ESTADISTICA
Páginas: 5 (1136 palabras)
Publicado: 14 de agosto de 2015
Los siguientes datos muestran las medidas en pulgadas de diámetros
en desorden de 110 tubos de ensayo de la empresa QUIMEX SAdeCV
12
64
38
46
26
36
54
90
55
32
45
30
33
77
74
30
42
27
37
15
47
49
33
35
45
12
34
57
31
43
28
98
55
35
38
50
15
88
52
95
47
31
45
28
38
71
18
30
42
16
37
56
25
68
32
40
45
22
34
47
31
43
27
38
62
35
1
46
13
60
38
52
35
77
31
44
28
38
49
30
34
68
26
37
55
80
5432
45
12
73
83
46
30
43
27
37
19
40
49
30
35
84
76
44
67
31
44
38
83
91
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3
1
2
1
1
1
1
1
26
27
28
29
30
31
32
33
34
35
36
37
38
39
2
3
3
6
5
3
2
3
5
1
4
7
40
41
42
43
44
45
46
47
48
49
50
51
52
53
2
2
3
3
5
3
3
3
1
2
54
55
56
57
58
59
60
61
62
63
64
65
66
67
2
3
1
1
1
1
1
1
2
68
69
70
71
72
73
74
75
76
77
78
79
80
81
2
1
1
1
1
2
1
8283
84
85
86
87
88
89
90
91
92
93
94
95
2
1
1
1
1
1
96
97
98
1
Distribución de Frecuencias de los diámetros de tubos en pulgadas de la empresa QUIMEX SAdeCV
Clases
Lim.
Inf.
Interval
os
Lim.
Sup.
frecuen
cia
Marca
de
clase X
Frec.
Relat
%
Frec.
Acum.
Asc.
Frec.
Acu
m.
Des.
Frec.
Rel.
Asc. %
Frec.
Rel.
Des. %
U=XiA/C
F* U
F*X
X2
F*X2
1
2
3
4
5
6
7
8
9
10
11
TOTAL
11.5
19.527.5
35.5
43.5
51.5
59.5
67.5
75.5
83.5
91.5
110
12-19
20-27
28-35
36-43
44-51
52-59
60-67
68-75
76-83
84-91
92-99
19.5
27.5
35.5
43.5
51.5
59.5
67.5
75.5
83.5
91.5
99.5
9
7
27
19
18
9
4
5
6
4
2
15.5
23.5
31.5
39.5
47.5
55.5
63.5
71.5
79.5
87.5
95.5
610.5
0.081
0.063
0.245
0.172
0.163
0.081
0.036
0.045
0.054
0.036
0.018
9
16
43
62
80
89
93
98
104
108
110
110
101
94
67
48
30
21
17
12
6
2
8.18114.545
39.090
56.363
72.727
80.909
84.545
89.090
94.545
98.181
100
100
91.818
85.454
60.909
43.636
27.272
19.090
15.454
10.909
5.454
1.818
-5.343
-4.343
-3.343
-2.343
-1.343
-0.343
0.656
1.656
2.656
3.656
4.656
-48.087
-30.401
-90.261
-44.517
-24.174
-3.087
2.624
8.280
15.936
14.624
9.312
139.5
164.5
850.5
750.5
855
499.5
254
357.5
477
350
191
4889
240.5
552.25
992.5
1560.25
2256.25
3080.254032.25
5112.25
6320.25
7656.25
9120.25
2162.25
3865.75
26790.75
29644.75
40612.5
27722.25
16129
25561.25
37921.5
30625
18240.5
259275.5
-189.751
3
Poligono de Frecuencias
30
25
FRECUENCIA
20
15
10
5
0
7.5
15.5
23.5
31.5
39.5
47.5
55.5
63.5
MARCAS DE CLASE
4
71.5
79.5
87.5
95.5
103.5
Histograma y Poligono de Frecuencias
30
25
FRECUENCIA
20
15
10
5
0
7.5
15.523.5
31.5
39.5
47.5
55.5
MARCAS DE CLASE
5
63.5
71.5
79.5
87.5
95.5
103.5
Histograma y Poligono de Frecuencias
30
25
FRECUENCIA
20
15
10
5
0
7.5
15.5
23.5
31.5
39.5
47.5
55.5
63.5
MARCAS DE CLASE
6
71.5
79.5
87.5
95.5
103.5
Grafico De Ojiva ascendente y descendente
120
100
80
60
40
20
0
7.5
15.5
23.5
31.5
39.5
47.5
55.5
Frec. Acum. Asc.
63.5
Frec.Acum. Des.
7
71.5
79.5
87.5
95.5
103.5
𝐴=
𝐴=
610.5
√110
=
∑𝑥
√𝑁
=
610.5
= 𝟓𝟖. 𝟐𝟓
10.48
Media Aritmetica
𝑋 =𝐴+
∑𝑓 ∗ 𝑈
∗𝐶 =
𝑁
−189.751
𝑋 = 58.25 + (
) ∗ 8 = 58.25 − 1.725 ∗ 8 = 𝟒𝟒. 𝟒𝟒
110
Moda
𝑀𝑜 = 𝐿𝑖 + [
𝑀𝑜 = 43.5 + [
∆1
]∗𝐶 =
∆1 + ∆2
−1
−1
] ∗ 8 = 43.5 + [ ] ∗ 8 = 43.5 + [−0.125] ∗ 8 = 43.5 − 1 = 𝟒𝟐. 𝟓
−1 + 9
8
∆1 = 𝑓 − 𝑓𝑖𝑛𝑓𝑒𝑟𝑖𝑜𝑟 = 18 − 19 = −1
∆2 = 𝑓 − 𝑓𝑠𝑢𝑝𝑒𝑟𝑖𝑜𝑟 = 18 − 9 = 9𝑈=
𝑋𝑖 − 𝐴
= 𝑣𝑎𝑙𝑜𝑟 𝑑𝑒 𝑙𝑎 𝑈 𝑒𝑛 𝑙𝑎 𝑡𝑎𝑏𝑙𝑎
𝐶
Media Geométrica
𝑛
11
11
𝐺 = √𝐹𝑖 = √9 ∗ 7 ∗ 27 ∗ 19 ∗ 18 ∗ 9 ∗ 4 ∗ 5 ∗ 6 ∗ 4 ∗ 2 = √5026250880 = 𝟕. 𝟔𝟏𝟗
8
Cuártiles
𝑘𝑁
𝑄𝑘 = 𝐿𝑖 + [ 4
𝑄1 =
𝐹𝑖
]∗𝐶 =
1(110) 110
=
= 27.5
4
4
𝑄1 = 27.5 + [
𝑄3 =
− 𝐹𝐴𝑐𝑢𝑚. 𝑎𝑠𝑐. −1
27.5 − 16
11.5
] ∗ 8 = 27.5 + [
] ∗ 8 = 27.5 + 0.425 ∗ 8 = 𝟑𝟎. 𝟒𝟎
27
27
3(110) 330
=
= 82.5
4
4
𝑄3 = 51.5 + [
82.5 − 80
2.5
] ∗ 8 = 51.5+ [ ] ∗ 8 = 51.5 + 0.277 ∗ 8 = 𝟓𝟑. 𝟕𝟐
9
9
9
Déciles
𝑘𝑁
− 𝐹𝐴𝑐𝑢𝑚. 𝑎𝑠𝑐. −1
10
𝐷𝑘 = 𝐿𝑖 + [
]∗𝐶 =
𝐹𝑖
𝐷1 =
1(110) 110
=
= 11
10
10
𝐷1 = 19.5 + [
𝐷4 =
11 − 9
2
] ∗ 8 = 19.5 + [ ] ∗ 8 = 19.5 + 0.285 ∗ 8 = 𝟐𝟏. 𝟕𝟖
7
7
4(110) 440
=
= 44
10
10
𝐷4 = 33.5 + [
𝐷8 =
44 − 43
1
] ∗ 8 = 33.5 + [ ] ∗ 8 = 33.5 + 0.052 ∗ 8 = 𝟑𝟑. 𝟗𝟐
19
19
8(110) 880
=
= 88
10
10
𝐷8 = 51.5 + [
88 − 80
8
] ∗ 8 = 51.5...
en desorden de 110 tubos de ensayo de la empresa QUIMEX SAdeCV
12
64
38
46
26
36
54
90
55
32
45
30
33
77
74
30
42
27
37
15
47
49
33
35
45
12
34
57
31
43
28
98
55
35
38
50
15
88
52
95
47
31
45
28
38
71
18
30
42
16
37
56
25
68
32
40
45
22
34
47
31
43
27
38
62
35
1
46
13
60
38
52
35
77
31
44
28
38
49
30
34
68
26
37
55
80
5432
45
12
73
83
46
30
43
27
37
19
40
49
30
35
84
76
44
67
31
44
38
83
91
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3
1
2
1
1
1
1
1
26
27
28
29
30
31
32
33
34
35
36
37
38
39
2
3
3
6
5
3
2
3
5
1
4
7
40
41
42
43
44
45
46
47
48
49
50
51
52
53
2
2
3
3
5
3
3
3
1
2
54
55
56
57
58
59
60
61
62
63
64
65
66
67
2
3
1
1
1
1
1
1
2
68
69
70
71
72
73
74
75
76
77
78
79
80
81
2
1
1
1
1
2
1
8283
84
85
86
87
88
89
90
91
92
93
94
95
2
1
1
1
1
1
96
97
98
1
Distribución de Frecuencias de los diámetros de tubos en pulgadas de la empresa QUIMEX SAdeCV
Clases
Lim.
Inf.
Interval
os
Lim.
Sup.
frecuen
cia
Marca
de
clase X
Frec.
Relat
%
Frec.
Acum.
Asc.
Frec.
Acu
m.
Des.
Frec.
Rel.
Asc. %
Frec.
Rel.
Des. %
U=XiA/C
F* U
F*X
X2
F*X2
1
2
3
4
5
6
7
8
9
10
11
TOTAL
11.5
19.527.5
35.5
43.5
51.5
59.5
67.5
75.5
83.5
91.5
110
12-19
20-27
28-35
36-43
44-51
52-59
60-67
68-75
76-83
84-91
92-99
19.5
27.5
35.5
43.5
51.5
59.5
67.5
75.5
83.5
91.5
99.5
9
7
27
19
18
9
4
5
6
4
2
15.5
23.5
31.5
39.5
47.5
55.5
63.5
71.5
79.5
87.5
95.5
610.5
0.081
0.063
0.245
0.172
0.163
0.081
0.036
0.045
0.054
0.036
0.018
9
16
43
62
80
89
93
98
104
108
110
110
101
94
67
48
30
21
17
12
6
2
8.18114.545
39.090
56.363
72.727
80.909
84.545
89.090
94.545
98.181
100
100
91.818
85.454
60.909
43.636
27.272
19.090
15.454
10.909
5.454
1.818
-5.343
-4.343
-3.343
-2.343
-1.343
-0.343
0.656
1.656
2.656
3.656
4.656
-48.087
-30.401
-90.261
-44.517
-24.174
-3.087
2.624
8.280
15.936
14.624
9.312
139.5
164.5
850.5
750.5
855
499.5
254
357.5
477
350
191
4889
240.5
552.25
992.5
1560.25
2256.25
3080.254032.25
5112.25
6320.25
7656.25
9120.25
2162.25
3865.75
26790.75
29644.75
40612.5
27722.25
16129
25561.25
37921.5
30625
18240.5
259275.5
-189.751
3
Poligono de Frecuencias
30
25
FRECUENCIA
20
15
10
5
0
7.5
15.5
23.5
31.5
39.5
47.5
55.5
63.5
MARCAS DE CLASE
4
71.5
79.5
87.5
95.5
103.5
Histograma y Poligono de Frecuencias
30
25
FRECUENCIA
20
15
10
5
0
7.5
15.523.5
31.5
39.5
47.5
55.5
MARCAS DE CLASE
5
63.5
71.5
79.5
87.5
95.5
103.5
Histograma y Poligono de Frecuencias
30
25
FRECUENCIA
20
15
10
5
0
7.5
15.5
23.5
31.5
39.5
47.5
55.5
63.5
MARCAS DE CLASE
6
71.5
79.5
87.5
95.5
103.5
Grafico De Ojiva ascendente y descendente
120
100
80
60
40
20
0
7.5
15.5
23.5
31.5
39.5
47.5
55.5
Frec. Acum. Asc.
63.5
Frec.Acum. Des.
7
71.5
79.5
87.5
95.5
103.5
𝐴=
𝐴=
610.5
√110
=
∑𝑥
√𝑁
=
610.5
= 𝟓𝟖. 𝟐𝟓
10.48
Media Aritmetica
𝑋 =𝐴+
∑𝑓 ∗ 𝑈
∗𝐶 =
𝑁
−189.751
𝑋 = 58.25 + (
) ∗ 8 = 58.25 − 1.725 ∗ 8 = 𝟒𝟒. 𝟒𝟒
110
Moda
𝑀𝑜 = 𝐿𝑖 + [
𝑀𝑜 = 43.5 + [
∆1
]∗𝐶 =
∆1 + ∆2
−1
−1
] ∗ 8 = 43.5 + [ ] ∗ 8 = 43.5 + [−0.125] ∗ 8 = 43.5 − 1 = 𝟒𝟐. 𝟓
−1 + 9
8
∆1 = 𝑓 − 𝑓𝑖𝑛𝑓𝑒𝑟𝑖𝑜𝑟 = 18 − 19 = −1
∆2 = 𝑓 − 𝑓𝑠𝑢𝑝𝑒𝑟𝑖𝑜𝑟 = 18 − 9 = 9𝑈=
𝑋𝑖 − 𝐴
= 𝑣𝑎𝑙𝑜𝑟 𝑑𝑒 𝑙𝑎 𝑈 𝑒𝑛 𝑙𝑎 𝑡𝑎𝑏𝑙𝑎
𝐶
Media Geométrica
𝑛
11
11
𝐺 = √𝐹𝑖 = √9 ∗ 7 ∗ 27 ∗ 19 ∗ 18 ∗ 9 ∗ 4 ∗ 5 ∗ 6 ∗ 4 ∗ 2 = √5026250880 = 𝟕. 𝟔𝟏𝟗
8
Cuártiles
𝑘𝑁
𝑄𝑘 = 𝐿𝑖 + [ 4
𝑄1 =
𝐹𝑖
]∗𝐶 =
1(110) 110
=
= 27.5
4
4
𝑄1 = 27.5 + [
𝑄3 =
− 𝐹𝐴𝑐𝑢𝑚. 𝑎𝑠𝑐. −1
27.5 − 16
11.5
] ∗ 8 = 27.5 + [
] ∗ 8 = 27.5 + 0.425 ∗ 8 = 𝟑𝟎. 𝟒𝟎
27
27
3(110) 330
=
= 82.5
4
4
𝑄3 = 51.5 + [
82.5 − 80
2.5
] ∗ 8 = 51.5+ [ ] ∗ 8 = 51.5 + 0.277 ∗ 8 = 𝟓𝟑. 𝟕𝟐
9
9
9
Déciles
𝑘𝑁
− 𝐹𝐴𝑐𝑢𝑚. 𝑎𝑠𝑐. −1
10
𝐷𝑘 = 𝐿𝑖 + [
]∗𝐶 =
𝐹𝑖
𝐷1 =
1(110) 110
=
= 11
10
10
𝐷1 = 19.5 + [
𝐷4 =
11 − 9
2
] ∗ 8 = 19.5 + [ ] ∗ 8 = 19.5 + 0.285 ∗ 8 = 𝟐𝟏. 𝟕𝟖
7
7
4(110) 440
=
= 44
10
10
𝐷4 = 33.5 + [
𝐷8 =
44 − 43
1
] ∗ 8 = 33.5 + [ ] ∗ 8 = 33.5 + 0.052 ∗ 8 = 𝟑𝟑. 𝟗𝟐
19
19
8(110) 880
=
= 88
10
10
𝐷8 = 51.5 + [
88 − 80
8
] ∗ 8 = 51.5...
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