2. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
x1 103 147 143 122 88 152 153 152 89 95 138 106 122 105 166 151 159 125 125 145
x2 107 145 167 165 149 143 165 128 117 98 155 112 109 125 179 204 132 133 115 144
x3 140 148 121 145 128 154 75 136 123 131 169 121 157 110 153 139 152 131 93 150
x4 118 109 156 127 128 170 155 108 132 90 152 155 89 110 139 138 175 164 108 145
x5 158 131 104 152 148 147 132 135 153 92 102 118 94 90 154 149 168 161 147 153
∑= 626 680 691 711 641 766 680 659 614 506 716 612 571 540 791 781 786 714 588 737
xm= 125.2 136.0 138.2 142.2 128.2 153.2 136.0 131.8 122.8 101.2 143.2 122.4 114.2 108.0 158.2 156.2 157.2 142.8 117.6 147.4

3. 170
160
150
140
130
120
110
100
90
50
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
x1 103 147 143 122 88 152 153 152 89 95 138 106 122 105 166 151 159 125 125 145
x2 107 145 167 165 149 143 165 128 117 98 155 112 109 125 179 204 132 133 115 144
x3 140 148 121 145 128 154 75 136 123 131 169 121 157 110 153 139 152 131 93 150
x4 118 109 156 127 128 170 155 108 132 90 152 155 89 110 139 138 175 164 108 145
x5 158 131 104 152 148 147 132 135 153 92 102 118 94 90 154 149 168 161 147 153
∑= 626 680 691 711 641 766 680 659 614 506 716 612 571 540 791 781 786 714 588 737
xm
125.2 136.0 138.2 142.2 128.2 153.2 136.0 131.8 122.8 101.2 143.2 122.4 114.2 108.0158.2 156.2 157.2 142.8 117.6 147.4
=

4. S1
Media Aritmetica de las Medias Aritmeticas S2+1
X Y X Y
UCL= 159.395 LIMITE SUPERIOR DE CONTROL
1.0 142.5 1 24.16
LC= 134.1 LIMITE CENTRAL DE CONTROL 20.0 142.5 20 24.16
LCL= 108.8 LIMITE INFERIOR DE CONTROL S2 S2+2
X Y X Y
1.0 150.96 1 30.60
MEDIA ARITMETICA DE LAS DESVIACIONES ESTANDAR 20.0 150.96
20 30.60
S-1
UCL= 37.0301 LIMITE SUPERIOR DE CONTROL S2-1
X Y
X Y
S= 17.7 LIMITE CENTRAL DE CONTROL
1.0 125.7
1 11.29
LCL= 0.0 LIMITE INFERIOR DE CONTROL 20.0 125.7
20 11.29
S-2
S2-2
X Y X Y
1.0 117.2 1 4.86
20.0 117.2 20 4.86

5. Graficar Limites DESVIACION
de Control ESTANDAR REAL LC
x y S= 8.43 X Y
1.0 134.1 S1= 142.53 1 17.7
20.0 134.1 S2= 150.96 20 17.7
UCL S-1= 125.67 UCL
x y X Y
S-2= 117.24
1.0 159.4 1 37.0301
20.0 159.4 20 37.0301
S2= 6.43
LCL LCL
S2+1= 24.16 X Y
x y S2+2= 30.60 1 0.0
1.0 108.8 S2-1= 11.29 20 0.0
20.0 108.8 S2-2= 4.86
1 492.8 121.0 23.0 408.0 1616.0 1.4 289.0 408.0 1142.4 38.4 27.0 269.0 60.8 9.0 60.8 27.0 3.2 316.8 54.8 5.8
2 331.2 81.0 829.4 519.8 432.6 104.0 841.0 14.4 33.6 10.2 139.2 108.2 27.0 289.0 432.6 2284.8 635.0 96.0 6.8 11.6
3 219.0 144.0 295.8 7.8 0.0 0.6 3721.0 17.6 0.0 888.0 665.6 2.0 1831.8 4.0 27.0 295.8 27.0 139.2 605.2 6.8
4 51.8 729.0 316.8 231.0 0.0 282.2 361.0 566.4 84.6 125.4 77.4 1062.8 635.0 4.0 368.6 331.2 316.8 449.4 92.2 5.8
5 1075.8 25.0 1169.6 96.0 392.0 38.4 16.0 10.2 912.0 84.6 1697.4 19.4 408.0 324.0 17.6 51.8 116.6 331.2 864.4 31.4
∑= 2170.8 1100.0 2634.8 1262.8 2440.8 5228.0 1016.8 2172.8 1146.8 2606.8 1461.2 2962.8 2990.8 1098.8 1332.8 1623.2
0 0 0 0 0 426.80 0 0 0 0 0 0 0 630.00906.80 0 0 0 0 61.20
1045.6
S2 = 434.16 220.00 526.96 252.56 488.16 85.36 0 203.36 434.56 229.36 521.36 292.24 592.56 126.00181.36 598.16 219.76 266.56 324.64 12.24
s= 20.84 14.83 22.96 15.89 22.09 9.24 32.34 14.26 20.85 15.14 22.83 17.10 24.34 11.22 13.47 24.46 14.82 16.33 18.02 3.50