = 168.98 % 0.90"#169.23 - 168.98& =

'et )

$#& = Nilai n


18/69

( =,ia !ila

$# % 1& = Nilai a!a

'et )

c+0.5

2.99+4

2.99+3

'et )

1/mla anakna !a

mla l* !ata ta

nolaan !ata

n-1 =

( ) =4 s ( ) 4^4∑ s

( ) =−∑ 2

X Xi

99.2

03.2=

( ) =−∑ 4

X Xi

=n/1


19/69

0.68

mok*tik latk*tik

a an !iakai..#k*a latk*titik /mn!ata*&

'et )

1/mla

mla l

nolaa

0.02

=

( ) =−∑ 3

X X

( ) =3 s ( ) 3^3∑ s

=V

=99.2

07.0

=n/1


20/69

nati;& mncn kanan # oiti

ncn kanan/oiti;&


21/69

BAB IV

GUMPULAN DAN PENGOLAHAN DATA


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l*an !ata $

mla anak !ata

mla !ata/2 #nilai tna&

ata kla ata #nilai tna&

ata kla a:a #nilai tna%1&


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a*na *!aa*kan ltak

kan koma !a*i nilai *!aa*kan ltak

tla nilai !a*i *!aa*kan ltak

a*na *!aa*kan ltak



.

a*na *!aa*kan ltak


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mla #kl*an !ata *t-man&+2

mla anakna !ata - 1

2.99

79.96

26.74

ta

l 4 tal


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anakna !ata

* !ata tal 4tal

an !ata


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;&


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IV.22.3 Pengolahan Data Be#golong ,'elo45ok

Ma6 !ata ma #a& 169.89

M!n !ata min #& 160.00

7ange ma - min 9.89

EEEEEE'ela 1 % 3.33 lo #n& 6.92

Inte#8al ,I *an/kla 1.43

;

'ela Inte#8al & &.'u4 +!

1 160.00 161.42 12 12

2 161.43 162.85 9 21

3 162.86 164.28 5 26

4 164.29 165.71 10 365 165.72 167.14 6 42

6 167.15 168.56 8 50

7 168.57 169.99 10 60

∑ 60 247

MEAN )

MEDIAN )

∑∑

= fi

xi fi

X

*=

=

c LO + { ( )m

oi

f

f n

∑−2 }(∑


52/69

Modu )

*berdasarkan letak

'1 =

'2 =

'3 =

Pe#ent!l )

*berdasarkan letak

"ua#t!l )

c LO +

{ 211

bb

b

+ }

4.niQi =

100

*ni P i =


53/69


54/69

'u#to!

S.E.Kurtosis

ltok*tik mok*tik

kt*anan

ika k*a ltok*tik #m*ncin&

k*a mok*tik #no*mal&

k*a latk*titik #mn!ata*&

%k(ene )

%TDV )

( )1

2

−

−= ∑ n

X X fiS i

( )

( ) 4

4

4

*1

σ

α

∑ −=

X X f n

ii

∑

STDV

4α

=

34>α

34=α

34


55/69

%.E.%k(ene

k*a imt*i mncn ki*i #nati;&

( )=

−

=∑

3

3

3

*

σ

α

X X f n

ii

STDV

3α

=


56/69


57/69

'et )Go Nilai ata a:a #BKB& !a*i kla an mnan!n mla ;*kni t*

1 ,lii ;*kni kla mo! !nan kla lmna

2 ,lii ;*kni kla mo! !nan kla lmna

c Nilai kla int*al

*berdasarkan nilai

'1 =

'2 =

'3 =

'et )

Nilai ata a:a kla -0.0005

#nilai ata a:a kla an mmat ka*til k-1 !ik*ani -0.0005%

F = mla ;*kni kmlati; lm kla an mnan!n

ka*til k-i

; F*kni !a*i kla an mnan!n ka*til k=i


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(5 =

(50 =

(95 =

'et )

Nilai ata a:a kla -0.0005

#nilai ata a:a kla an mmat ka*til k-1 !ik*ani -0.0005%

F = mla ;*kni kmlati; lm kla an mnan!n

ka*til k-i

; F*kni !a*i kla an mnan!n ka*til k=i


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mncn kanan # oiti;&


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anak -0.0005


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