López-torres.xlsx
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17 40 22 25 43 21 17 25 37 12
9 37 32 35 30 21 13 27
MARCA DE CLASE
Clases Limites Aparentes Limites Reales
(Xi)
41 45 36 40 30 48 45 41 39
7
12
6.50
12.50
9.50
39 40 38 28
7 33 35 22 34
13
18
12.50
18.50
15.50
23 18 40 33 12 39 47 17 26
19
24
18.50
24.50
21.50
42 31 25 19 47
25
30
24.50
30.50
27.50
31
36
30.50
36.50
33.50
37
42
36.50
42.50
39.50
43
48
42.50
48.50
45.50
Cálculos Importantes h= √N h= √50 h=
SUMA
7 c=Rango/h
Dm=48
c=
6
Dm= 7
c=
6
Rango= 41
FREC. FRECUEN FRECUENCIA ACUMULADA CIA RELATIVA ASCENDENT E
FRECUENCIA RELATIVA ACUMULADA ASCEDENTE
XiFi
FRECUENCIA ACUMULADA DESCENDENTE
(fi)
(hi)
(faai)
(faari)
4
8.00%
4
8.00%
38
50
5
10.00%
9
18.00%
77.5
46
6
12.00%
15
30.00%
129
41
8
16.00%
23
46.00%
220
35
8
16.00%
31
62.00%
268
27
13
26.00%
44
88.00%
513.5
19
6
12.00%
50
100.00%
273
6
50
(faadi)
1519
FRECUENCIA RELATIVA ACUMULADA DESCENDENTE (faadri)
(Xi)²
Xi²fi
Xi-
Xi-
Xi-f
100%
90.25
361
-20.88
20.88
83.52
92%
240.25
1201.25
-14.88
14.88
74.4
82%
462.25
2773.5
-8.88
8.88
53.28
70%
756.25
6050
-2.88
2.88
23.04
54%
1122.25
8978
3.12
3.12
24.96
38%
1560.25
20283.25
9.12
9.12
118.56
12%
2070.25
12421.5
15.12
15.12
90.72
6301.75
52068.5
74.88
468.48
(Xi-)² 435.9744 221.4144 78.8544 8.2944 9.7344 83.1744 228.6144 1066.0608
Media Aritmética
Moda
=
li+(Δ₁ ⁄ Mo= Δ₁+Δ₂)*c
∑fixi N
Mo= =
=
1519 50 30.38
39.5
Δ₁= fi-fi_₁ Δ₁=
5
Δ₂= fi-fi+1 Δ₂=
7
Mediana
Med= Med=
li+(RM-faa-₁/fi)*c 32.9
RM= (N+1)/2 RM= 25.5
RQₓ=
N+1 (X) 4
CUARTILES Qₓ= li+((RQₓ-faai-₁)/fi)*c
RDₓ=
N+1 (X) 10
DECILES Dₓ= li+((RDₓ-faai-₁)/fi)*c
RQ₁= 12.75
Q₁=
22.75
RD₃=
15.3
D₃=
25.23
RQ₂=
25.5
Q₂=
32.88
RD₅=
25.5
D₅=
32.88
RQ₃= 38.25
Q₃=
40.35
RD₇=
35.7
D₇=
39.17
+((RDₓ-faai-₁)/fi)*c
PERCENTILES
RPₓ=
N+1 (X)
Pₓ=
li+((RPₓ-faai-₁)/fi)*c
100 RP₁₈=
9.18
P₁₈=
19.18
RP₅₀=
25.5
P₅₀=
32.88
RP₈₆=
43.86
P₈₆=
42.94
Varianza DM= ∑ Xi- f N
Desviación Típica σ= √(∑(Xi-)²)/N σ= 4.61749023
DM=
Varianza σ²=∑(Xi-)² N σ²= 21.32122
9.3696
es bastante repres
Coeficiente de Variación CV=
σ *100 CV= 15 es bastante representativa
9 37 32 35 30 21 13 27
MARCA DE CLASE
Clases Limites Aparentes Limites Reales
(Xi)
41 45 36 40 30 48 45 41 39
7
12
6.50
12.50
9.50
39 40 38 28
7 33 35 22 34
13
18
12.50
18.50
15.50
23 18 40 33 12 39 47 17 26
19
24
18.50
24.50
21.50
42 31 25 19 47
25
30
24.50
30.50
27.50
31
36
30.50
36.50
33.50
37
42
36.50
42.50
39.50
43
48
42.50
48.50
45.50
Cálculos Importantes h= √N h= √50 h=
SUMA
7 c=Rango/h
Dm=48
c=
6
Dm= 7
c=
6
Rango= 41
FREC. FRECUEN FRECUENCIA ACUMULADA CIA RELATIVA ASCENDENT E
FRECUENCIA RELATIVA ACUMULADA ASCEDENTE
XiFi
FRECUENCIA ACUMULADA DESCENDENTE
(fi)
(hi)
(faai)
(faari)
4
8.00%
4
8.00%
38
50
5
10.00%
9
18.00%
77.5
46
6
12.00%
15
30.00%
129
41
8
16.00%
23
46.00%
220
35
8
16.00%
31
62.00%
268
27
13
26.00%
44
88.00%
513.5
19
6
12.00%
50
100.00%
273
6
50
(faadi)
1519
FRECUENCIA RELATIVA ACUMULADA DESCENDENTE (faadri)
(Xi)²
Xi²fi
Xi-
Xi-
Xi-f
100%
90.25
361
-20.88
20.88
83.52
92%
240.25
1201.25
-14.88
14.88
74.4
82%
462.25
2773.5
-8.88
8.88
53.28
70%
756.25
6050
-2.88
2.88
23.04
54%
1122.25
8978
3.12
3.12
24.96
38%
1560.25
20283.25
9.12
9.12
118.56
12%
2070.25
12421.5
15.12
15.12
90.72
6301.75
52068.5
74.88
468.48
(Xi-)² 435.9744 221.4144 78.8544 8.2944 9.7344 83.1744 228.6144 1066.0608
Media Aritmética
Moda
=
li+(Δ₁ ⁄ Mo= Δ₁+Δ₂)*c
∑fixi N
Mo= =
=
1519 50 30.38
39.5
Δ₁= fi-fi_₁ Δ₁=
5
Δ₂= fi-fi+1 Δ₂=
7
Mediana
Med= Med=
li+(RM-faa-₁/fi)*c 32.9
RM= (N+1)/2 RM= 25.5
RQₓ=
N+1 (X) 4
CUARTILES Qₓ= li+((RQₓ-faai-₁)/fi)*c
RDₓ=
N+1 (X) 10
DECILES Dₓ= li+((RDₓ-faai-₁)/fi)*c
RQ₁= 12.75
Q₁=
22.75
RD₃=
15.3
D₃=
25.23
RQ₂=
25.5
Q₂=
32.88
RD₅=
25.5
D₅=
32.88
RQ₃= 38.25
Q₃=
40.35
RD₇=
35.7
D₇=
39.17
+((RDₓ-faai-₁)/fi)*c
PERCENTILES
RPₓ=
N+1 (X)
Pₓ=
li+((RPₓ-faai-₁)/fi)*c
100 RP₁₈=
9.18
P₁₈=
19.18
RP₅₀=
25.5
P₅₀=
32.88
RP₈₆=
43.86
P₈₆=
42.94
Varianza DM= ∑ Xi- f N
Desviación Típica σ= √(∑(Xi-)²)/N σ= 4.61749023
DM=
Varianza σ²=∑(Xi-)² N σ²= 21.32122
9.3696
es bastante repres
Coeficiente de Variación CV=
σ *100 CV= 15 es bastante representativa
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