TAREA ESTADISTICA 2015
27
4 X d 2.5 0.82 DM= d /N 2.5 0.82 3.1 0.22 DM= 4.34/6 3.0 0.32 3.4 0.08 DM= 0.72 5.4 2.08 19.9 4.34 N= 6 19.9/6 = 3.32 3.32 5.1 X |d| 9 17.93 DM= d /N 10 16.93 12 14.93 DM= 178.86/14 15 11.93 17 9.93 DM= 12.78 18 8.93 20 6.93 25 1.93 28 1.07 35 8.07 40 13.07 46 19.07 50 23.07 52 25.07 377 178.86 N=14 377/14 = 26.93 26.93 ¯= ▒ ∑ 〖 / 〗 ▒ ∑ = ▒ ∑ = ¯= ▒ ∑ ▒ ∑ = ¯= ▒ ∑ 〖 / 〗 ¯= ▒ ∑ = ▒ ∑
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70 ejercicios de estadistica resueltos
Transcript of TAREA ESTADISTICA 2015
4 2
X d
2.5 0.82 DM= d /N2.5 0.823.1 0.22 DM= 4.34/63.0 0.323.4 0.08 DM= 0.725.4 2.08
19.9 4.34
N= 6
19.9/6 = 3.32
3.32
5.1 5.2
X |d|
9 17.93 DM= d /N10 16.9312 14.93 DM= 178.86/1415 11.9317 9.93 DM= 12.7818 8.9320 6.9325 1.9328 1.0735 8.0740 13.0746 19.0750 23.0752 25.07377 178.86
N=14377/14 = 26.93
26.93
¯𝑥=∑▒ 〖𝑋 /𝑁〗∑▒= ∑▒=
¯𝑥=
∑▒
¯𝑥=∑▒ 〖𝑋 /𝑁〗
∑▒=¯𝑥=∑▒ 〖𝑋 /𝑁〗¯𝑥=
∑▒=
∑▒
¯𝑥=∑▒ 〖𝑋 /𝑁〗
5.3 5.4
X |d|
400 93.55 DM= d /N450 43.55456 37.55 DM= 178.86/14466 27.55470 23.55 DM= 46.69476 17.55480 13.55 46.694545 51.45550 56.45566 72.45570 76.45
5429 513.64N= 11
5429/16 = 493.5
493.5
5.3
X |d|
24 32.28 DM= d /N28 28.2834 22.28 DM= 269/1836 20.2844 12.28 DM= 14.9448 8.2850 6.28 14.94452 4.2856 0.2860 3.7264 7.7266 9.7270 13.7272 15.7272 15.7274 17.7280 23.7283 26.72
1013 269N= 18
∑▒=¯𝑥=∑▒ 〖𝑋 /𝑁〗¯𝑥=
∑▒=
∑▒
¯𝑥=∑▒ 〖𝑋 /𝑁〗
∑▒=¯𝑥=∑▒ 〖𝑋 /𝑁〗
∑▒=
∑▒
1013/18 56.3
56.28
¯𝑥=∑▒ 〖𝑋 /𝑁〗¯𝑥=
|d|
X |D|= X -
1000000 206000 DM= |d| /N1100000 1060001350000 144000 DM= 624000/51275000 690001305000 99000 DM= 124800.006030000 624000
N= 5
6030000/5 ###
1206000
X |d|
40 31.56 DM= d /N45 26.5658 13.56 DM= 199/1660 11.5665 6.56 DM= 12.4467 4.5668 3.5670 1.5672 0.4472 0.4476 4.4485 13.4489 17.4489 17.4493 21.4496 24.441145 199.00
N= 161145/16 = ###
71.56
¯𝑥∑▒= ∑▒=
∑▒
¯𝑥=∑▒ 〖𝑋 /𝑁〗¯𝑥=
∑▒= ∑▒=¯𝑥=∑▒ 〖𝑋 /𝑁〗¯𝑥=
∑▒
X |d|
3000 433.17 DM= d /N3200 233.173300 133.17 DM= 178.86/143337 96.173390 43.17 DM= 156.473450 16.833450 16.83 156.473456 22.833500 66.833500 66.833565 131.834050 616.83
41198 1877.67N= 12
41198/12 = ###
3433.17
∑▒=¯𝑥=∑▒ 〖𝑋 /𝑁〗¯𝑥=
∑▒=
∑▒
x f fx |d| f|d|60 1 60 17.87 17.87 DM=66 4 264 11.87 47.4770 5 350 7.867 39.33 DM= 231.73/3076 6 456 1.867 11.2081 6 486 3.133 18.80 DM= 2.9890 8 720 12.13 97.07
443 30 2336 54.73 231.73
N= 3077.87
x f fx |d| f|d|14 4 56 1.811 7.24324 DM=15 9 135 0.811 7.297316 15 240 0.189 2.83784 DM= 29.08/3717 8 136 1.189 9.5135118 1 18 2.189 2.18919 DM= 1.8480 37 585 6.189 29.08
N= 3715.81
x f fx |d| f|d|58 2 116 7.379 14.7586 DM=59 4 236 6.379 25.517260 3 180 5.379 16.1379 DM= 115.86/2965 4 260 0.379 1.5172468 5 340 2.621 13.1034 DM= 4.0069 6 414 3.621 21.724170 5 350 4.621 23.1034
449 29 1896 30.38 115.862
N= 2965.38
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
x f fx |d| f|d|65 3 195 7.20 21.59 DM=66 4 264 6.20 24.7867 2 134 5.20 10.39 DM= 189.37/5168 4 272 4.20 16.7869 3 207 3.20 9.59 DM= 3.7170 2 140 2.20 4.3971 5 355 1.20 5.9872 6 432 0.20 1.1873 4 292 0.80 3.2274 3 222 1.80 5.4175 2 150 2.80 5.6176 2 152 3.80 7.6177 3 231 4.80 14.4178 1 78 5.80 5.8079 2 158 6.80 13.6180 5 400 7.80 39.02
1160 51 3682 64.00 189.37
N= 5172.20
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
X Xs F FXs |d| f|d|10500 11499 10999.5 1 10999.5 1714.29 1714.2911500 12499 11999.5 2 23999 714.29 1428.5712500 13499 12999.5 2 25999 285.71 571.4313500 14499 13999.5 2 27999 1285.71 2571.43
49998 7 88996.5 4000.00 6285.71
N= 712713.79
DM=
DM= 6285.71/7
DM= 897.96
X Xs F FXs |d| f|d|60 69 64.5 2 129 19.71 39.4370 79 74.5 6 447 9.71 58.2980 89 84.5 18 1521 0.29 5.1490 99 94.5 9 850.5 10.29 92.57
318 35 2947.5 40 195.43
N= 3584.21
DM=
DM= 195.43/35
DM= 5.58
X Xs F FXs |d| f|d|1.52 1.59 1.56 15 23.325 0.08 1.15
1.6 1.67 1.64 18 29.43 0.00 0.061.68 1.75 1.71 13 22.295 0.08 1.09
4.91 46 75.05 0.16 2.30
N= 461.63
DM=
DM= 195.43/35
DM= 0.05
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
∑▒=¯𝑥=
∑▒ 〖𝑓 |𝑑|/𝑛 〗
X2 43 97 498 648 649 81
10 10012 14412 14412 14414 19616 25618 32420 400
151 1979
151/14 = 10.79
116.42
X2
x10.792 =
∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=
𝑠=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑠=√(1979 /14 −116.42 ) 𝑠=√(24.94 )= 4.99
X3 94 166 368 64
10 10012 14415 22516 256
74 850
74/8 = 9.25
85.56
X2
x9.252 =
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(850 /8 −85.56 ) 𝑆=√(20.69 )= 4.55
∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=
MATEMATICA HISTORIA
X X16 256 39 152118 324 42 176431 961 46 211640 1600 49 240152 2704 54 291664 4096 58 336468 4624 60 360075 5625 60 360078 6084 61 372194 8836 67 4489
536 35110 536 29492
536/10 = 53.60 536/10 = 53.60
2872.96 2872.96
X2 X2
x53.602 = x53.602 =
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(35110 /10 −2872.96 ) 𝑆=√(638.04 )= 25.26
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(76.24 )= 8.73
∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=¯𝑥=∑▒ 〖𝑋 /𝑁〗=𝑥 ̅�^2=
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(29492 /10 −2872.96 )
X X9 81 40 1600
10 100 45 202512 144 58 336415 225 60 360017 289 65 422518 324 67 448920 400 68 462425 625 70 490028 784 72 518435 1225 72 518440 1600 76 577646 2116 85 722550 2500 89 792152 2704 89 7921
377 13117 93 864996 9216
1145 85903377/14 = 26.93
725.22 1145/16 = 71.56
5120.83
X2 X2
x26.932 =
x71.562 =
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(13117 /14 −725.22 ) 𝑆=√(211.71 )= 14.55
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(248.11 )= 15.75
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(85903 /16 −5120.83 )
∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗= ∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=
X X400 160000 3000 9000000450 202500 3200 10240000456 207936 3300 10890000466 217156 3337 11135569470 220900 3390 11492100476 226576 3450 11902500480 230400 3450 11902500545 297025 3456 11943936550 302500 3500 12250000566 320356 3500 12250000570 324900 3565 12709225
5429 2710249 4050 1640250041198 142118330
5429/11 = 493.5541198/12 = 3433.17
243591.60
11786656.25
X2 X2
x493.552 =
x3433.172 =
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(2710249 /11 −243591.60 )
𝑆=√(2794.67 )= 52.86 𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 )
𝑆=√(56537.92 )= 237.78 𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 )
𝑆=√(142118330 /12 −11786656.25 )
∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗= ∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=
X24 57628 78434 115636 129644 193648 230450 250052 270456 313660 360064 409666 435670 490072 518472 518474 547680 640083 6889
1013 62477
1013/18 = 56.28
3167.44
X2
x56.282 =
𝑆=√( ∑▒ 〖𝑋 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(62477 /18 −3167.44 ) 𝑆=√(303.51 )= 17.42
∑▒=
𝑥 ̅�^2=
¯𝑥=∑▒ 〖𝑋 /𝑁〗=
Demuestre que la media y la desviacion tipica de la distribucion siguiente es de x 4.7 y s3.52
x f fx0 2 0 0 02 2 4 4 83 1 9 3 96 1 36 6 368 3 64 24 192
10 1 100 10 10029 10 213 47 345
N= 104.70
22.09
hallar la desviacion estandar de las pruebas obtenidas en un examen final de artes plasticas por 73 alumnos de primero basico
x f fx3 1 9 3 94 1 16 4 165 2 25 10 506 5 36 30 1807 21 49 147 10298 14 64 112 8969 14 81 126 1134
10 15 100 150 150052 73 380 582 4814 65.9452055 2.38
N= 737.97
63.56
X2 fX2
X2 fX2
𝑆=√( ∑▒ 〖〖𝑓𝑋〗 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(12.41 )= 3.52
𝑆=√(345 /10 −22.09 ) ∑▒=
¯𝑥=
∑▒=
¯𝑥=
𝑋 ̅�̂ 2
𝑋 ̅�̂ 2
𝑆=√( ∑▒ 〖〖𝑓𝑋〗 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(2.38 )= 1.54
𝑆=√(4814/73 −63.56 )
hallar la desviacion estandar de las pruebas obtenidasde 35 alumnos en un test de habilidad matematica
x f fx9 8 81 72 6488 6 64 48 3847 5 49 35 2456 10 36 60 3605 3 25 15 754 1 16 4 163 1 9 3 92 1 4 2 4
44 35 284 239 1741 49.7428571 3.11N= 35
6.8346.63
calcule la desviacion media y la desviacion estandar de los precios de 34 botellas de aceite comestible
x f fx |d| f|d|6.75 6 45.56 40.50 273.38 1.31875 7.91257.20 3 51.84 21.60 155.52 0.86875 2.606257.80 8 60.84 62.40 486.72 0.26875 2.158.00 4 64.00 32.00 256.00 0.06875 0.2758.25 9 68.06 74.25 612.56 0.18125 1.631259.00 6 81.00 54.00 486.00 0.93125 5.58759.50 4 90.25 38.00 361.00 1.43125 5.725
56.50 40 461.56 322.75 2631.18 5.07 25.89N= 40
8.0765.10 DM=
DM= 25.89/40
X2 fX2
X2 fX2
∑▒=
¯𝑥=∑▒=
¯𝑥=𝑋 ̅�̂ 2
𝑆=√( ∑▒ 〖〖𝑓𝑋〗 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(3.11 )= 1.76
𝑆=√(1741 /35 −46.63 )
∑▒=
¯𝑥=∑▒=
¯𝑥=𝑋 ̅�̂ 2 𝑆=√( ∑▒ 〖〖𝑓𝑋〗 ^2/𝑁 − ̅�〗 𝑋 ^2 ) 𝑆=√(2631.18 /40 −65.10 )
∑▒ 〖𝑓 |𝑑|/𝑛 〗
DM= 0.65𝑆=√(0.67 )= 0.82
Los punteos obtenidos por 49 alumnos en una prueba objetiva de calculo mercantil y matematica financiera
X f60 69 2 64.50 4160.25 66.50 8320.5070 79 15 74.50 5550.25 89.50 83253.7580 89 19 84.50 7140.25 103.50 135664.7590 99 13 94.50 8930.25 107.50 116093.25
49 318 25781 367.00 343332.25N= 49
7.4956.10
Las puntuaciones obtenidas por 30 alumnos en un test de hábitos de estudio
X f45 49 1 47.00 2209.00 48.00 2209.0050 54 1 52.00 2704.00 53.00 2704.0055 59 1 57.00 3249.00 58.00 3249.0060 64 3 62.00 3844.00 65.00 11532.0065 69 2 67.00 4489.00 69.00 8978.0070 74 5 72.00 5184.00 77.00 25920.0075 79 5 77.00 5929.00 82.00 29645.0080 84 4 82.00 6724.00 86.00 26896.0085 89 5 87.00 7569.00 92.00 37845.0090 94 3 92.00 8464.00 95.00 25392.00
30 695 50365 725 174370N= 30
24.17584.03
XS XS2 fXs fXS
2
XS XS2 fXs fXS
2
𝑆=√((∑▒ 〖𝑓𝑋 _𝑠 2 ∕〗𝑁 )−𝑋 ̅�̂ 2 ) 𝑆=√((343332.25/49))−56.10 ∑▒=
¯𝑥=∑▒=
¯𝑥=𝑋 ̅�^2
𝑆=√(7006.78 −56.10) 𝑆=√6950.68=83.37
∑▒=
¯𝑥=∑▒=
¯𝑥=𝑋 ̅�^2
𝑆=√((∑▒ 〖𝑓𝑋 _𝑠 2 ∕〗𝑁 )−𝑋 ̅�̂ 2 ) 𝑆=√((174370/30))−584.03 𝑆=√(5812.33 −584.03) 𝑆=√5228.31=72.31
