Graficas en excel

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3. Según las especificaciones del problema estos son nuestros datos aleatorios a usar
16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2.6 2.8 3.1 2.8 2.9 2.7 3.2 2.1 2.7 3.3 3.0 2.4 2.9 2.7 2.4 2.7 2.9 2.8 2.6 3.2 3.0 2.9 2.9 2.5 3.1 2.7 3.2 2.7 3.1 2.8
2 2.5 2.4 2.7 2.7 3.0 2.9 2.8 2.8 3.0 3.4 2.5 2.6 3.4 2.6 2.7 3.4 2.8 2.6 2.4 2.6 3.1 2.6 2.7 2.6 3.1 2.7 2.9 2.6 2.7 3.2
3
4
5
6
7
8
9
10
2.9 2.4 3.1 2.7 3.2 2.5 3.2 2.0 2.2 2.7 2.8 2.6 3.0 2.9 2.8 2.8 2.5 2.3 2.6 2.9 2.4 2.9 3.3 3.1 3.1 3.2 3.0 2.8 2.8 3.0
2.7 2.8 3.2 2.4 3.0 2.7 2.2 2.6 3.0 3.0 2.5 2.5 3.0 3.4 2.8 2.3 2.7 3.0 2.6 2.4 3.1 2.9 3.0 2.9 2.9 2.5 3.0 3.2 2.4 2.7
2.9 2.6 2.4 2.8 2.8 3.3 3.0 2.7 2.7 2.9 2.4 2.6 2.7 2.6 2.7 2.6 3.1 2.7 3.3 3.1 2.9 2.7 2.8 3.1 2.6 2.8 2.8 3.0 2.2 3.2
3.1 2.9 3.3 2.5 2.8 2.5 3.2 2.7 2.3 2.6 3.1 2.3 2.6 2.6 2.8 3.4 2.7 2.7 3.1 2.9 2.7 2.8 2.8 3.0 3.0 2.8 2.5 2.7 2.6 2.7
2.5 3.1 3.3 2.5 2.7 2.3 3.3 2.5 2.6 2.9 2.7 2.9 3.0 2.2 2.6 2.7 3.5 2.8 2.6 2.8 2.7 3.1 2.9 2.9 2.3 3.1 2.6 2.8 2.9 2.8
3.4 3.0 2.9 2.6 2.6 2.8 2.6 3.0 2.6 2.7 2.7 2.8 2.4 2.8 2.6 3.1 3.1 2.5 2.5 2.3 2.5 2.9 3.2 2.9 3.0 2.8 2.6 2.9 3.2 3.1
3.0 3.0 2.0 2.5 3.1 3.0 2.9 2.9 2.8 2.6 3.2 2.6 2.5 2.8 2.6 3.0 2.6 2.8 2.9 3.0 3.3 2.9 2.7 2.7 3.1 2.5 2.7 2.2 3.0 2.5
2.9 3.1 3.8 3.0 2.9 2.7 2.7 2.5 2.5 3.1 2.9 3.5 2.3 2.5 2.5 2.5 2.6 2.7 2.7 2.7 3.0 3.1 2.5 2.9 2.4 2.4 2.5 2.9 2.9 2.8

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5. Frecuencias
Categorias o clases
xi
2.0
2.1
2.2
Moda
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Media
Aritmética
Desviación
Media
fi
2
1
5
8
14
28
37
44
36
38
30
26
14
8
6
2
0
0
1
fai
2
3
8
16
30
58
95
139
175
213
243
269
283
291
297
299
299
299
300
Medidas de tendencia central
y dispersion
fri
frai
f ix i
|x i-x|f i
(x i-x) 2 f i
0.0067 0.67%
4
1.59
1.26
0.0033 1.00%
2.1
0.69
0.48
0.0167 2.67%
11
2.97
1.76
0.0267 5.33% 18.4
3.95
1.95
0.0467 10.00% 33.6
5.51
2.17
0.0933 19.33%
70
8.22
2.41
Mediana
0.1233 31.67% 96.2
7.17
1.39
0.1467 46.33% 118.8
4.12
0.39
0.1200 58.33% 100.8
0.23
0.00
0.1267 71.00% 110.2
4.04
0.43
0.1000 81.00%
90
6.19
1.28
0.0867 89.67% 80.6
7.96
2.44
0.0467 94.33% 44.8
5.69
2.31
0.0267 97.00% 26.4
4.05
2.05
0.0200 99.00% 20.4
3.64
2.21
0.0067 Desviación
99.67%
7
1.41
1.00
0.0000 99.67%
0
0.00
0.00
Estándar
0.0000 99.67%
0
0.00
0.00
0.0033 100.00% 3.8
1.01
1.01
Totales 838.1
68.44
24.54
x=
2.79
Desviación Media= 0.2281311
Varianza=
0.081793222
Desviación=
0.285995144
•
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•
•
•
•
•
Varianza

6. Frecuencias
Categorias o clases
xi
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
fi
2
1
5
8
14
28
37
44
36
38
30
26
14
8
6
2
0
0
1
fai
2
3
8
16
30
58
95
139
175
213
243
269
283
291
297
299
299
299
300
fri
0.0067
0.0033
0.0167
0.0267
0.0467
0.0933
0.1233
0.1467
0.1200
0.1267
0.1000
0.0867
0.0467
0.0267
0.0200
0.0067
0.0000
0.0000
0.0033
frai
0.67%
1.00%
2.67%
5.33%
10.00%
19.33%
31.67%
46.33%
58.33%
71.00%
81.00%
89.67%
94.33%
97.00%
99.00%
99.67%
99.67%
99.67%
100.00%
Medidas de tendencia central
y dispersion
Frecuencia
Absolutai-x|f i
fix i
|x
(x i-x) 2 f i
4
2.1
11
18.4
33.6
70
96.2
118.8
100.8
110.2
90
80.6
44.8
26.4
20.4
7
0
0
3.8
1.59
0.69
2.97
3.95
5.51
8.22
7.17
4.12
0.23
4.04
6.19
7.96
5.69
4.05
3.64
1.41
0.00
0.00
1.01
1.26
0.48
1.76
1.95
2.17
2.41
1.39
0.39
0.00
0.43
1.28
2.44
2.31
2.05
2.21
1.00
0.00
0.00
1.01
•

7. Medidas de tendencia
Medidas de tendencia central central
Frecuencias
Frecuencias
rias o claseso clases
y dispersion
Categorias
y dispersion
xi
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
xi
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
fi
2
1
5
8
14
28
37
44
36
38
30
26
14
8
6
2
0
0
1
fai fi frfai
i
2 0.0067
2 2
3 0.0033
1 3
5 8
8 0.0167
16 0.0267
8 16
30 14 30
0.0467
58 28 58
0.0933
95 37 95
0.1233
139 44 139
0.1467
175 36 175
0.1200
213 38 213
0.1267
243 30 243
0.1000
269 26 269
0.0867
283 14 283
0.0467
291 0.0267
8 291
297 0.0200
6 297
299 0.0067
2 299
299 0.0000
0 299
299 0.0000
0 299
300 0.0033
1 300
fri i
fraii Frecuencia(x i-x) 2 fi (x i-x) 2 fi
fii
fra
fix
|xix-x|f i |x i-x|f
0.67%
4
1.59 1.59
0.0067 0.67% Relativa 1.26 1.26
4
1.00% 2.1
0.69 0.69 0.48 0.48
0.0033 1.00% 2.1
0.0167 2.67%
11
2.67%
11
2.97 2.97 1.76 1.76
5.33% 18.4
3.95 3.95 1.95 1.95
0.0267 5.33% 18.4
0.0467 10.00% 33.6
10.00% 33.6
5.51 5.51 2.17 2.17
19.33% 70
8.22 8.22 2.41 2.41
0.0933 19.33% 70
0.1233 31.67% 96.2
31.67% 96.2
7.17 7.17 1.39 1.39
46.33% 118.8
4.12 4.12 0.39 0.39
0.1467 46.33% 118.8
0.1200 58.33% 100.8
58.33% 100.8
0.23 0.23 0.00 0.00
71.00% 110.2
4.04 4.04 0.43 0.43
0.1267 71.00% 110.2
0.1000 81.00% 90
81.00% 90
6.19 6.19 1.28 1.28
89.67% 80.6
7.96 7.96 2.44 2.44
0.0867 89.67% 80.6
94.33% 44.8
5.69 5.69 2.31 2.31
0.0467 94.33% 44.8
97.00% 26.4
4.05 4.05 2.05 2.05
0.0267 97.00% 26.4
99.00% 20.4
3.64 3.64 2.21 2.21
0.0200 99.00% 20.4
99.67% 7
0.0067 99.67% 1.41 1.41 1.00 1.00
7
99.67% 0
0.0000 99.67% 0.00 0.00 0.00 0.00
0
99.67% 0
0.0000 99.67% 0.00 0.00 0.00 0.00
0
100.00%100.00% 3.8
3.8
1.01 1.01 1.01 1.01
0.0033
•

8. Medidas de tendencia central
Medidas de tendencia central
Frecuencias
Frecuencia R.
y dispersion y dispersion
Acumulada 2
fa
frai
|x i fi
(x i-x) fi
fri fi fraii friix i |x i-x|f i fix i (x i-x) 2-x|f i
f
0.0067 20.67% 0.0067 0.67%
4
1.59 4 1.26
2
1.59
1.26
•
0.0033 11.00% 0.0033 1.00% 2.1 0.48
2.1
0.69
3
0.69
0.48
8
2.97
1.76
0.0167 52.67% 0.0167 2.67%
11
2.97 11 1.76
0.0267 85.33% 0.0267 5.33% 18.4 1.95
18.4
3.95
16
3.95
1.95
5.51
2.17
0.0467 14 30 0.0467 10.00% 33.6 2.17
10.00% 33.6
5.51
0.0933 28 58 0.0933 19.33% 70 2.41
19.33% 70
8.22
8.22
2.41
7.17
1.39
0.1233 37 95 0.1233 31.67% 96.2 1.39
31.67% 96.2
7.17
0.1467 44 139 0.1467 46.33% 118.8 0.39
46.33% 118.8
4.12
4.12
0.39
0.23
0.00
0.1200 36 175 0.1200 58.33% 100.8 0.00
58.33% 100.8
0.23
0.1267 38 213 0.1267 71.00% 110.2 0.43
71.00% 110.2
4.04
4.04
0.43
6.19
1.28
0.1000 30 243 0.1000 81.00% 90 1.28
81.00% 90
6.19
0.0867 26 269 0.0867 89.67% 80.6 2.44
89.67% 80.6
7.96
7.96
2.44
0.0467 14 283 0.0467 94.33% 44.8 2.31
94.33% 44.8
5.69
5.69
2.31
0.0267 8 291 0.0267 97.00% 26.4 2.05
97.00% 26.4
4.05
4.05
2.05
0.0200 6 297 0.0200 99.00% 20.4 2.21
99.00% 20.4
3.64
3.64
2.21
0.0067 2 299 0.0067 99.67% 7 1.00
99.67% 7
1.41
1.41
1.00
0.0000 0 299 0.0000 99.67% 0 0.00
99.67% 0
0.00
0.00
0.00
0.0000 0 299 0.0000 99.67% 0 0.00
99.67% 0
0.00
0.00
0.00
0.0033 100.00% 3.8 100.00% 3.8 1.01
1.01
1 300 0.0033
1.01
1.01
Frecuencias
ases
Categorias o clases
fi xi i
fa
2 2.0
2
1 2.1
3
5 2.2
8
8 2.3
16
14 2.4
30
28 2.5
58
37 2.6
95
44 2.7
139
36 2.8
175
38 2.9
213
30 3.0
243
26 3.1
269
14 3.2
283
8 3.3
291
6 3.4
297
2 3.5
299
0 3.6
299
0 3.7
299
1 3.8
300

9. Frecuencias
Categorias o clases
xi
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
fi
2
1
5
8
14
28
37
44
36
38
30
26
14
8
6
2
0
0
1
fai
2
3
8
16
30
58
95
139
175
213
243
269
283
291
297
299
299
299
300
fri
0.0067
0.0033
0.0167
0.0267
0.0467
0.0933
0.1233
0.1467
0.1200
0.1267
0.1000
0.0867
0.0467
0.0267
0.0200
0.0067
0.0000
0.0000
0.0033
frai
0.67%
•
1.00%
2.67%
5.33%
10.00%
19.33%
31.67%
46.33%
58.33%
71.00%
81.00%
89.67%
94.33%
97.00%
99.00%
99.67%
99.67%
99.67%
100.00%
Medidas de tendencia central
Frecuencia
y dispersion
Absoluta
fix i |x i-x|f i
(x i-x) 2 fi
4
1.59
1.26
2.1
0.69
0.48
11
2.97
1.76
18.4
3.95
1.95
33.6
5.51
2.17
70
8.22
2.41
96.2
7.17
1.39
118.8
4.12
0.39
100.8
0.23
0.00
110.2
4.04
0.43
90
6.19
1.28
80.6
7.96
2.44
44.8
5.69
2.31
26.4
4.05
2.05
20.4
3.64
2.21
7
1.41
1.00
0
0.00
0.00
0
0.00
0.00
3.8
1.01
1.01

10. Medidas de tendencia central
Mínimo = 2.0
Frecuencias
Categorias o clases
y dispersion
Cuartil 1 = 2.45
2
xi
f i Cuartil fri = 2.90 i
fai
fra
fix i
|x i-x|f i
(x i-x) 2 f i
2.0
2 Cuartil 3 = 3.35
2 0.0067 0.67%
4
1.59
1.26
•
Máximo = 3.8
2.1
1 3 0.0033 1.00%
2.1
0.69
0.48
2.2
5 8 0.0167 2.67%
11
2.97
1.76
Rango Inter-cuartilico (RI)
2.3
8 16 0.0267 5.33% 18.4
3.95
1.95
2.4
14 30 0.0467 10.00% 33.6
5.51
2.17
Q1
2.5
28 58 0.0933 19.33% 70
8.22
2.41
2.6
37 95 0.1233 31.67% 96.2
7.17
1.39
2.7
44 139 0.1467 46.33% 118.8
4.12
0.39
2.8
36 175 0.1200 58.33% 100.8
0.23
0.00
Q2
2.9
38 213 0.1267 71.00% 110.2
4.04
0.43
3.0
30 243 0.1000 81.00% 90
6.19
1.28
3.1
26 269 0.0867 89.67% 80.6
7.96
2.44
3.2
14 283 0.0467 94.33% 44.8
5.69
2.31
3.3
8 291 0.0267 97.00% 26.4
4.05
2.05
3.4
6 297 0.0200 99.00% 20.4
3.64
2.21
Q3
3.5
2 299 0.0067 99.67%
7
1.41
1.00
3.6
0 299 0.0000 99.67%
0
0.00
0.00
3.7
0 299 0.0000 99.67%
0
0.00
0.00
3.8
1 300 0.0033 100.00% 3.8
1.01
1.01
Valores Atípicos