Lista 1 Exercícios Estatística ENC Respostas!

Prévia do material em texto

Questão 1: 
Estatura cm fi Fi fri% Fri% Xi fi*xi fi log Xi fi/xi lXi-X_l*fi fi*(Xi-X-)² 
40,00 l-- 116,67 10 10 16,67 16,67 78,34 783,40 18,94 0,13 2057,30 423248,33 
116,67 l-- 193,34 8 18 13,33 30,00 155,01 1240,08 17,52 0,05 1032,48 133251,87 
193,34 l-- 270,01 11 29 18,33 48,33 231,68 2548,48 26,01 0,05 576,29 30191,83 
270,01 l-- 346,68 6 35 10,00 58,33 308,35 1850,10 14,93 0,02 145,68 3537,11 
346,68 l-- 423,35 12 47 20,00 78,33 385,02 4620,24 31,03 0,03 1211,40 122290,83 
423,35 l-- 500,02 13 60 21,67 100,00 461,69 6001,97 34,64 0,03 2309,06 410135,24 
Σ 60 --- 100,00 --- --- 17044,27 143,07 0,31 7332,21 1.122.655,21 
 h= 76,67 
 
Mo= 428,83 
 
Q3= 410,57 
 
45,00 
 Média= 284,07 
 
DM= 122,20 
 
D2= 135,84 
 
12,00 
 Mg= 242,38 239,88 k= 2,38 S²= 19028,05 
 
C45= 256,07 
 
27,00 
 Mh= 193,55 
 
S= 137,94 
 Md= 282,79 
 
CV= 48,56 
 
 
 
 40,00 
 
92,00 
 
134,00 198,00 226,00 284,00 357,00 388,00 425,00 475,00 
 
 40,00 
 
100,00 
 
147,00 198,00 226,00 299,00 372,00 394,00 465,00 479,00 
 
 48,00 
 
101,00 
 
156,00 200,00 229,00 308,00 375,00 410,00 468,00 481,00 
 
 61,00 
 
114,00 
 
178,00 208,00 251,00 337,00 381,00 416,00 469,00 482,00 
 
 78,00 
 
133,00 
 
189,00 222,00 252,00 339,00 383,00 420,00 474,00 492,00 
 
 81,00 
 
133,00 
 
190,00 224,00 284,00 347,00 386,00 424,00 474,00 500,00 
 
Questão 2: 
Frequências fi Fi fri% Fri% Xi fi*xi fi log Xi fi/xi lXi-X_l*fi fi*(Xi-X-)² 
4,00 l-- 15,00 6 6 10,00 10,00 9,50 57,00 5,87 0,63 272,82 12405,13 
15,00 l-- 26,00 2 8 3,33 13,33 20,50 41,00 2,62 0,10 68,94 2376,36 
26,00 l-- 37,00 10 18 16,67 30,00 31,50 315,00 14,98 0,32 234,70 5508,41 
37,00 l-- 48,00 8 26 13,33 43,33 42,50 340,00 13,03 0,19 99,76 1244,01 
48,00 l-- 59,00 7 33 11,67 55,00 53,50 374,50 12,10 0,13 10,29 15,13 
59,00 l-- 70,00 5 38 8,33 63,33 64,50 322,50 9,05 0,08 47,65 454,10 
70,00 l-- 81,00 11 49 18,33 81,66 75,50 830,50 20,66 0,15 225,83 4636,29 
81,00 l-- 92,00 5 54 8,33 89,99 86,50 432,50 9,69 0,06 157,65 4970,70 
92,00 l--l 103,00 6 60 10,00 99,99 97,50 585,00 11,93 0,06 255,18 10852,81 
Σ 60 --- 99,99 --- --- 3298,00 99,93 1,72 1372,82 42462,94 
 h= 11,00 
 
Mo= 75,50 
 
Q1= 33,70 
 
15,00 
 Média= 54,97 
 
DM= 22,88 
 
D4= 45,25 
 
24,00 
 Mg= 46,29 46,77 k= 1,67 S²= 719,71 
 
C75= 77,00 
 
45,00 
 Mh= 34,88 
 
S= 26,83 
 Md= 54,29 
 
CV= 48,81 
 
 4 24 31 38 45 53 68 72 80 94 
 6 25 33 39 47 54 69 73 81 95 
 8 27 33 40 49 58 70 75 82 95 
 9 29 34 41 49 61 70 75 85 99 
 11 30 35 41 52 63 71 76 85 99 
 12 30 36 45 52 63 72 79 90 100 
 
Questão 3: 
Questão 3 fi Fi fri% Fri% Xi fi*xi fi log Xi fi/xi lXi-Mél*fi fi*(Xi-Mé)² 
100,00 l-- 250,00 10 10 16,67 16,67 175,00 1750,00 22,43 0,06 3725,00 1387562,50 
250,00 l-- 400,00 11 21 18,33 35,00 325,00 3575,00 27,63 0,03 2447,50 544568,75 
400,00 l-- 550,00 9 30 15,00 50,00 475,00 4275,00 24,09 0,02 652,50 47306,25 
550,00 l-- 700,00 8 38 13,33 63,33 625,00 5000,00 22,37 0,01 620,00 48050,00 
700,00 l-- 850,00 14 52 23,33 86,66 775,00 10850,00 40,45 0,02 3185,00 724587,50 
850,00 l--l 1000,00 8 60 13,33 99,99 925,00 7400,00 23,73 0,01 3020,00 1140050,00 
Σ 60 --- 99,99 --- --- 32850,00 160,70 0,15 13.650,00 3.892.125,00 
 h= 150,00 
 
Mo= 775,00 
 
Q3= 775,00 
 
45,00 
 Média= 547,50 
 
DM= 227,50 
 
D2= 277,27 
 
12,00 
 Mg= 476,80 478,63 k= 2,68 S²= 65968,22 
 
C45= 500,00 
 
27,00 
 Mh= 400,00 
 
S= 256,84 
 Md= 550,00 
 
CV= 46,91 
 
 100,00 198,00 258,00 378,00 475,00 558,00 658,00 764,00 825,00 940,00 
 104,00 212,00 261,00 388,00 479,00 570,00 684,00 764,00 834,00 940,00 
 108,00 212,00 289,00 393,00 492,00 582,00 717,00 765,00 845,00 946,00 
 116,00 221,00 330,00 416,00 520,00 588,00 727,00 772,00 846,00 955,00 
 117,00 252,00 337,00 428,00 538,00 602,00 744,00 779,00 859,00 983,00 
 170,00 253,00 368,00 444,00 546,00 647,00 751,00 817,00 924,00 1000,00 
 
Questão 4: 
Q4 fi Fi fri% Fri% Xi fi*xi fi log Xi fi/xi lXi-X_l*fi fi*(Xi-X-)² 
0,00 l-- 16,70 4 4 10,00 10,00 8,35 33,40 3,69 0,48 200,40 10040,04 
16,70 l-- 33,40 5 9 12,50 22,50 25,05 125,25 6,99 0,20 167,00 5577,80 
33,40 l-- 50,10 7 16 17,50 40,00 41,75 292,25 11,34 0,17 116,90 1952,23 
50,10 l-- 66,80 4 20 10,00 50,00 58,45 233,80 7,07 0,07 0,00 0,00 
66,80 l-- 83,50 11 31 27,50 77,50 75,15 826,65 20,64 0,15 183,70 3067,79 
83,50 l-- 100,20 9 40 22,50 100,00 91,85 826,65 17,67 0,10 300,60 10040,04 
Σ 40 --- 100,00 --- --- 2338,00 67,40 1,17 968,60 30677,90 
 h= 16,70 
 
Mo= 79,79 
 
Q3= 81,98 
 
30,00 
 Média= 58,45 
 
DM= 24,22 
 
D7= 78,95 
 
28,00 
 Mg= 48,42 48,98 k= 1,69 S²= 786,61 
 
C51= 67,41 
 
20,40 
 Mh= 34,19 
 
S= 28,05 
 Md= 66,80 
 
CV= 47,99 
 
 
 0,0 17,9 32,5 43,3 51,0 67,6 73,1 77,8 90,1 93,5 
 5,9 19,5 37,0 45,4 51,1 68,6 74,6 81,2 90,7 95,9 
 12,7 22,5 37,7 47,7 52,8 69,2 75,8 82,2 92,6 99,0 
 14,6 31,4 37,9 49,4 56,0 72,5 77,4 88,3 93,1 100,0 
 
Questão 5: 
Aluminios fi Fi fri% Fri% Xi fi * Xi fi*logXi fi/Xi l(Xi-X_)l*fi fi*(Xi-X_)² 
13,30 l- 105,10 7 7 17,5000 17,50 59,20 414,40 12,4063 0,1182 1445,8500 298640,3175 
105,10 l- 196,90 7 14 17,5000 35,00 151,00 1057,00 15,2528 0,0464 803,2500 92172,9375 
196,90 l- 288,70 10 24 25,0000 60,00 242,80 2428,00 23,8525 0,0412 229,5000 5267,0250 
288,70 l- 380,50 6 30 15,0000 75,00 334,60 2007,60 15,1472 0,0179 413,1000 28441,9350 
380,50 l- 472,30 5 35 12,5000 87,50 426,40 2132,00 13,1491 0,0117 803,2500 129042,1125 
472,30 l- 564,10 5 40 12,5000 100,00 518,20 2591,00 13,5725 0,0096 1262,2500 318655,0125 
Total 40 --- 100,00 --- --- 10630,00 93,3804 0,2450 4957,2000 872219,3400 
 h= 91,80 
 
Mo= 236,2429 
 
Q1= 144,4429 
 
10,00 
 Media= 265,7500 
 
DM= 123,9300 
 
D4= 215,2600 
 
16,00 
 Mg= 216,0280 
 
S²= 22364,5985 
 
C75= 380,5000 
 
30,00 
 Mh= 163,2653061 
 
S= 149,5480 
 Md= 251,9800 
 
CV= 56,2739 
 
Questão 6: 
Aço (mm²) fi Fi fri% Fri% Xi fi * Xi fi*logXi fi/Xi l(Xi-X_)l*fi fi*(Xi-X_)² 
2,19 l- 14,08 9 9 22,50 22,50 8,1350 73,2150 8,1932 1,1063 246,1230 6730,7257 
14,08 l- 25,97 5 14 12,50 35,00 20,0250 100,1250 6,5079 0,2497 77,2850 1194,5942 
25,97 l- 37,86 8 22 20,00 55,00 31,9150 255,3200 12,0320 0,2507 28,5360 101,7879 
37,86 l- 49,75 7 29 17,50 72,50 43,8050 306,6350 11,4907 0,1598 58,2610 484,9063 
49,75 l- 61,64 5 34 12,50 85,00 55,6950 278,4750 8,7291 0,0898 101,0650 2042,8268 
61,64 l-l 73,53 6 40 15,00 100,00 67,5850 405,5100 10,9791 0,0888 192,6180 6183,6157 
Total 40 --- 100,00 --- --- 1419,2800 57,9320 1,9451 703,8880 16738,4566 
h= 11,89 
 
Moda 
= 10,4215 
 
Q1 = 16,46 
 Media = 35,4820 
 
DM = 17,5972 
 
D4 = 28,94 
 Mg= 28,0737 
 
S² = 429,1912 
 
C75 = 52,13 
 Mh= 20,5645 
 
S = 20,7169 
 Mediana = 34,8875 
 
CV = 58,3871 
 
Questão 7: 
Renda Diária (R$) fi Fi fri% Fri% Xi fi * Xi fi*logXi fi/Xi l(Xi-X_)l*fi fi*(Xi-X_)² 
50,0 l- 100,0 5 5 10,0 10,0 75,0000 375,00 9,3753 0,0667 675,0000 91125,0000 
100,0 l- 150,06 11 12,0 22,0 125,0000 750,00 12,5815 0,0480 510,0000 43350,0000 
150,0 l- 200,0 13 24 26,0 48,0 175,0000 2275,00 29,1595 0,0743 455,0000 15925,0000 
200,0 l- 250,0 9 33 18,0 66,0 225,0000 2025,00 21,1696 0,0400 135,0000 2025,0000 
250,0 l- 300,0 9 42 18,0 84,0 275,0000 2475,00 21,9540 0,0327 585,0000 38025,0000 
300,0 l-l 350,0 8 50 16,0 100,0 325,0000 2600,00 20,0951 0,0246 920,0000 105800,0000 
Total 50 --- 100,0 --- --- 10500,0 114,3 0,3 3280,0 296250,0 
 h= 50,0 
 
Mo = 181,8182 
 
Q1 = 155,7692 
 Media = 210,0000 
 
DM = 65,6000 
 
D7 = 261,1111 
 Mg= 193,5085 
 
S² = 6045,9184 
 
C51 = 208,3333 
 Mh= 174,6420 
 
S = 77,7555 
 Md = 205,5556 
 
CV = 37,0264 
 
Questão 8: 
Consumo Mensal (KWH) fi Fi fri% Fri% Xi fi * Xi fi*logXi fi/Xi l(Xi-X_)l*fi fi*(Xi-X_)² 
8,0 l- 30,0 5 5 10,0 10,0 19,0000 95,0000 6,3938 0,2632 15,0000 45,0000 
30,0 l- 52,0 3 8 6,0 16,0 41,0000 123,0000 4,8384 0,0732 57,0000 1083,0000 
52,0 l- 74,0 10 18 20,0 36,0 63,0000 630,0000 17,9934 0,1587 410,0000 16810,0000 
74,0 l- 96,0 19 37 38,0 74,0 85,0000 1615,0000 36,6590 0,2235 1197,0000 75411,0000 
96,0 l- 118,0 3 40 6,0 80,0 107,0000 321,0000 6,0882 0,0280 255,0000 21675,0000 
118,0 l- 140,0 6 46 12,0 92,0 129,0000 774,0000 12,6635 0,0465 642,0000 68694,0000 
140,0 l- 162,0 4 50 8,0 100,0 151,0000 604,0000 8,7159 0,0265 516,0000 66564,0000 
Total 50 --- 100,0 --- --- 4162,0000 93,3522 0,8196 3092,0000 250282,0000 
 h= 22,0 
 
Mo = 81,9200 
 
Q3 = 99,6667 
 Media = 83,2400 
 
DM = 61,8400 
 
D7 = 93,6842 
 Mg= 73,6282 
 
S² = 5107,7959 
 
C51 = 82,6842 
 Mh= 61,0054 
 
S = 71,4688 
 Md = 82,1053 
 
CV = 85,8587 
 
Questão 9: 
Vendas fi Fi fri% Fri% Xi fi * Xi fi*logXi fi/Xi l(Xi-X_)l*fi fi*(Xi-X_)² 
18,0 l- 181,0 8 8 20,0 20,0 99,5000 796,0000 15,9826 0,0804 3031,8000 1148976,4050 
181,0 l- 344,0 10 18 25,0 45,0 262,5000 2625,0000 24,1913 0,0381 2159,7500 466452,0063 
344,0 l- 507,0 4 22 10,0 55,0 425,5000 1702,0000 10,5156 0,0094 211,9000 11225,4025 
507,0 l- 670,0 4 26 10,0 65,0 588,5000 2354,0000 11,0790 0,0068 440,1000 48422,0025 
670,0 l- 833,0 7 33 17,5 82,5 751,5000 5260,5000 20,1315 0,0093 1911,1750 521798,5544 
833,0 l-l 996,0 7 40 17,5 100,0 914,5000 6401,5000 20,7283 0,0077 3052,1750 1330824,6044 
Total 40 --- 100,0 --- --- 19139,0000 102,6283 0,1517 10806,9000 3527698,9751 
 h= 163,0 
 
Mo = 221,7500 
 
Q1 = 213,6000 
 Media= 478,4750 
 
DM = 270,1725 
 
D7 = 716,5714 
 Mg= 367,8811 
 
S² = 90453,8199 
 
C51 = 441,8000 
 Mh= 263,6783 
 
S = 300,7554 
 Md= 425,5000 
 
CV= 62,8571 
 
Questão 10: 
Temperatura fi Fi fri% Fri% Xi fi * Xi fi*logXi fi/Xi l(Xi-X_)l*fi fi*(Xi-X_)² 
26,50 l- 28,00 9 9 17,31 17,31 27,2500 245,2500 12,9183 0,3303 37,9035 159,6306 
28,00 l- 29,50 5 14 9,62 26,92 28,7500 143,7500 7,2932 0,1739 13,5575 36,7612 
29,50 l- 31,00 7 21 13,46 40,38 30,2500 211,7500 10,3651 0,2314 8,4805 10,2741 
31,00 l- 32,50 8 29 15,38 55,77 31,7500 254,0000 12,0139 0,2520 2,3080 0,6659 
32,50 l- 34,00 12 41 23,08 78,85 33,2500 399,0000 18,2615 0,3609 21,4620 38,3848 
34,00 l- 35,50 11 52 21,15 100,00 34,7500 382,2500 16,9505 0,3165 36,1735 118,9566 
Total 52 --- 100,00 --- --- 1636,0000 77,8025 1,6650 119,8850 364,6732 
 h= 1,50 
 
Mo= 33,7000 
 
Q3 = 33,7500 
 Media= 31,4615 
 
DM = 2,3055 
 
D6 = 32,7750 
 Mg= 31,3474 
 
S² = 7,1505 
 
C62 = 32,9050 
 Mh= 31,2312 
 
S = 2,6740 
 Md= 31,9375 
 
CV = 8,4993