Proyecto mermelada(tipos de muestreo)

datos Bºrix
1 24
2 24 DE UNA POBLACION DE 200 DATOS SE SELECCIONA UNA MUESTR
3 24
4 26
5 26
6 27
7 27 NUMEROS ALEATORIOS
8 29 MUESTRA 1 MUESTRA2 MUESTRA3 MUESTRA4
9 30 1 79.01 3.17 65.79 25.76
10 31 2 45.39 119.77 51.07 119.39
11 33 3 28.56 38.16 83.6 44.79
12 34 4 94.09 36.48 116.32 109.01
13 35 5 105.42 18.2 7.76 24.13
14 36 6 119.69 2.61 82.76 39.35
15 36 7 24.23 94.47 48.96 24.05
16 36 8 58.26 14.74 18.12 48.09
17 38 9 71.71 43.62 75.15 117.36
18 38 10 63.21 4.93 27.97 90.85
19 40 11 102.15 111.7 18.1 112.96
20 41 12 118.93 48 108.6 29.78
21 41 13 53.58 66.73 79.49 62.96
22 44 14 109.96 113.86 59.27 8.84
23 47 15 105.07 105.11 64.99 27.82
24 51 16 2.54 66.07 117.31 107.13
25 51 17 27.69 105 66.3 85.21
26 51 18 25.84 37.22 50.06 28.86
27 51 19 91.3 46.81 10.97 80.17
28 51 20 79.11 80.86 34.1 55.11
29 51
31 52 79 3 65 25
32 52 45 119 51 119
33 53 28 38 83 44
34 54 94 36 116 109
35 54 105 18 7 24
36 55 119 2 82 39
37 55 24 94 48 24
38 56 58 14 18 48
39 57 71 43 75 117
40 57 63 4 27 90
41 58 102 111 18 112
42 59 118 47 108 29
43 59 53 66 79 62
44 60 109 113 59 8
45 60 105 105 64 27
46 60 2 66 117 107
47 60 27 105 66 85
48 60 25 37 50 28
49 60 91 46 10 80
50 61 79 80 34 55
52 61 1 64 24 63 51
53 62 2 60 65 61 65
54 62 3 51 56 64 60

55 62 4 64 55 65 65
56 63 5 64 38 27 51
57 63 6 65 24 64 57
58 63 7 51 64 60 51
59 63 8 63 36 38 60
60 63 9 63 59 64 65
61 63 10 63 26 51 64
62 63 11 64 65 38 65
63 63 12 65 60 64 51
64 63 13 62 63 64 63
65 63 14 65 65 63 29
66 63 15 64 64 63 51
67 63 16 24 63 65 64
68 63 17 51 64 63 64
69 63 18 51 55 61 51
70 63 19 64 60 31 64
71 63 20 64 64 54 62
72 63 median 59.10 53.50 56.15 57.65
73 63 var. 95.88 220.37 151.92 80.13
74 63 desv. 9.79 14.84 12.33 8.95
75 64
76 64
77 64 TABLA DE RESUMEN POR AFIJACION PR
78 64 ESTRATO Ne ye We Se^2
79 64 1 20 59.10 0.071 95.88
80 64 2 20 53.50 0.071 220.37
81 64 2 20 56.15 0.071 151.92
82 64 4 20 57.65 0.071 80.13
83 64 5 20 54.60 0.071 217.31
84 64 totales 100 281.000 0.356 765.62
85 64
86 64 N 100
87 64 n 96 N * Z 2 * ∑We * Se 2
88 64 e 0.2 n=
=
89 64 alfa 0.01 N * e 2 + 2 * ∑We * Se 2
Z
90 64 Z 2.58
91 64
92 64 calculode promedio por faij. Proporcional
93 64
94 64
95 64
1
96
97
64
64
ye =
=
N
∑ Ne * Ye 56.2000

98 64
99 64
100 64
1
101
102
64
64 calculo de la varianza del estimador
ye =
por faij. Proporcional
=
N
∑N
103 64
104 64
105 64 1 Se 2
106
107
64
64
V ( ye) = 2 * ∑ Ne( Ne ne)
= 0.06

108 64 N ne
109 65

110 65
111 65 calculo de la varianza del estimador por faij. Proporcional
112 65
113 65
114 65 S ( yes) = V ( y es)
= 0.25
115 65
116 65
117 65 INTERVALO DE CONFIANZA
118 65
119 65
120 65

=e ± V ( yes ) = γ
y t
LI 55.55
Ls 56.85

FIJACION OPTIMA

ESTRATO Ne ye We Se^2
1 20 59.10 0.071 95.884
2 20 53.50 0.071 220.368
2 20 56.15 0.071 151.92
4 20 57.65 0.071 80.13
5 20 54.60 0.071 217.31
totales 100 281.000 0.356 765.616
N 100
n 96
e 0.2
alfa 0.01
Z 2.58

calculo de la varianza del estimador por faij. Proporcional

1 Se 2
V ( ye ) = 2 * ∑ Ne ( Ne
= ne)
N ne

calculo de la varianza del estimador por faij. Proporcional

S ( ye s) = V ( y e s)
=

MUESTRA ASIGNACION IGUAL
ESTRATO Ne ye We Se^2
1 20 59.10 0.0712 95.884
2 20 53.50 0.0712 220.368

2 20 56.15 0.0712 151.92
4 20 57.65 0.0712 80.13
5 20 54.60 0.0712 217.31
totales 100 281 0.36 765.616
N 100
n 96.04
e 0.2
alfa 0.01
Z 2.58

calculode promedio por asisganacion igual

1
ye =
=
N
∑ Ne * Ye 56.2


1 Se2
v = 2 ) = ∑ Ne(Ne ne) *
= 0.06
N ne


s ) == v
= 0.24

calculode del intervalo de confianza

1 Se2
X ± Z ± 2 ∑ Ne(Ne ne) * ) = γ
 =
N ne

56.2586
56.1414

ECCIONA UNA MUESTRA 100 Y DE DE TAMAÑO 50

MUESTRA5
88.38
5.59
38.58
110.09
74
58.54
116.14
88.75
61.22
59.77
41.04
6.47
47.51
105.79
76.16
15.67
3.25
101.33
19.77
69.95

MUESTRA5
88
5
38
110
73
58
116
88
61
59
41
6
47
105
76
15
3
101
19
69
MUESTRA5
64
26
56

65
63
63
65
64
63
63
58
27
60
64
64
36
24
64
40
63
54.60
217.31
14.74 N e* S e
ne=n*
=
∑ N e* S e
MEN POR AFIJACION PROPORCIONAL
Se Ne-ye We*ye We*Se^2 ne Ne*Se^2 (Ne-ne)
9.79 1182 4.2 6.824 19 1917.68 1
14.84 1070 3.8 15.685 19 4407.37 1
12.33 1123 4.0 10.813 19 3038.47 1
8.95 1153 4.1 5.704 19 1602.68 1
14.74 1092 3.9 15.467 19 4346.11 1
60.66 5620 20.00 54.492 96 15312.316 4

We * Se 2

We * Se 2
∑e
e = = W * ye * α

1
ye =
=
N
∑ Ne * Ye

N e* S e
ne=n*
=
CION OPTIMA ∑ N e* S e
9.792 1182.000 4.2 6.824 19 1917.68 1
14.845 1070.000 3.8 15.685 19 4407.37 1
12.33 1123.000 4.0 10.813 19 3038.47 1
8.95 1153.000 4.1 5.704 19 1602.68 1
14.74 1092.000 3.9 15.467 19 4346.11 1
60.656 5620.000 20.00 54.492 96 15312.316 4

0.0586

0.242

ASIGNACION IGUAL
9.792 1182 4.21 6.82 19 1917.68 1
14.845 1070 3.81 15.68 19 4407.37 0.8

12.33 1123 4 10.81 19 3038.47 0.8
8.95 1153 4.1 5.7 19 1602.68 0.8
14.74 1092 3.89 15.47 19 4346.11 0.8
60.656 5620.000 20.000 54.492 96 15312.316 4.200

Ne(Ne-ne)Se^2/ne
79.90
183.64
126.60
66.78
181.09
638.01

Ne(Ne-ne)Se^2/ne Ne*Se
27.583 195.841
183.640 296.896
126.603 246.515
66.779 179.035
181.088 294.826
586 1213

Ne(Ne-ne)Se^2/ne Ne*Se
27.58 195.84
183.64 296.9

126.6 246.51
66.78 179.04
181.09 294.83
586 1213

Nº.datos ºBrix
1 24
2 24 DE UNA POBLACION DE 200 DATOS SE SELECCIONA UNA MUEST
3 24
4 26
5 26
6 27
8 29 MUESTRA 1 MUESTRA2 MUESTRA3
9 30 1 68.27 42.77 60.31
10 31 2 12.09 100.31 110.02
11 33 3 33.02 63.53 98.38
12 34 4 55.83 16.91 97.28
13 35 5 99.98 114.72 6.27
14 36 6 110.97 97.37 117.37
15 36 7 16.79 106.81 79.74
16 36 8 56.27 55.74 74.41
17 38 9 109.04 81.49 85.92
18 38 10 14.48 63.94 29.68
19 40 11 26.58 99.3 60.32
20 41 12 24 104.04 82.74
21 41 13 19.68 26.79 58.92
22 44 14 53.4 5.74 15.69
23 47 15 7.59 24.8 90.64
24 51 16 118.3 80.66 75.83
25 51 17 85.11 72.05 97.78
26 51 18 91.42 10.65 114.91
27 51 19 21.35 10.24 115.37
28 51 20 77.77 4.78 71.01
29 51 valores truncados
31 52 68 42 60
32 52 12 100 110
33 53 33 63 98
34 54 55 16 97
35 54 99 114 6
36 55 110 97 117
37 55 16 106 79
38 56 56 55 74
39 57 109 81 85
40 57 14 63 29
41 58 26 99 60
42 59 23 104 82
43 59 19 26 58
44 60 53 5 15
45 60 7 24 90
46 60 118 80 75
47 60 85 72 97
48 60 91 10 114
49 60 21 10 115
50 61 77 4 71
52 61 63 59 63
53 62 34 64 65
54 62 53 63 64

55 62 62 36 64
56 63 64 65 27
57 63 65 64 65
58 63 36 64 64
59 63 63 62 63
60 63 65 64 64
61 63 36 63 51
62 63 51 64 63
63 63 47 64 64
64 63 40 51 63
65 63 62 26 36
66 63 27 51 64
67 63 65 64 64
68 63 64 63 64
69 63 64 31 65
70 63 41 31 65
71 63 64 26 63
72 63 median 53.30 53.75 60.05
73 63 var. 170.75 216.83 106.26
74 63 desv. 13.07 14.73 10.31
75 64
76 64
77 64
78 64
79 64
∑X = 55.940
X ==
80 64 K
279.70
81
82
64
64
X = 2
∑ (X _ X )2 =
5 σ X ==
83 64 7.83 K _1
84 64
X = 55.940
((E73 - F80)^2 + (F
σ2 X =
85
86
64
64 σ X = =
∑ (X _ X ) 2 =
87 64 K _1 2.8 σ 2 X = 7.83425
88 64
7.83425
89 64 σ X = =
90 64 4
91 64 σ X = =.7989 2
92 64
93 64 max 65 Li Ls
94 64 min 24 1 24 29.1744
95 64 rango 41 2 29.17 34.35
96 64 aintervalo(m) 8 3 34.35 39.52
97 64 amplitud ( C ) 5.174 4 39.52 44.70
98 64 alfa 1.96 5 44.70 49.87
99 64 6 49.87 55.05
100 64 7 55.05 60.22
101 64 8 60.22 65.39
102 64 totales
103 64
104 64
105 64
106 64
107 64 IC X  z *
108 64
109 65

110 65 Li
111 65 Ls
112 65
113 65 1 2
114 65 simple sistematico
115 65 promedio 55.94 47.5
116 65 varianza 7.83 4.88
117 65 desviacion 2.8 23.82
118 65 Ls 56.44 47.97
119 65 Li 55.44 47.02
120 65

si vale la pena aplicar este tratamiento

DATOS SE SELECCIONA UNA MUESTRA 100 Y DE DE TAMAÑO 50

EROS ALEATORIOS
MUESTRA4 MUESTRA5
35.19 56.18
91.15 76.83
83.62 71.82
76.43 45.11
2.73 104.68
74.68 105.99
1.22 28.18
62.24 101.95
58.58 28.88
51.6 103.86
114.34 97.37
34.35 23.88
111.22 80.99
97.99 75.45
85.57 108.9
101.71 115.26
12.8 15.44
85.99 12.29
4.78 81.56
47.87 18.85

MUESTRA4 MUESTRA5
35 56
91 76
83 71
76 45
2 104
74 105
1 28
62 101
58 28
51 103
114 97
34 23
111 80
97 75
85 108
101 115
12 15
85 12
4 81
47 18
MUESTRA4 MUESTRA5
54 63
64 64
64 63

64 60
24 64
63 64
24 51
63 64
63 51
61 64
65 64
54 47
65 64
64 64
64 64
64 65
34 36
64 34
26 64
60 38
55.20 57.40
222.38 112.36
14.91 10.60
median 279.70 55.94
sumdsuma var. 828.57
desv. 63.61

2
∑ (X _ X )2 =
σ X ==
K _1
((E73 - F80)^2 + (F73 - F80)^2 + (G73 - F80)^2 + (H73 - F80)^2 + (I73 - F80)^2)
σ2 X =
4
2
σ X = 7.83425

Xc f fa fr fra f*Xc
26.587 8 8 0.067 0.07 212.7
31.762 4 12 0.033 0.10 127.05
36.936 6 18 0.050 0.15 221.62
42.110 4 22 0.033 0.18 168.44
47.285 1 23 0.008 0.19 47.28
52.459 12 35 0.100 0.29 629.51
57.633 14 49 0.117 0.41 806.87
62.808 71 120 1 4459.35
357.580 120 0.41 6672.81

σ
IC X  z *
n

55.44
56.44

3
estratificadi conglomerado IC
56.2 58.26
0.06 1.54 si vale la pena aplicar este tratamiento
0.25 1.24
56.26
56.14

aplicar este tratamiento

2 24
3 24
4 26
5 26
8 29 1 68.86 16.21 117.52
9 30 2 35.85 8.58 56.43
10 31 3 6.45 24.44 3.46
11 33 4 76.75 116.87 103.72
12 34 5 10.11 33.93 44.82
13 35 6 13.42 39.92 74.23
14 36 7 63.35 75.44 10.24
15 36 8 48.79 36.54 77.09
16 36 9 30.07 82.35 103.89
17 38 10 20.83 17.06 63.18
18 38 11 35.58 1.7 58.47
19 40 12 115.03 44.92 42.67
20 41 13 34.45 53.77 39.94
21 41 14 35.06 52.78 89.21
22 44 15 29.21 98.51 99.58
23 47 16 52.62 83.09 38.95
24 51 17 65.75 47.9 2.98
25 51 18 89.32 10.33 19.4
26 51 19 24.55 105.83 26.27
27 51 20 19.51 36.65 104.51
28 51 78.17 39.63 19.99
30 52 68 16 117
31 52 35 8 56
32 52 6 24 3
33 53 76 116 103
34 54 10 33 44
35 54 13 39 74
36 55 63 75 10
37 55 48 36 77
38 56 30 82 103
39 57 20 17 63
40 57 35 1 58
41 58 115 44 42
42 59 34 53 39
43 59 35 52 89
44 60 29 98 99
45 60 52 83 38
46 60 65 47 2
47 60 89 10 19
48 60 24 105 26
49 60 19 36 104
50 61 valores buscados
51 61 1 63 36 65
52 61 2 54 29 63
53 62 3 27 51 24
54 62 4 64 65 64
55 62 5 31 53 60

56 63 6 35 57 63
57 63 7 63 64 31
58 63 8 60 55 64
59 63 9 52 64 64
60 63 10 41 38 63
61 63 11 54 24 63
62 63 12 65 60 59
63 63 13 54 62 57
64 63 14 54 61 64
65 63 15 51 64 64
66 63 16 61 64 56
67 63 17 63 60 24
68 63 18 64 31 40
69 63 19 51 64 51
70 63 20 40 55 64
71 63 median 52.35 52.85 55.15
72 63 var. 136.87 180.77 190.87
73 63 desv. 11.70 13.44 13.82
74 63
75 64 MUESTREO SISTEMATICO
76 64
77 64 N 100
78 64 n 20
79 64 n ubicación de datos
80 64 1 2 47.1
81 64 2 7 46.3
82 64 3 12 40.8
83 64 4 17 53.30
84 64 5 22 45.9
85 64 6 27 45.5
86 64 7 32 42
87 64 8 37 47.1
88 64 9 42 47.7
89 64 10 47 45.8
90 64 11 52 54.5
91 64 12 57 40.3
92 64 13 62 54.8
93 64 14 67 45.9
94 64 15 72 40.2
95 64 16 77 56.3
96 64 17 82 45.2
97 64 18 87 53.1
98 64 19 92 50.4
99 64 20 97 47.7
100 64 promedio 47.5
101 64 var 23.82
102 64 desv. 4.88
103 64 z=95% 1.96
104 64 INTERVALOS DE CONFIANZA
105 64
106 64 s
107 64 I X  z* ±_ γ
=
108 64 n
109 65
110 65 li 47.02

111 65 ls 47.97
112 65
113 65
114 65
115 65
116 65
117 65
118 65
119 65
120 65

OS SE SELECCIONA UNA MUESTRA 100 Y DE DE TAMAÑO 50

MUESTRA4 MUESTRA5
41.58 71.27
57.95 24.22
8.1 106.72
7.43 86.4
113.88 42.52
14.28 42.63
8.75 87.51
76.94 87.78
116.04 96.04
55.04 115.23
54.11 10.94
38.18 68.84
35.7 104.2
19.29 78.99
98.61 51.95
11.85 89.36
39.09 40.23
90.57 88.34
91.65 111.34
22.72 70.24
11.6 51.29

41 71
57 24
8 106
7 86
113 42
14 42
8 87
76 87
116 96
55 115
54 10
38 68
35 104
19 78
98 51
11 89
39 40
90 88
91 111
22 70

58 63
63 51
29 64
27 64
65 59

36 59
29 64
64 64
65 64
62 65
62 31
56 63
54 64
40 64
64 61
33 64
57 57
64 64
64 65
44 63
51.80 60.65
201.22 60.34
14.19 7.77

MUESTREO SISTEMATICO

Intervalos N 5
I ==
n

1 24
3 24
4 26
5 26
6 27
9 30 1 77.95 8.55 35.85 118.88
10 31 2 34.45 51.9 91.94 34.83
11 33 3 55.88 47.02 94 104.89
12 34 4 4.56 20.48 27.53 8.76
13 35 5 68 13.33 36.54 14.3
14 36 6 101.07 10.82 86.8 105.61
15 36 7 43.68 75.13 95.79 16.16
16 36 8 51.19 92.82 21.93 59.95
17 38 9 43.05 93.56 35.6 77.26
18 38 10 62.24 115.94 97.65 2.97
19 40 11 16.43 96.37 25.09 100.7
20 41 12 99.25 71.31 64.58 30.51
21 41 13 55.78 96.63 58.12 43.08
22 44 14 17.77 4.24 35.94 14.87
23 47 15 52.91 43.92 109.35 11.63
24 51 16 30.34 119.68 60.1 30.4
25 51 17 8.05 14.63 23.29 51.3
26 51 18 25.59 78.83 115.06 52.57
27 51 19 56.49 17.34 85.32 16.02
28 51 20 39.72 19.43 97.66 3.73
29 51
31 52 77 8 35 118
32 52 34 51 91 34
33 53 55 47 93 104
34 54 4 20 27 8
35 54 67 13 36 14
36 55 101 10 86 105
37 55 43 75 95 16
38 56 51 92 21 59
39 57 43 93 35 77
40 57 62 115 97 2
41 58 16 96 25 100
42 59 99 71 64 30
43 59 55 96 58 43
44 60 17 4 35 14
45 60 52 43 109 11
46 60 30 119 60 30
47 60 8 14 23 51
48 60 25 78 115 52
49 60 56 17 85 16
50 61 39 19 97 3
51 61
52 61 MUESTREO POR CONGLOMERADO

53 62
54 62 valores buscados
55 62 C1 C2 C3 C4
56 63 64 29 54 65
57 63 54 61 64 54
58 63 62 60 64 64
59 63 26 41 51 29
60 63 63 35 55 36
61 63 64 31 64 64
62 63 59 64 64 36
63 63 61 64 41 63
64 63 59 64 54 64
65 63 63 65 64 24
66 63 36 64 51 64
67 63 64 63 63 52
68 63 62 64 63 59
69 63 38 26 54 36
70 63 61 59 65 33
71 63 52 65 63 52
72 63 29 36 47 61
73 63 51 64 65 61
74 63 63 38 64 36
75 64 57 40 64 24
76 64 yi 1088 1033 1174 977
77 64 Pro.yi 54.40 51.65 58.70 48.85
78 64 SUMAyi 269.60
79 64
80 64 N 20
81 64 n 100
82 64 M 10
83 64 m 5
84 64
85 64 CALCULO DE LA VARIANZA DEL ESTIMADOR
86 64
87 64 ( Y j)
88 64 Y.. = 53.92
m
89 64
90 64
91 64 CALCULO DE LA VARIANZA DEL ESTIMADOR
92 64
93 64 2 58.26
64
( j
Y - y..)
94
95 64
96 64 CALCULO DE LA VARIANZA ENTRE CONGLOMERADOS
97 64
98 64
99 64
2
N * ∑ (yj - y..) 2
100 64 SE =
101 64 m -1
102 64
103 64 2 * 5 .2
0 8 6
104 64 SE 2 = 291.32
5 -1
SE 2 = 2 1 .3
9

2 * 5 .2
0 8 6
SE 2 =
105 64 5 -1
106 64 SE 2 = 2 1 .3
9
107 64
108 64
109 65 CALCULO DE LA VARIANZA DENTRO DE CONGLOMERADOS
110 65
111 65
2
∑∑ (yij - y j ) 2

112 65 SD =
113 65 M(N - 1)
114 65
115 65 C1 C2 C3 C4
116 65 1 92.16 513.02 22.09 260.82
117 65 2 0.16 87.42 28.09 26.52
118 65 3 57.76 69.72 28.09 229.52
119 65 4 806.56 113.42 59.29 394.02
120 65 5 73.96 277.22 13.69 165.12
6 92.16 426.42 28.09 229.52
7 21.16 152.52 28.09 165.12
8 43.56 152.52 313.29 200.22
9 21.16 152.52 22.09 229.52
10 73.96 178.22 28.09 617.52
11 338.56 152.52 59.29 229.52
12 92.16 128.82 18.49 9.92
13 57.76 152.52 18.49 103.02
14 268.96 657.92 22.09 165.12
15 43.56 54.02 39.69 251.22
16 5.76 178.22 18.49 9.92
17 645.16 244.92 136.89 147.62
18 11.56 152.52 39.69 147.62
19 73.96 186.32 28.09 165.12
20 6.76 135.72 28.09 617.52
TOTALES 2827 4167 980 4365
SUMA.SUM.

178
46
SD 2 = 14.9173
1( 0
010 -1)
SD 2 = 1. 12
4 7
9

CALCULO DE LA VARIANZA TOTAL.

2 (M 1) SE 2 + 8 N 1) SD 2
M
ST =
(N * M) - 1
(10 1)291 .315 > +
+MAS + (20 1)14 .9173
10
ST 2 =
(20 * 10) - 1
5456.122 27.42
ST 2 =
199
2
ST = 27.4176

(20 * 10) - 1
5456.122
ST 2 =
199
ST 2 = 27.4176

CALCULO DE LA VARIANZA DEL ESTIMADOR

1 [ M − _ m] [ M ( N _ 1)]
V (y..)= *( )* 2 * SE 2
m M N ( M _ 1)

1 [10 _ 5] [10(20 _ 1)]
V (y..)= * ( )* 2 * 291.315
5 10 20 (10 _ 1)
V (y..)= 0.2* 0.5* 0.05277 291.315
*
V (y..)= 1.53727

1.54
1.24

ECCIONA UNA MUESTRA 100 Y DE DE TAMAÑO 50

MUESTRA5
91.78
7.99
108.08
92.97
52.27
23.98
99.25
91.21
82.1
77.62
78.82
23.73
55.9
11.43
21.59
29.57
42.32
44.04
39.82
58.17

91
7
108
92
52
23
99
91
82
77
78
23
55
11
21
29
42
44
39
58

C5
64
27
64
64
61
47
64
64
64
64
64
47
62
33
41
51
59
60
57
63
1120
56.00

C5
64
841
64
64
25
81
64
64
64
64
64
81
36
529
225
25
9
16
1
49
2430
14768

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