The document contains a series of numbers ranging from 5.961 to 6.345. It then provides statistical analysis of these numbers including calculations of minimum, maximum, range, number of intervals, mean, standard deviation, variance and limits. Two histograms are presented with the data divided into classes and the corresponding frequencies. Measures of central tendency, dispersion and process capability are reported.

1. 6.144 6.222 6.165 6.115 6.163 6.230 6.000 6.148 6.107 6.035
6.091 6.233 6.117 6.108 6.185 6.240 6.102 6.154 6.040 6.239
6.251 6.345 6.081 6.212 6.166 6.065 6.107 6.208 6.145 6.131
6.188 6.287 6.227 6.09 6.177 6.041 6.205 6.029 6.155 6.147
6.139 6.21 6.048 6.074 6.001 6.150 6.257 6.176 6.118 6.192
6.136 6.106 6.127 6.228 6.240 6.297 6.232 6.055 6.151 6.118
6.176 6.189 6.000 6.195 6.107 6.135 6.094 6.156 6.216 6.07
6.058 6.195 6.17 6.07 6.077 6.123 6.148 5.983 6.028 6.085
6.156 6.196 6.082 6.011 6.259 6.116 6.135 6.204 6.087 6.135
6.31 6.121 6.241 6.143 6.097 6.164 6.157 6.212 6.118 6.149
Maximo 6.345 Intervalos LI LS LI LS
Minimo 5.961 1 5.8020 5.8020 5.8015 5.8025
Rango 0.384 2 5.8447 5.8447 5.8442 5.8452
N. intervalos= 9 3 5.8873 5.8873 5.8868 5.8878
TI= 0.042667 4 5.9300 5.9300 5.9295 5.9305
0.04 5 5.9727 5.9727 5.9722 5.9732
6 6.0153 6.0153 6.0148 6.0158
7 6.0580 6.0580 6.0575 6.0585
8 6.1007 6.1007 6.1002 6.1012
9 6.1433 -0.0427 6.1428 -0.0422
5.8015 0
5.8015 7 6.349
5.8446 7 6.349
5.8446 0
5.8446 12
5.8877 12 6.809
5.8877 0 6.809
5.8877 27
5.9308 27
5.9308 0 7.269
5.9308 38 7.269
5.9739 38
5.9739 0
histograma número 1 5.9739 49 5.8889
6.0171 49 5.8889
6.0171 0
6.0171 27
Media aritmetica +2s
Limites aparentes Limites reales
Media aritmetica +1s
Media aritmetica +3s
Media
Media aritmetica -1s

2. 6.0602 27 5.429
6.0602 0 5.429
6.0602 26
6.1033 26
6.1033 0 4.969
6.1033 9 4.969
6.1464 9
6.1464 0
6.1464 5 4.508
6.1895 5 4.508
6.1895 0
histograma número
Maximo 6.345 Intervalos LI LS LI LS
Minimo 5.961 1 5.8020 5.8437 5.8015 5.8442
Rango 0.384 2 5.8447 5.8863 5.8442 5.8868
N. intervalos= 9 3 5.8873 5.9290 5.8868 5.9295
TI= 0.042667 4 5.9300 5.9717 5.9295 5.9722
0.04 5 5.9727 6.0143 5.9722 6.0148
6 6.0153 6.0570 6.0148 6.0575
7 6.0580 6.0997 6.0575 6.1002
8 6.1007 6.1423 6.1002 6.1428
9 6.1433 6.1850 6.1428 6.1855
5.8015 0
5.8015 7 6.186
5.8446 7 6.186
5.8446 0
5.8446 12
5.8877 12 6.342
5.8877 0 6.342
5.8877 27
5.9308 27
Media aritmetica -2s
Media aritmetica -3s
Limites aparentes Limites reales
Media aritmetica +1s
Media aritmetica +2s
Media aritmetica +3s

3. 5.9308 0 6.498
5.9308 38 6.498
5.9739 38
5.9739 0
5.9739 49 6.0301
6.0171 49 6.0301
6.0171 0
6.0171 27
6.0602 27 5.874
6.0602 0 5.874
6.0602 26
6.1033 26
6.1033 0 5.718
6.1033 9 5.718
6.1464 9
6.1464 0
6.1464 5 5.563
6.1895 5 5.563
6.1895 0
Media aritmetica -3s
Media
Media aritmetica -1s
Media aritmetica -2s

4. 6.110 6.067 6.203 6.05 6.248 6.216 6.14 6.134
6.213 5.998 6.157 6.044 6.041 6.199 6.133 6.215
6.312 6.170 6.165 6.135 6.084 6.119 6.068 6.185
6.018 6.054 6.120 6.217 6.286 6.061 6.149 6.127
6.017 6.167 6.151 6.003 6.090 6.213 6.039 6.165
6.083 6.131 6.113 6.188 6.154 6.128 6.185 6.166
6.113 6.147 5.961 6.189 6.169 6.179 6.155 6.103
6.18 6.194 6.198 6.200 6.175 6.166 6.065 6.013
6.225 6.099 6.226 6.065 6.110 6.095 6.122 6.182
6.126 6.047 6.259 6.059 6.133 6.180 6.164 6.127
Marcas de
clase
xi fi fai fri fra fixi |xi-x|fi (xi-x)^2 fi
5.802 7 7 0.035 0.035 40.614 0.6086 0.053
5.845 12 19 0.060 0.095 70.136 0.5313 0.024
5.887 27 46 0.135 0.230 158.958 0.0434 0.000
5.930 38 84 0.190 0.420 225.340 -1.5602 0.064
5.973 49 133 0.245 0.665 292.661 4.1025 0.343
6.015 27 160 0.135 0.800 162.414 3.4126 0.431
6.058 26 186 0.130 0.930 157.508 4.3955 0.743
6.101 9 195 0.045 0.975 54.906 1.9055 0.403
3.050 5 200 0.025 1.000 15.252 -14.1930 40.288
total 1177.788 -0.7538 42.350
x 5.889
desv. Media -0.00377
varianza 0.211752012
desv. Est. 0.4601652
0
44.1
0
34.3
0
24.5
0
53.9
Media aritmetica +2s
FRECUENCIA Medidas de tendencia central y dispersion
Media aritmetica +1s
Media aritmetica +3s
Media
Media aritmetica -1s
0
10
20
30
40
50
60
5.7 5.8 5.9 6 6.1 6.2 6.3

5. 0
44.1
CP= 0.13908049
0
34.3
0 Cpk Ise= 0.33035841
24.5
Cpk Lie= 0.05219744
Marcas de
clase
xi fi fai fri fra fixi |xi-x|fi (xi-x)^2 fi
5.823 7 7 0.035 0.035 40.760 0.4628 0.031
5.866 12 19 0.060 0.095 70.386 0.2813 0.007
5.908 27 46 0.135 0.230 159.521 -0.5191 0.010
5.951 38 84 0.190 0.420 226.132 -2.3519 0.146
5.994 49 133 0.245 0.665 293.682 5.1234 0.536
6.036 27 160 0.135 0.800 162.977 3.9751 0.585
6.079 26 186 0.130 0.930 158.050 4.9372 0.938
6.122 9 195 0.045 0.975 55.094 2.0930 0.487
6.164 5 200 0.025 1.000 30.821 1.3761 0.379
total 1197.420 15.3779 3.117
x 5.987
desv. Media 0.076889
varianza 0.015583361
desv. Est. 0.124833331
0
44.1 6.030
0.155833
0
34.3
Media aritmetica -2s
Media aritmetica -3s
x + 43 milesimas=
desv. Est. + 31 milesimas=
FRECUENCIA Medidas de tendencia central y dispersion
Media aritmetica +1s
Media aritmetica +2s
Media aritmetica +3s
Cp= 𝐿𝐼𝑀𝐼𝑇𝐸 𝑆𝑈𝑃𝐸𝑅𝐼𝑂𝑅 −𝐿𝐼𝑀𝐼𝑇𝐸 𝐼𝑁𝐹𝐸𝑅𝐼𝑂𝑅
6 ∗𝐷𝐸𝑆𝑉.𝐸𝑆𝑇.
𝐶𝑝𝑘 𝐼𝑠𝑒 = 𝐿𝐼𝑀𝐼𝑇𝐸 𝑆𝑈𝑃𝐸𝑅𝐼𝑂𝑅 −𝑃𝑅𝑂𝑀𝐸𝐷𝐼𝑂
3 ∗𝐷𝐸𝑆𝑉.𝐸𝑆𝑇.
𝐶𝑝𝑘 𝐿𝑖𝑒 = 𝐿𝐼𝑀𝐼𝑇𝐸 𝐼𝑁𝐹𝐸𝑅𝐼𝑂𝑅 −𝑃𝑅𝑂𝑀𝐸𝐷𝐼𝑂
3 ∗𝐷𝐸𝑆𝑉.𝐸𝑆𝑇.
50
60

6. 0
24.5
0
53.9
0
44.1
0
34.3
CP= 0.41069519
0
24.5
Cpk Ise= 0.6735829
Cpk Lie= -0.14780749
Media aritmetica -3s
Media
Media aritmetica -1s
Media aritmetica -2s
0
10
20
30
40
50
5.7 5.8 5.9 6 6.1 6.2 6.3 6.4
Cp= 𝐿𝐼𝑀𝐼𝑇𝐸 𝑆𝑈𝑃𝐸𝑅𝐼𝑂𝑅 −𝐿𝐼𝑀𝐼𝑇𝐸 𝐼𝑁𝐹𝐸𝑅𝐼𝑂𝑅
6 ∗𝐷𝐸𝑆𝑉.𝐸𝑆𝑇.
𝐶𝑝𝑘 𝐼𝑠𝑒 = 𝐿𝐼𝑀𝐼𝑇𝐸 𝑆𝑈𝑃𝐸𝑅𝐼𝑂𝑅 −𝑃𝑅𝑂𝑀𝐸𝐷𝐼𝑂
3 ∗𝐷𝐸𝑆𝑉.𝐸𝑆𝑇.
𝐶𝑝𝑘 𝐿𝑖𝑒 = 𝐿𝐼𝑀𝐼𝑇𝐸 𝐼𝑁𝐹𝐸𝑅𝐼𝑂𝑅 −𝑃𝑅𝑂𝑀𝐸𝐷𝐼𝑂
3 ∗𝐷𝐸𝑆𝑉.𝐸𝑆𝑇.

7. 6.200 6.173
6.064 6.146
6.153 6.052
6.103 6.055
6.213 6.001
6.108 6.159
6.084 6.082
6.145 6.29
6.033 6.233
6.162 6.168

8. La media se mejora en 43 milésimas
La desviación estándar en 31 milésimas.

9. 8713058359