Tugas Statistika Dan Probabilitas

1

TUGAS STATISTIKA DAN PROBABILITAS

Oleh Devi / 1206243601 / Teknik Kimia

Tabel 1. Titik didik senyawa-senyawa alkohol, aldehida, dan fenol

No. Nama Senyawa Titik Didih

(C)

1 Methanol 65

2 Ethanol 78

3 2-Propanol 83

4 2-Methyl-2-propanol 83

5 2-Propen-1-ol 97

6 1-Propanol 97

7 2-Butanol 99

8 2-Methyl-2-butanol 102

9 2-Methyl-1-propanol 108

10 1-Butanol 116

11 3-Pentanol 116

12 2-Pentanol 119

13 3-Methyl-3-pentanol 123

14 2-Methoxyethanol 124

15 1-Chloro-2-propanol 127

16 2-Methyl-1-butanol 129

17 3-Methyl-1-butanol 131

18 2-Chloroetanol 131

19 4-Methyl-2-pentanol 132

20 2-Ethoxyethanol 135

21 3-Hexanol 135

22 1-Pentanol 138

23 2-Hexanol 139

24 Cyclopentanol 140

25 3-Hydroxy-2-butanone 145

26 3,2,2-Trichloroethanol 151

27 1-Hexanol 157

28 2-Heptanol 159

29 Cyclohexanol 161

30 1-Amino-2-propanol 163

31 4-Hydroxy-4-methyl-2-pentanone 166

32 2-Furylmethanol 171

33 1-Heptanol 176

34 2-Octanol 179

35 1,2-Propanediol 187

36 1-Octanol 194

37 1,2-Ethanediol 197

38 1-Phenylethanol 202

39 Benzyl alcohol 205

40 1,3-Propanediol 214

2

41 2-Phenylethanol 219

42 1-Decanol 231

43 3-Phenyl-1-propanol 236

44 Cinnamyl alcohol 257

45 1-Deodecanol 259

46 4-Methoxybenzyl alcohol 259

47 Glycerol 290

48 2,2-Dimethyl-1-propanol 113

49 Diphenylmethanol 288

50 Propanal 49

51 2-Butenal 103

52 Hexanal 128

53 Heptanal 155

54 2-Furancarboxaldehyde 161

55 Cyclohexane-carboxaldehyde 161

56 Octanal 171

57 Benzaldehyde 179

58 Phenylethanal 194

59 2-Hydroxy-benzaldehyde 196

60 4-Methylbenzaldehyde 204

61 2-Chlorobenzaldehyde 213

62 3-Phenylpropanol 224

63 3-Bromobenzaldehyde 235

64 2-Methoxybenzaldehyde 245

65 4-Methoxybenzaldehyde 247

66 Cinnamaldehyde 252

67 3,4-Methylenedioxy-benzaldehyde 263

68 3,4-Dimethoxy-benzaldehyde 214

69 2-Hydroxybenzaldehyde 196

70 2-Methoxyphenol 205

71 4-Chlorophenol 217

72 Methyl 2-hydroxybenzoate 223

73 2-tert-Butylphenol 224

74 Ethyl 2-hydroxybenzoate 234

3

UKURAN PEMUSATAN

1. Mean Aritmatika

= =1

= 12619

74= 170,52

2. Median Penentuan median perlu diawali dengan pengurutan data dari yang kecil ke yang besar.

Dengan demikian, data di atas dapat diurut sebagai berikut.

Tabel 2. Data terjajar titik didik senyawa-senyawa alkohol, aldehida, dan fenol

No. Nama Senyawa Titik Didih

(C)

1 Propanal 49

2 Methanol 65

3 Ethanol 78

4 2-Propanol 83

5 2-Methyl-2-propanol 83

6 2-Propen-1-ol 97

7 1-Propanol 97

8 2-Butanol 99

9 2-Methyl-2-butanol 102

10 2-Butenal 103

11 2-Methyl-1-propanol 108

12 2,2-Dimethyl-1-propanol 113

13 1-Butanol 116

14 3-Pentanol 116

15 2-Pentanol 119

16 3-Methyl-3-pentanol 123

17 2-Methoxyethanol 124

18 1-Chloro-2-propanol 127

19 Hexanal 128

20 2-Methyl-1-butanol 129

21 3-Methyl-1-butanol 131

22 2-Chloroetanol 131

23 4-Methyl-2-pentanol 132

24 2-Ethoxyethanol 135

25 3-Hexanol 135

26 1-Pentanol 138

27 2-Hexanol 139

28 Cyclopentanol 140

29 3-Hydroxy-2-butanone 145

30 3,2,2-Trichloroethanol 151

31 Heptanal 155

32 1-Hexanol 157

4

33 2-Heptanol 159

34 Cyclohexanol 161

35 2-Furancarboxaldehyde 161

36 Cyclohexane-carboxaldehyde 161

37 1-Amino-2-propanol 163

38 4-Hydroxy-4-methyl-2-pentanone 166

39 2-Furylmethanol 171

40 Octanal 171

41 1-Heptanol 176

42 2-Octanol 179

43 Benzaldehyde 179

44 1,2-Propanediol 187

45 1-Octanol 194

46 Phenylethanal 194

47 2-Hydroxy-benzaldehyde 196

48 2-Hydroxybenzaldehyde 196

49 1,2-Ethanediol 197

50 1-Phenylethanol 202

51 4-Methylbenzaldehyde 204

52 Benzyl alcohol 205

53 2-Methoxyphenol 205

54 2-Chlorobenzaldehyde 213

55 1,3-Propanediol 214

56 3,4-Dimethoxy-benzaldehyde 214

57 4-Chlorophenol 217

58 2-Phenylethanol 219

59 Methyl 2-hydroxybenzoate 223

60 3-Phenylpropanol 224

61 2-tert-Butylphenol 224

62 1-Decanol 231

63 Ethyl 2-hydroxybenzoate 234

64 3-Bromobenzaldehyde 235

65 3-Phenyl-1-propanol 236

66 2-Methoxybenzaldehyde 245

67 4-Methoxybenzaldehyde 247

68 Cinnamaldehyde 252

69 Cinnamyl alcohol 257

70 1-Deodecanol 259

71 4-Methoxybenzyl alcohol 259

72 3,4-Methylenedioxy-benzaldehyde 263

73 Diphenylmethanol 288

74 Glycerol 290

5

=

2 +

2 + 1

2

= 37 + 38

2

= 163 + 166

2= 164,5

3. Modus = 161

4. Kuantil

Kuartil Kuartil pertama :

1 = + 2

4

1 = 19 = 128

Kuartil kedua :

2 = = 164,5

Kuartil ketiga :

3 = 3 + 2

4

3 = 56 = 214 Desil

Desil pertama :

1 = 1( + 1)

10

1 =7 + 8

2= 98

Desil kedua :

2 = 2( + 1)

10

2 = 15 = 119

Desil ketiga :

3 = 3( + 1)

10

3 =22 + 23

2= 131,5

Desil keempat :

4 = 4( + 1)

10

4 = 30 = 151

Desil kelima :

5 = 5( + 1)

10

6

5 =37 + 38

2= 164,5

Desil keenam :

6 = 6( + 1)

10

6 = 45 = 194

Desil ketujuh :

7 = 7( + 1)

10

7 =52 + 53

2= 205

Desil kedelapan :

8 = 8( + 1)

10

8 = 60 = 224

Desil kesembilan :

9 = 9( + 1)

10

9 =67 + 68

2= 249,5

- Persentil Persentil 1 :

1 = 1( + 1)

100

1 = 0,75 = 0 + 0,75 1 0 = 36,75 Persentil 2 :

2 = 2( + 1)

100

2 = 1 + 0,5 2 1 = 57 Persentil 3 :

3 = 3( + 1)

100

3 = 2 + 0,25 3 2 = 68,25 Persentil 4 :

4 = 4( + 1)

100

4 = 3 = 78 Persentil 5 :

5 = 5( + 1)

100

5 = 3 + 0,75 4 3 = 81,75 Persentil 6 :

6 = 6( + 1)

100

6 = 4 + 0,5 5 4 = 83 Persentil 7 :

7 = 7( + 1)

100

7

7 = 5 + 0,25 6 5 = 86,5 Persentil 8 :

8 = 8( + 1)

100

8 = 6 = 97 Persentil 9 :

9 = 9( + 1)

100

9 = 6 + 0,75 7 6 = 97 Persentil 10 :

10 = 10( + 1)

100

10 = 7 + 0,5 8 7 = 98 Persentil 11 :

11 = 11( + 1)

100

11 = 8 + 0,25 9 8 = 99,75 Persentil 12 :

12 = 12( + 1)

100

12 = 9 = 102 Persentil 13 :

13 = 13( + 1)

100

13 = 9 + 0,75 10 9 = 102,75 Persentil 14 :

14 = 14( + 1)

100

14 = 10 + 0,5 11 10 = 105,5 Persentil 15 :

15 = 15( + 1)

100

15 = 11 + 0,25 12 11 = 109,25 Persentil 16 :

16 = 16( + 1)

100

16 = 12 = 113 Persentil 17 :

17 = 17( + 1)

100

17 = 12 + 0,75 13 12 = 115,25 Persentil 18 :

18 = 18( + 1)

100

18 = 13 + 0,5 14 13 = 116

Persentil 19 :

19 = 19( + 1)

100

19 = 14 + 0,25 15 14 = 116,75 Persentil 20 :

20 = 20( + 1)

100

20 = 15 = 119

8

Persentil 21 :

21 = 21( + 1)

100

21 = 15 + 0,75 16 15 = 122 Persentil 22 :

22 = 22( + 1)

100

22 = 16 + 0,5 17 16 = 123,5 Persentil 23 :

23 = 23( + 1)

100

23 = 17 + 0,25 18 17 = 124,75 Persentil 24 :

24 = 24( + 1)

100

24 = 18 = 127 Persentil 25 :

25 = 25( + 1)

100

25 = 18 + 0,75 19 18 = 127,75 Persentil 26 :

26 = 26( + 1)

100

26 = 19 + 0,5 20 19 = 128,5 Persentil 27 :

27 = 27( + 1)

100

27 = 20 + 0,25 21 20 = 129,5 Persentil 28 :

28 = 28( + 1)

100

28 = 21 = 131 Persentil 29 :

29 = 29( + 1)

100

29 = 21 + 0,75 22 21 = 131 Persentil 30 :

30 = 30( + 1)

100

30 = 22 + 0,5 23 22 = 131,5 Persentil 31 :

31 = 31( + 1)

100

31 = 23 + 0,25 24 23 = 132,75 Persentil 32 :

32 = 32( + 1)

100

32 = 24 = 135 Persentil 33 :

33 = 33( + 1)

100

33 = 24 + 0,75 25 24 = 135

9

Persentil 34 :

34 = 34( + 1)

100

34 = 25 + 0,5 26 25 = 136,5 Persentil 35 :

35 = 35( + 1)

100

35 = 26 + 0,25 27 26 = 138,25 Persentil 36 :

36 = 36( + 1)

100

36 = 27 = 139 Persentil 37 :

37 = 37( + 1)

100

37 = 27 + 0,75 28 27 = 139,75 Persentil 38 :

38 = 38( + 1)

100

38 = 28 + 0,5 29 28 = 142,5 Persentil 39 :

39 = 39( + 1)

100

39 = 29 + 0,25 30 29 = 146,5 Persentil 40 :

40 = 40( + 1)

100

40 = 30 = 151 Persentil 41 :

41 = 41( + 1)

100

41 = 30 + 0,75 31 30 = 154 Persentil 42 :

42 = 42( + 1)

100

42 = 31 + 0,5 32 31 = 156 Persentil 43 :

43 = 43( + 1)

100

43 = 32 + 0,25 33 32 = 157,5 Persentil 44 :

44 = 44( + 1)

100

44 = 33 = 159 Persentil 45 :

45 = 45( + 1)

100

45 = 33 + 0,75 34 33 = 160,5

Persentil 46 :

46 = 46( + 1)

100

46 = 34 + 0,5 35 34 = 161

10

Persentil 47 :

47 = 47( + 1)

100

47 = 35 + 0,25 36 35 = 161 Persentil 48 :

48 = 48( + 1)

100

48 = 36 = 161 Persentil 49 :

49 = 49( + 1)

100

49 = 36 + 0,75 37 36 = 162,5 Persentil 50 :

50 = 50( + 1)

100

50 = 37 + 0,5 38 37 = 164,5 Persentil 51 :

51 = 51( + 1)

100

51 = 38 + 0,25 39 38 = 167,25 Persentil 52 :

52 = 52( + 1)

100

52 = 39 = 171 Persentil 53 :

53 = 53( + 1)

100

53 = 39 + 0,75 40 39 = 171 Persentil 54 :

54 = 54( + 1)

100

54 = 40 + 0,5 41 40 = 173,5 Persentil 55 :

55 = 55( + 1)

100

55 = 41 + 0,25 42 41 = 176,75 Persentil 56 :

56 = 56( + 1)

100

56 = 42 = 179 Persentil 57 :

57 = 57( + 1)

100

57 = 42 + 0,75 43 42 = 179 Persentil 58 :

58 = 58( + 1)

100

58 = 43 + 0,5 44 43 = 183

Persentil 59 :

59 = 59( + 1)

100

59 = 44 + 0,25 45 44 = 188,75

11

Persentil 60 :

60 = 60( + 1)

100

60 = 45 = 194 Persentil 61 :

61 = 61( + 1)

100

61 = 45 + 0,75 46 45 = 194 Persentil 62 :

62 = 62( + 1)

100

62 = 46 + 0,5 47 46 = 195 Persentil 63 :

63 = 63( + 1)

100

63 = 47 + 0,25 48 47 = 196 Persentil 64 :

64 = 64( + 1)

100

64 = 48 = 196 Persentil 65 :

65 = 65( + 1)

100

65 = 48 + 0,75 49 48 = 196,75 Persentil 66 :

66 = 66( + 1)

100

66 = 49 + 0,5 50 49 = 199,5 Persentil 67 :

67 = 67( + 1)

100

67 = 50 + 0,25 51 50 = 202,5 Persentil 68 :

68 = 68( + 1)

100

68 = 51 = 204 Persentil 69 :

69 = 69( + 1)

100

69 = 51 + 0,75 52 51 = 204,75 Persentil 70 :

70 = 70( + 1)

100

70 = 52 + 0,5 53 52 = 205 Persentil 71 :

71 = 71( + 1)

100

71 = 53 + 0,25 54 53 = 207 Persentil 72 :

72 = 72( + 1)

100

72 = 54 = 213

12

Persentil 73 :

73 = 73( + 1)

100

73 = 54 + 0,75 55 54 = 213,75 Persentil 74 :

74 = 74( + 1)

100

74 = 55 + 0,5 56 55 = 214 Persentil 75 :

75 = 75( + 1)

100

75 = 56 + 0,25 57 56 = 214,75 Persentil 76 :

76 = 76( + 1)

100

76 = 57 = 217 Persentil 77 :

77 = 77( + 1)

100

77 = 57 + 0,75 58 57 = 218,5 Persentil 78 :

78 = 78( + 1)

100

78 = 58 + 0,5 59 58 = 221 Persentil 79 :

79 = 79( + 1)

100

79 = 59 + 0,25 60 59 = 223,25 Persentil 80 :

80 = 80( + 1)

100

80 = 60 = 224 Persentil 81 :

81 = 81( + 1)

100

81 = 60 + 0,75 61 60 = 224 Persentil 82 :

82 = 82( + 1)

100

82 = 61 + 0,5 62 61 = 227,5 Persentil 83 :

83 = 83( + 1)

100

83 = 62 + 0,25 61 60 = 224 Persentil 84 :

84 = 84( + 1)

100

84 = 63 = 234

Persentil 85 :

85 = 85( + 1)

100

85 = 63 + 0,75 64 63 = 234,75

13

Persentil 86 :

86 = 86( + 1)

100

86 = 64 + 0,5 65 64 = 235,5 Persentil 87 :

87 = 87( + 1)

100

87 = 65 + 0,25 66 65 = 238,25 Persentil 88 :

88 = 88( + 1)

100

88 = 66 = 245 Persentil 89 :

89 = 89( + 1)

100

89 = 66 + 0,75 67 66 = 246,5 Persentil 90 :

90 = 90( + 1)

100

90 = 67 + 0,5 68 67 = 249,5 Persentil 91 :

91 = 91( + 1)

100

91 = 68 + 0,25 69 68 = 253,25 Persentil 92 :

92 = 92( + 1)

100

92 = 69 = 257 Persentil 93 :

93 = 93( + 1)

100

93 = 69 + 0,75 70 69 = 258,5 Persentil 94 :

94 = 94( + 1)

100

94 = 70 + 0,5 71 70 = 259 Persentil 95 :

95 = 95( + 1)

100

95 = 71 + 0,25 72 71 = 260 Persentil 96 :

96 = 96( + 1)

100

96 = 72 = 263 Persentil 97 :

97 = 97( + 1)

100

97 = 72 + 0,75 73 72 = 281,75

Persentil 98 :

98 = 98( + 1)

100

98 = 73 + 0,5 74 73 = 289

14

Persentil 99 :

99 =

UKURAN PENYEBARAN

1. Jangkauan =

= 290 49 = 241

2. Jangkauan Persentil 1090 = 90 10

1090 = 249,5 98 = 151,5

3. Simpangan Kuartil

=3 1

2

=214 128

= 2= 43

4. Simpangan Mutlak Rata-Rata

= =1

= 49170,52 + 65170,52 ++ 288170,52 + 290170,52

74 = 47,595

5. Simpangan Baku

=

2=1

1

= 49170,52 2+ 65170,52 2++ 288170,52 2+ 290170,52 2

73 = 56,522

6. Varians

2 =

2

=1

1= 3194,773

Koefisien variasi

=

= 56,522

170,52= 0,331

7. Moment - Moment ke-r

=

=1

- Moment ke-r simpangan terhadap mean

, =

=1

- Moment ke-r simpangan terhadap sembarang

, =

=1

15

8. Koefisien Skewness

Terdapat beberapa koefisien yang bdapat dijadika koefisien kemencengan (skewness

factor/coefficient), antara lain :

, =

, = 3( )

, =3 22 + 1

3 1= 0,151

,1090 =90 250 + 10

90 10= 0,122

Koefisien kurtosis

=

90 10=

3 1

90 10= 0,284