1. X1
X2
X3
X4
Gráficos de
X5
X6
X7
X8
X9
X10
X11
∑
control
Varianza
S
Xm
Sm
Ejercicio 10
30x11
19.567

2. Cálculo de las desviaciones estándar
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
X1 0.79 57.07 79.86 17.79 7.00 0.40 21.58 3.54 10.47 0.89 3.17 0.58 52.36 1.17 29.46 0.13 40.96 1.64 0.24 8.57 6.67 0.86 57.76 13.36 3.64 6.76 2.89 18.96 0.68 3.05
X2 21.08 0.06 17.95 2.50 8.73 15.49 5.04 205.01 39.23 2.74 0.34 0.02 0.40 0.61 9.16 5.94 1.69 103.67 8.46 47.99 43.32 6.90 0.16 6.48 1.19 0.04 77.44 18.02 9.44 40.38
X3 0.50 1.57 118.02 12.83 30.75 3.01 7.54 15.07 1.60 4.18 0.27 4.56 55.71 6.85 60.42 22.69 12.96 4.07 1.93 38.10 25.82 6.11 14.44 69.65 1.67 8.41 72.25 40.26 1.76 0.42
X4 0.37 1.55 0.54 9.11 7.05 0.11 20.74 0.34 1.29 11.93 2.20 27.42 14.16 54.49 1.38 61.41 5.29 36.22 15.28 0.33 1.48 2.33 0.81 23.57 30.35 9.61 57.76 8.10 4.11 0.13
de
X5 21.08 33.01 120.20 1.40 42.96 1.07 3.08 28.96 45.38 0.02 4.33 7.09 1.79 45.99 47.23 26.66 15.21 37.43 14.37 2.65 39.92 24.73 12.96 19.84 4.45 36.00 6.25 3.82 2.80 8.68
X6 1.42 2.42 4.68 1.64 17.26 6.57 0.13 116.25 10.47 1.31 0.15 30.95 0.06 112.75 2.80 1.86 37.21 1.64 12.31 6.62 2.30 5.63 9.00 109.11 44.77 1.96 4.41 0.71 0.05 6.02
X7 7.89 0.43 3.11 90.60 3.05 2.68 14.86 31.56 29.85 3.78 16.96 0.00 14.16 0.08 0.76 0.07 1.00 0.17 0.48 0.18 25.18 0.39 6.25 19.84 8.36 6.25 16.81 3.05 0.02 11.19
X8 1.71 8.10 2.68 14.30 3.41 3.11 10.53 0.67 52.36 11.93 0.01 30.65 104.78 13.09 3.14 2.68 14.44 28.96 24.10 15.78 2.95 11.07 4.41 4.22 3.58 23.04 0.16 45.62 0.18 0.20
X9 11.50 6.48 5.46 4.07 3.41 0.40 3.08 6.16 34.38 74.74 5.21 3.37 0.32 14.58 29.46 55.30 0.00 0.10 0.65 20.50 2.50 1.27 19.36 3.44 2.28 2.25 12.96 4.22 0.05 28.57
X10 10.95 1.81 5.94 45.99 1.31 10.65 25.55 10.36 14.93 24.55 4.33 0.13 36.77 33.43 69.34 17.34 38.44 2.30 14.37 29.95 11.68 6.90 6.25 14.10 0.83 29.16 11.56 0.91 1.06 1.81
X11 34.92 8.73 29.55 0.34 2.39 5.59 19.76 1.04 1.29 1.83 35.02 29.85 3.75 2.01 4.30 10.65 0.04 2.95 34.70 5.42 11.44 8.84 1.44 14.03 3.64 10.24 7.29 0.00 2.17 44.28
∑ 112.21 121.23 387.99 200.58 127.31 49.11 131.89 418.96 241.27 137.93 72.00 134.65 284.27 285.06 257.44 204.73 167.24 219.18 126.91 176.08 173.28 75.04 132.84 297.63 104.75 133.72 269.78 143.69 22.32 144.73
Varianza 10.20 11.02 35.27 18.23 11.57 4.46 11.99 38.09 21.93 12.54 6.55 12.24 25.84 25.91 23.40 18.61 15.20 19.93 11.54 16.01 15.75 6.82 12.08 27.06 9.52 12.16 24.53 13.06 2.03 13.16
S 3.19 3.32 5.94 4.27 3.40 2.11 3.46 6.17 4.68 3.54 2.56 3.50 5.08 5.09 4.84 4.31 3.90 4.46 3.40 4.00 3.97 2.61 3.48 5.20 3.09 3.49 4.95 3.61 1.42 3.63
Xm 20.96
Sm 3.89
2.641
Cálculo de los límites de control 0.880
10
Media 20.96 1 3.606 S Media 3.89 1
20.96 30 1.202 3.89 30
LCL UCL LCL UCL
17.163 1 24.561 1 1.249 1 6.531 1
17.163 30 24.561 30 1.249 30 6.531 30
18.365 1 23.359 1 2.129 1 5.650 1
18.365 30 23.359 30 2.129 30 5.650 30
19.567 1 22.157 1 3.009 1 4.770 1
19.567 30 22.157 30 3.009 30 4.770 30

3. Límites de control para la media aritmética Límites de control para la desviación estándar
LCL = 17.16 CL = 20.96 UCL = 24.56 LCL = 1.248 CL = 3.889 UCL = 6.53
25
24
2. cinco puntos
disminuyendo
Gráfico de medias
23
(tendencia)
22
21
20
19
18
17
7
Gráfico Desv. Estándar
6
5
4
3
2
1
0
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
X1 20.1 29.5 11.8 26.6 19.4 22.0 16.5 21.9 24.5 19.3 23.1 24.0 12.6 19.5 15.9 19.9 13.7 20.8 21.8 23.2 24.1 17.8 15.3 25.7 20.7 22.9 23.4 24.7 21.4 21.7
X2 16.4 21.7 16.5 20.8 25.0 25.3 18.9 5.7 15.0 21.9 21.9 23.1 19.2 19.8 18.3 17.1 21.4 29.7 25.2 27.2 28.1 16.1 23.3 19.5 17.7 20.5 12.9 16.1 25.3 13.6
X3 21.7 23.2 31.6 18.8 16.5 23.1 18.4 23.9 20.0 18.2 20.8 21.1 27.3 23.2 29.1 24.3 16.5 17.5 20.9 14.1 26.6 21.2 19.1 13.7 17.5 23.2 30.2 14.0 20.9 20.6
X4 21.6 20.7 20.0 25.4 24.7 21.7 25.7 20.6 22.4 23.7 22.8 18.0 23.6 13.2 22.5 11.7 17.8 13.5 26.2 19.7 20.3 17.2 22.0 26.9 24.3 17.2 14.1 17.5 20.2 19.6
X5 16.4 16.2 31.7 21.2 28.6 22.4 22.9 25.4 28.0 20.1 23.4 25.9 18.5 13.8 28.2 24.7 16.2 13.4 18.5 21.9 15.2 23.7 26.5 26.5 20.9 14.3 19.2 22.3 23.9 22.9
X6 19.8 23.5 22.9 21.1 26.2 18.8 21.5 30.8 24.5 19.1 21.7 28.8 19.6 31.2 23.0 20.9 26.2 20.8 25.8 17.7 20.0 21.1 25.9 11.6 12.1 18.9 23.8 19.5 22.0 17.5
X7 23.8 22.6 22.5 31.9 20.3 23.0 25.0 14.4 15.8 18.3 17.2 23.3 23.6 20.3 22.2 19.8 19.1 19.1 21.6 20.7 16.5 18.1 25.4 26.5 15.9 22.8 25.8 18.6 22.1 23.3
X8 22.3 19.1 19.1 18.6 20.2 19.6 17.9 19.2 28.5 23.7 21.2 17.7 9.6 24.2 23.1 17.9 23.9 24.9 27.2 16.3 19.8 15.4 25.0 24.1 16.9 15.5 21.3 27.1 21.8 20.4
X9 17.6 19.4 18.4 24.4 20.2 22.0 22.9 22.5 15.4 11.6 23.6 21.4 20.4 24.4 15.9 12.1 20.1 19.2 23.1 24.8 23.1 17.6 27.3 23.9 20.3 18.8 25.3 22.4 22.0 25.3
X10 24.3 20.6 18.3 15.6 20.9 18.1 26.2 16.8 17.4 25.2 23.4 23.6 25.9 14.8 13.0 23.7 26.3 18.0 18.5 14.8 18.1 16.1 20.4 25.8 19.7 25.7 18.3 21.3 21.2 21.3
X11 26.9 24.9 15.3 21.8 20.5 19.0 16.7 19.0 22.4 21.6 15.4 28.7 17.9 22.0 23.4 22.8 19.9 17.8 16.4 22.6 24.9 21.7 21.7 18.3 20.7 23.5 24.4 20.3 23.7 13.3
∑ 230.9 241.4 228.1 246.2 242.5 235.0 232.6 220.2 233.9 222.7 234.5 255.6 218.2 226.4 234.6 214.9 221.1 214.7 245.2 223.0 236.7 206.0 251.9 242.5 206.7 223.3 238.7 223.8 244.5 219.5
X 21.0 21.9 20.7 22.4 22.0 21.4 21.1 20.0 21.3 20.2 21.3 23.2 19.8 20.6 21.3 19.5 20.1 19.5 22.3 20.3 21.5 18.7 22.9 22.0 18.8 20.3 21.7 20.3 22.2 20.0
S 3.194 3.320 5.939 4.270 3.402 2.113 3.463 6.171 4.683 3.541 2.558 3.499 5.084 5.091 4.838 4.314 3.899 4.464 3.397 4.001 3.969 2.612 3.475 5.202 3.086 3.487 4.952 3.614 1.425 3.627