histogramas en excel

1. 200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.7491518
Media +1S,
222.3701146
Media -1S,
213.1281889
Media +2S ,
226.9910775
Media -2S,
208.5072261
Media +3s,
231.6120403
Media -3S,
203.8862632
-7
3
13
23
33
43
53
200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
218.3373214
Media +1S,
222.6340939
Media -1S,
214.0405489
Media +2S,
226.9308664
Media -2S,
209.7437764
Media +3s,
231.2276389
Media -3S,
205.4470039
-5
0
5
10
15
20
25
30
200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.1609821
Media +1S,
222.0409403
Media -1S,
212.281024
Media +2S,
226.9208984
Media -2S,
207.4010659
Media +3s,
231.8008565
Media -3S,
202.5211078
-5
0
5
10
15
20
25
200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.5539286
Media +1S,
222.2526026
Media -1S,
212.8552545
Media +2S,
226.9512767
Media -2S,
208.1565804
Media +3s,
231.6499508
Media -3S,
203.4579064
-5
0
5
10
15
20
25
José Enrique López Palacio 3 “A”

2. Días Operario
1 A 216.9 218.2 214.3 218.3 218.3 210 222.9 217.5
2 B 222.1 221.2 219.3 223.2 212.8 210.1 216.9 218.4
3 B 214.2 221.3 223.2 222.4 221.4 217.5 207.6 216.7
4 B 228.3 219.7 218.6 215.1 216.1 215.4 220.1 214.2
5 A 210.6 221.1 217.6 210.4 213.9 224.3 222.6 222.1
6 A 221.5 211.9 220.5 220.5 221.4 215.4 214.2 223.4
7 A 208.2 213.4 208.4 216.6 208.9 219.1 215 211.1
8 B 219.1 213.5 223.7 214.1 212.5 218.5 221.2 222.9
9 B 216.8 212.1 214.9 219.8 219.3 222.1 221.5 213.3
10 A 220.4 217.3 213.4 225.6 213.6 211.2 222.9 219.2
11 B 215 218 215.6 215.6 222.2 212.3 217.5 214.8
12 B 216.2 220.2 226.4 224 208.5 218.1 220.3 214.5
13 B 222.3 218.6 217.9 221 213.7 221.8 217.2 224
14 A 214.6 217.7 214.1 218.5 211.4 219.7 221.4 206.4
15 A 215.1 215.1 220.4 224.9 220.2 219.1 216.9 213.9
16 B 218.4 220.5 219.9 221.2 222.2 208.7 223.9 220.4
17 B 217.7 216.7 222.2 219 209.1 213.1 215.3 218.6
18 A 221.4 214.2 224.7 219.9 226.8 209.3 213.1 221.6
19 A 218.5 222 227.6 218.3 212.9 222 219.7 222.7
20 A 209.7 218.1 223.1 220.3 211.2 221.9 217.9 218.1
Máquina 1 Máquina 2
Se realizaronunaserie de histogramasparadeterminarcómoesque se desarrollaunaempresa.
Se analizarandiversosfactoresobservadosenloshistogramas,yse llegaraaunaconclusión
individualsobre cadaunode lossiete histogramasque se realizaranposteriormente.
Histogramasobre lamuestratotal.
Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.58 207.96 9 9 0.05625 0.05625 1871.6786 88.0638 861.6924
209.58 212.71 211.14 13 22 0.08125 0.1375 2744.8571 85.8818 567.3607
212.71 215.84 214.27 33 55 0.20625 0.34375 7070.9571 114.7649 399.1204
215.84 218.96 217.40 35 90 0.21875 0.5625 7609.0000 12.2203 4.2667
218.96 222.09 220.53 41 131 0.25625 0.81875 9041.6714 113.9562 316.7321
222.09 225.22 223.66 24 155 0.15000 0.96875 5367.7714 141.7918 837.7046
225.22 228.35 226.79 5 160 0.03125 1 1133.9286 45.1828 408.2973
34839.8643 601.8616 3395.1743
Media 217.7492
Mediana 3.761635045
Varianza 21.3532976
Des. Estandar 4.62096285

3. 200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.7491518
Media +1S,
222.3701146
Media -1S,
213.1281889
Media +2S ,
226.9910775
Media -2S,
208.5072261
Media +3s,
231.6120403
Media -3S,
203.8862632
-7
3
13
23
33
43
53
En el histogramade la muestratotal,podemosobservarque todaslasfrecuenciasse encuentran
dentrode las dos desviacionesestándar,locual esbuenoyaque nosindicaque no existe tanta
variaciónenla elaboraciónde laspiezas.

4. 200.1
203.2
206.4
209.6
212.7
215.8
219.0
222.1
225.2
228.4
Media ,
216.1069643
"Media +1S,
219.8605782
Media - 1S,
212.3533503
Media +2S,
223.6141922
Media -2S,
208.5997364
Media + 3S,
227.3678061Media -3S,
204.8461225
-10
-5
0
5
10
15
20
25
30
35
40
Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.578571 207.964286 4 4 0.05 0.05 831.857143 32.57071429 265.212857
209.578571 212.707143 211.142857 7 11 0.0875 0.1375 1478 34.74875 172.496518
212.707143 215.835714 214.271429 30 41 0.375 0.5125 6428.14286 55.06607143 101.075741
215.835714 218.964286 217.4 21 62 0.2625 0.775 4565.4 27.15375 35.1107685
218.964286 222.092857 220.528571 13 75 0.1625 0.9375 2866.87143 57.48089286 254.157926
222.092857 225.221429 223.657143 5 80 0.0625 1 1118.28571 37.75089286 285.025982
225.221429 228.35 226.785714 0 80 0 1 0 0 0
17288.5571 244.7710714 1113.07979
Media 216.106964
Mediana 3.059638393
Varianza 14.0896176
Des. Estandar 3.75361394
Histograma operario A
En este histogramapodemosobservar,que existe unaligerainclinaciónhacialaderecha,la
cual nosindicaque la mayorparte de las piezasrealizadasporel operarioA,se encuentran
entre 217.7 y 222.1, locual nosindicaque el operarioA esta dejandounligeroexcedente en
laspiezasrealizadas.

5. Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.578571 207.964286 2 2 0.02564103 0.02564103 415.928571 19.35018315 187.214794
209.578571 212.707143 211.142857 7 9 0.08974359 0.11538462 1478 45.47564103 295.433418
212.707143 215.835714 214.271429 15 24 0.19230769 0.30769231 3214.07143 50.51923077 170.146179
215.835714 218.964286 217.4 21 45 0.26923077 0.57692308 4565.4 5.026923077 1.20333122
218.964286 222.092857 220.528571 26 71 0.33333333 0.91025641 5733.74286 75.11904762 217.033512
222.092857 225.221429 223.657143 6 77 0.07692308 0.98717949 1341.94286 36.10659341 217.281015
225.221429 228.35 226.785714 1 78 0.01282051 1 226.785714 9.146336996 83.6554805
16975.8714 240.743956 1171.96773
Media 217.639377
Mediana 3.086460975
Varianza 15.2203601
Des. Estandar 3.90132799
200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.6393773
Media +1S,
221.5407053
Media -1S,
213.7380493
Media +2S,
225.4420333
Media -2S,
209.8367213
Media +3s,
229.3433613
Media -3S,
205.9353933
-5
0
5
10
15
20
25
30
35
Histogramaoperario B
En este histogramapodemosobservar,que todaslaspiezasse encuentrandentrode lastres
desviacionesestándar,locual esbuenoyaque ningunapiezatieneel margende errortan
grande,a pesarde que lamayoría de lasfrecuenciasse encuentranlejanasalamedia.

6. Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.578571 207.964286 2 2 0.025 0.025 415.928571 20.74607143 215.19974
209.578571 212.707143 211.142857 5 7 0.0625 0.0875 1055.71429 35.97232143 258.801582
212.707143 215.835714 214.271429 16 23 0.2 0.2875 3428.34286 65.05428571 264.503756
215.835714 218.964286 217.4 20 43 0.25 0.5375 4348 18.74642857 17.5714292
218.964286 222.092857 220.528571 22 65 0.275 0.8125 4851.62857 48.2075 105.634684
222.092857 225.221429 223.657143 11 76 0.1375 0.95 2460.22857 58.51803571 311.3055
225.221429 228.35 226.785714 4 80 0.05 1 907.142857 33.79357143 285.501367
17466.9857 281.0382143 1458.51806
Media 218.337321
Mediana 3.512977679
Varianza 18.4622539
Des. Estandar 4.2967725
200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
218.3373214
Media +1S,
222.6340939
Media -1S,
214.0405489
Media +2S,
226.9308664
Media -2S,
209.7437764
Media +3s,
231.2276389
Media -3S,
205.4470039
-5
0
5
10
15
20
25
30
Histograma máquina1
La máquina1, trabajade unabuenamaneraya que la mayor parte de las piezasproducidasporla
misma,se encuentrancercanasa la media.

7. Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.578571 207.964286 7 7 0.0875 0.0875 1455.75 64.376875 592.054576
209.578571 212.707143 211.142857 8 15 0.1 0.1875 1689.14286 48.145 289.742628
212.707143 215.835714 214.271429 17 32 0.2125 0.4 3642.61429 49.12241071 141.941837
215.835714 218.964286 217.4 15 47 0.1875 0.5875 3261 3.585267857 0.85694304
218.964286 222.092857 220.528571 19 66 0.2375 0.825 4190.04286 63.98419643 215.472494
222.092857 225.221429 223.657143 13 79 0.1625 0.9875 2907.54286 84.45008929 548.601352
225.221429 228.35 226.785714 1 80 0.0125 1 226.785714 9.624732143 92.6354688
17372.8786 323.2885714 1881.3053
Media 217.160982
Mediana 4.041107143
Varianza 23.8139911
Des. Estandar 4.87995811
200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.1609821
Media +1S,
222.0409403
Media -1S,
212.281024
Media +2S,
226.9208984
Media -2S,
207.4010659
Media +3s,
231.8008565
Media -3S,
202.5211078
-5
0
5
10
15
20
25
Histograma máquina2
El trabajoque realizalamáquinados,esmuy buenoyaque una gran cantidadde piezasse encuentran
dentrode las dosdesviacionesestándar,ycercanasa lamedia,locual nosindicaque no ay mucha
variabilidadenlaproducciónde laspiezas.

8. 200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.5539286
Media +1S,
222.2526026
Media -1S,
212.8552545
Media +2S,
226.9512767
Media -2S,
208.1565804
Media +3s,
231.6499508
Media -3S,
203.4579064
-5
0
5
10
15
20
25
Histograma 10días
Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.578571 207.964286 4 4 0.05 0.05 831.857143 38.35857143 367.845001
209.578571 212.707143 211.142857 9 13 0.1125 0.1625 1900.28571 57.69964286 369.916532
212.707143 215.835714 214.271429 17 30 0.2125 0.375 3642.61429 55.8025 183.171706
215.835714 218.964286 217.4 16 46 0.2 0.575 3478.4 2.462857143 0.37910408
218.964286 222.092857 220.528571 19 65 0.2375 0.8125 4190.04286 56.51821429 168.121502
222.092857 225.221429 223.657143 13 78 0.1625 0.975 2907.54286 79.34178571 484.23992
225.221429 228.35 226.785714 2 80 0.025 1 453.571429 18.46357143 170.451735
17404.3143 308.6471429 1744.1255
Media 217.553929
Mediana 3.858089286
Varianza 22.077538
Des. Estandar 4.69867407
En losprimerosdiezdías,podemosobservar que laspiezasse realizaron de unamaneramuy
uniforme,yaque ningunapiezasobrepasa lastresdesviacionesestándar,ylamayorparte de las
piezasse encuentrandentrode unadesviaciónestándar.

9. 200.1 203.2 206.4 209.6 212.7 215.8 219.0 222.1 225.2 228.4 231.5 234.6
Media ,
217.944375
Media +1S,
222.5075058
Media -1S,
213.3812442
Media +2S,
227.0706367
Media -2S,
208.8181133
Media +3s,
231.6337675
Media -3S,
204.2549825
-5
0
5
10
15
20
25
30
Histogramade 11 a 20 días
Lim Inf Lim Sup Xi Fi Abs. Acum. Relativ a Rel. Ac um Fi Xi | x1-x| fi | x1-x| 2
fi
206.35 209.578571 207.964286 5 5 0.0625 0.0625 1039.82143 49.90044643 498.010911
209.578571 212.707143 211.142857 4 9 0.05 0.1125 844.571429 27.20607143 185.042581
212.707143 215.835714 214.271429 16 25 0.2 0.3125 3428.34286 58.76714286 215.848567
215.835714 218.964286 217.4 19 44 0.2375 0.55 4130.6 10.343125 5.63053867
218.964286 222.092857 220.528571 22 66 0.275 0.825 4851.62857 56.85232143 146.917566
222.092857 225.221429 223.657143 11 77 0.1375 0.9625 2460.22857 62.84044643 358.992882
225.221429 228.35 226.785714 3 80 0.0375 1 680.357143 26.52401786 234.507841
17435.55 292.4335714 1644.95089
Media 217.944375
Mediana 3.655419643
Varianza 20.8221631
Des. Estandar 4.56313085
Despuésde losdiezdías,podemosdarnoscuentaque laspiezascomienzanainclinarse
un pocoa la derecha,locual nosindicaque despuésde losdiezdíascomenzarona
dejarse pequeñosexcesosenlaelaboraciónde laspiezas.