[1] 100.93730855 90.78737290 31.43347250 70.04161421 114.72725633
[6] 119.48971504 39.59619123 81.81619913 18.66636591 87.17608029
[11] 155.08897515 137.78907540 88.08832220 149.37223517 137.06950642
[16] 104.46736332 52.25280719 90.24248077 146.27606310 124.14892624
[21] 70.18446816 -9.26434191 66.25670311 -5.95305960 36.74009892
[26] 81.31692224 65.62222848 56.39205866 94.91194969 87.31097349
[31] 7.31297728 96.10269670 148.42831703 109.24629800 31.00282108
[36] 28.22428188 118.10436143 12.04566231 83.77279952 67.42185057
[41] 154.32756997 61.87275600 58.56687325 141.72369515 51.61740066
[46] 98.55923323 111.62625763 84.93956592 66.11927084 132.76138181
[51] 79.96812265 83.27217175 168.39769766 206.88835518 125.29096323
[56] 139.31711921 54.88940279 126.64484962 67.70528732 114.54937442
[61] 38.12027656 77.19118624 58.48386726 117.00578218 153.31881978
[66] 160.80629190 136.78453288 75.93956913 128.13723814 37.68401441
[71] 119.04611063 28.47863736 47.57772476 89.07482247 25.50318816
[76] 158.63531406 26.00864892 78.48060920 47.41806790 176.12931720
[81] 129.64140273 88.86692455 135.64471381 135.83004169 122.01209322
[86] 107.94153107 132.98820692 211.02598315 40.80274630 96.30220828
[91] 79.18226626 90.42588281 103.47723907 157.76741590 129.74786735
[96] 29.01774458 19.66613773 144.64629498 107.40839776 161.35141951
[101] 61.90978304 120.96877029 48.00283177 135.57869830 68.33934925
[106] 128.15873322 133.04933429 17.09745713 151.40839885 156.39768070
[111] 35.99226983 156.44341137 76.79327364 84.21198952 146.21465734
[116] 103.85723620 151.99618026 137.09431034 162.77724291 147.54594832
[121] 75.93171964 110.14408890 98.41301281 40.22098498 131.18406184
[126] 54.25977582 112.43790039 46.86886034 81.80088764 39.65025733
[131] 171.46063907 131.67179455 0.15921912 65.90839135 76.99722603
[136] 50.84654029 124.76658564 136.29087501 133.36493659 147.73932182
[141] 16.23339104 39.74073038 1.83737554 173.53761549 118.62361693
[146] 153.29396670 126.53249342 105.09917229 166.88912329 104.36173842
[151] 80.44478963 87.50662577 157.75523729 56.76363801 56.66608288
[156] -16.05085152 130.44150845 157.50030241 40.02011641 20.99996227
[161] 132.65830968 72.52957574 126.05272627 65.02984668 78.05453426
[166] 66.13403519 147.95705974 26.59133353 109.18819463 28.24264087
[171] 43.13000509 79.26773366 107.19671441 153.10121653 71.46030486
[176] 163.85906882 111.41446603 84.55934677 147.99145653 127.44111874
[181] 121.27565469 132.17500176 31.98469282 90.07469468 130.96513384
[186] 203.41048025 84.73576229 114.06228061 134.56586684 102.31807191
[191] 105.65146808 149.76659371 65.94243193 36.14713767 26.56511251
[196] 84.32629667 14.81702537 32.47426719 44.89531614 45.02284927
[201] 160.77568881 116.54382426 169.51375596 143.60234925 45.95914887
[206] 124.79107957 152.63137781 36.26750249 90.31666358 35.24581787
[211] 107.09401423 163.08575260 78.42498360 8.86437052 117.62719794
[216] 32.57742793 135.38441590 79.45545316 77.69774100 47.94218492
[221] 83.53876419 85.85891879 121.62145627 84.61964525 97.16818461
[226] 136.67577101 104.86558098 181.54458683 128.03053495 166.47823822
[231] 86.05882522 36.66342279 87.54258030 100.89942073 118.85363636
[236] 139.80042788 57.96612915 -10.27358754 43.59720045 32.93450206
[241] 180.25570214 137.22118642 143.10411030 119.75779077 125.45593482
[246] 93.87249371 104.62923236 82.10600428 82.01723878 151.42853604
[251] 153.89462962 146.58906076 26.96030665 54.69622119 65.98260843
[256] 153.15830184 65.37934239 43.31858674 45.26922831 49.35481906
[261] 120.51386629 123.88702210 -16.49397725 100.81277326 149.01767616
[266] 140.31741324 105.98004444 -21.83078022 101.55112381 83.21266510
[271] 86.81119190 82.20737696 75.94226009 111.13677339 221.49551593
[276] 174.81490594 64.13958986 76.64730499 133.14617264 215.00884455
[281] 116.37550706 103.19317408 43.02195300 159.02051018 102.06942385
[286] 39.32032183 103.65978883 87.13377028 113.34032055 169.38621629
[291] 109.65398175 129.61583113 58.50127365 119.62866408 119.24338053
[296] 152.55223329 157.78987423 48.27810205 87.27659671 163.68421330
[301] 175.12723195 129.52047336 68.46572743 139.61747686 106.26922851
[306] 116.13774856 77.72083953 138.34219672 29.82484891 41.19766102
[311] 125.57982346 165.83826319 219.64564735 96.61152958 89.81074668
[316] 199.82172261 177.16088972 38.58311869 232.22439961 137.85068541
[321] 152.76725961 147.89724477 141.69395288 91.53622150 79.77831785
[326] 114.78007869 88.40627464 77.59608842 101.11553983 102.22336486
[331] 124.03605826 131.78099276 -0.03711965 65.46722481 93.46774053
[336] 82.78741085 97.37935880 104.80619603 113.32035266 127.73967376
[341] 161.77229393 114.25666907 77.06035361 131.17390109 63.80024542
[346] 180.97093517 69.16632949 119.22705287 205.72606564 48.57163169
[351] 55.66060172 163.55730007 19.74572794 156.11366915 207.92193209
[356] 121.41233065 160.05893452 151.58450581 132.69371264 200.60408866
[361] 154.73149209 136.32046770 30.01714317 35.61024184 51.57922612
[366] 13.16571211 141.58486790 62.05234457 207.75385005 78.83705599
[371] 99.71750317 120.01808643 81.71610990 78.54280824 112.23485634
[376] 210.98881244 115.71349040 71.81074627 25.71519208 120.76492965
[381] 73.59681587 82.47646913 136.53109686 72.16879175 27.51197319
[386] 47.40017859 65.85806906 69.35294107 194.53900175 92.72947332
[391] 68.02881397 79.44119774 117.13959392 43.33766227 103.30351513
[396] 101.89998830 146.05323738 206.74828192 70.00865342 162.22232293
[401] 96.02714914 159.08757749 209.30720313 120.30874654 63.08204477
[406] 2.17566485 2.49771492 52.95010922 159.88933843 68.78803048
[411] 93.35651724 99.13895389 77.01853589 173.64683953 208.46598063
[416] -50.07156532 11.40072085 81.75803886 118.72668903 38.29610367
[421] 123.74467110 161.65287285 70.34356716 137.61312197 130.60227534
[426] 88.56713174 64.75803251 161.47580236 175.92575649 167.25470902
[431] 93.81542355 146.69512268 100.97484228 141.54260549 84.77526660
[436] 97.03593614 150.36983487 31.11024570 49.78986365 98.83598475
[441] 177.33736369 62.03183745 150.33963287 113.71074582 95.98088177
[446] 54.82237523 123.65725515 169.42444890 101.73730469 35.37074860
[451] 158.19837525 23.83077015 -25.91675268 64.62353847 85.62835586
[456] 78.23458443 82.84606146 98.03445580 144.34829939 82.00257996
[461] 63.55228647 187.58728096 95.69807049 155.31815079 99.04110814
[466] 25.32699108 235.03183115 62.81527889 153.25974905 98.39591342
[471] 73.00201553 3.71782162 150.39156881 86.03826016 37.52170724
[476] 162.42455639 90.38933117 145.59881155 -7.91348400 164.48052662
[481] 78.59450172 87.24985535 166.35791194 141.93450603 26.74996614
[486] 69.18736511 105.30529197 7.79916211 19.17885731 111.38383521
[491] 146.06083510 83.43982803 164.36170155 102.86304012 -10.19665626
[496] 73.85448259 154.03926551 87.84293312 54.52767189 56.58502463
[501] 143.47375225 65.99952011 108.66072694 92.02809805 139.67497163
[506] 184.71752457 161.99843432 101.47183716 182.86072495 156.56115701
[511] 29.87946839 107.83852306 143.37542982 98.33824214 147.70322782
[516] 156.50483626 119.68486560 118.84041640 87.41285465 125.20474454
[521] 33.50982643 94.08502737 68.33757667 133.88456724 85.10591176
[526] 131.39611236 183.92153640 -20.00012703 32.50785575 160.10039479
[531] 164.69213597 97.02028269 65.74688274 27.32803478 164.70632806
[536] 158.80845447 143.20225391 -14.83662617 30.40949940 30.70616275
[541] 46.34765780 52.92872484 70.67828451 151.73606100 122.94811033
[546] 40.32774640 139.59446358 11.38475446 70.61387890 35.88148437
[551] 84.39326695 65.06123497 -32.19248839 141.25111884 115.34631566
[556] 97.09802709 146.32847054 89.06540697 149.65667487 3.83328288
[561] 47.36424078 144.51988810 277.05701388 137.07553713 89.62643730
[566] 108.99692271 171.31824247 77.84166053 118.35949933 134.79108481
[571] 146.67223643 174.59445413 157.97614951 111.33979785 35.22674076
[576] 96.86106542 149.66414684 49.70345300 62.45075262 187.20081912
[581] 40.61999543 79.15147911 21.50899203 85.97629824 70.73365181
[586] 133.01595988 68.12437255 73.04891834 147.57601168 94.72100771
[591] 81.29653636 91.18837096 113.82416540 111.81662963 203.08370797
[596] 35.49700071 128.55947237 189.26951134 110.64701215 144.23460730
[601] 54.90148678 97.26250210 32.16226445 115.86152886 169.78595597
[606] 39.43880916 89.79291696 22.37743370 125.90248343 79.05798484
[611] 14.52733922 224.15813357 124.90168675 66.30658974 55.65093022
[616] 13.43113246 130.22745607 56.43624609 136.26708232 98.46340099
[621] 94.13888128 104.91114693 66.15713891 97.53768225 71.96401200
[626] 219.95774326 95.50639492 58.91757911 85.65191192 106.56394370
[631] 46.89580248 136.67905179 116.13460992 82.55101143 164.17628321
[636] 49.27559756 74.49678629 91.64151269 84.86661072 201.32352362
[641] 145.04528192 106.77145202 89.93555229 59.65816295 132.20620619
[646] 83.16704397 13.41482444 113.09603313 54.16512009 71.57177624
[651] 56.70897791 141.27469559 59.99338579 148.79150434 235.00377654
[656] 93.23052016 94.69844180 32.79680974 122.15609143 148.05588708
[661] 87.92820917 104.14774456 81.91376211 116.69300999 113.28047105
[666] 250.64528733 82.76349312 153.12787266 63.51574630 102.82738605
[671] 123.39148560 81.36773747 110.50808438 164.48041528 18.65802251
[676] 60.82317452 125.54565517 160.88130280 115.25546238 110.51468167
[681] 123.44329828 4.78287139 161.92011423 119.54994457 98.44005416
[686] 19.05997391 122.56331391 65.45783182 170.27228110 14.93286561
[691] 109.61227986 64.85216193 59.57220683 68.09006292 186.86727140
[696] -13.02391316 19.37639531 132.68700994 145.14403643 137.73042439
[701] 88.65946156 65.20156862 125.33236787 130.81171468 16.65603627
[706] 83.18728871 125.35899284 15.13046492 89.65363880 80.07014859
[711] 40.56900863 122.62827021 110.37948520 39.49388119 138.37075271
[716] 70.04861544 21.95136136 50.21679785 154.66255042 145.85714430
[721] 61.34753224 76.20820912 43.46484080 78.55822842 58.02081751
[726] 69.95066635 61.30546109 55.37538244 98.21340765 84.79109488
[731] -50.60818918 -0.42615289 97.68142953 82.02314677 90.24891691
[736] 24.27649323 55.39834764 56.86467543 127.59770740 90.58830433
[741] 83.74266282 73.15307754 81.42612936 136.14035118 160.28459417
[746] 159.20765628 133.55952177 158.77510367 109.42632364 124.95317984
[751] 2.61908443 121.03686231 158.67381249 27.68842215 81.66243970
[756] 69.61018826 115.99356887 154.99238361 79.69816862 220.53732134
[761] 157.94499424 116.91947958 122.80886720 84.29776668 170.21720101
[766] 79.48650255 95.59487419 116.24377974 159.25499001 87.22457133
[771] 144.22239604 75.57194652 63.63119134 40.58723635 73.10287920
[776] 105.96756087 165.90890477 172.15402788 112.45131058 140.78511634
[781] 63.26960968 112.90766390 57.35696156 110.78243793 64.53948940
[786] 135.54327616 77.63140706 83.08508479 125.86167111 104.93517972
[791] 137.18428079 86.07249293 126.95358403 95.58302652 62.71212459
[796] 21.99607744 154.14782627 -17.05280013 110.31526330 138.23712856
[801] -6.25342905 126.05893332 97.67885500 42.52641395 131.46691539
[806] 63.67642620 80.67913388 66.41428051 145.01930952 144.34208453
[811] 119.51390559 53.62442549 137.29196144 124.74120783 98.90342691
[816] 129.40111631 137.82455370 75.29868637 63.33421857 99.94898030
[821] 140.29128484 155.46546909 84.51602589 54.57108759 113.15130638
[826] 98.95410962 89.38287462 48.44480401 106.97553698 108.31089923
[831] 50.76701755 101.13170354 139.26650163 41.04052379 195.53953888
[836] 73.09992525 144.21382145 107.36548184 49.57863186 141.90944961
[841] 41.58804313 122.71590665 110.62864338 72.34568263 101.17150126
[846] 132.40894452 12.86026324 129.75813305 56.07354935 132.22187856
[851] 68.54507487 95.08999052 134.21088496 30.76569845 177.74727930
[856] 59.28293291 57.81844571 151.24637129 105.78516882 112.07470199
[861] 30.45919292 176.30304223 102.32581184 161.99911798 115.42863177
[866] 139.28138023 155.87393524 99.75088638 91.07908949 134.81145345
[871] 126.08986042 77.60867049 120.27003020 63.15177877 112.78740072
[876] 85.75332475 98.44393375 75.70705565 93.24559579 25.96406386
[881] 162.81845628 110.45208250 115.65783948 153.75741193 85.66874127
[886] 98.40112863 62.86333017 204.26100961 142.74452052 150.02229981
[891] 40.79410450 22.94487224 89.41334996 108.51762850 65.46113128
[896] 184.88603695 96.36550187 64.11955719 79.17427808 209.67933805
[901] 127.11739129 151.18338045 140.64130544 165.05135387 128.39782055
[906] 93.99642789 75.39986469 110.03859877 108.23996494 134.68288481
[911] 106.66621267 63.02684207 80.12405924 112.85793197 85.99130404
[916] 150.39837961 157.76098120 89.86025254 83.92952265 18.94730415
[921] 128.40526295 133.56401236 173.01297609 18.11403129 164.92505411
[926] 92.31500856 178.95744228 202.76175928 164.22433254 120.87016586
[931] 157.99268036 124.57951279 155.10043589 128.42852151 81.80414574
[936] 106.84781854 136.21377136 176.99908030 149.34961674 52.69890010
[941] 69.36596579 164.34432952 72.16749200 98.85111389 166.23705613
[946] 113.19488345 142.06695095 86.79312555 144.33846460 111.27428778
[951] 127.24163623 158.81253634 84.32123791 125.26883443 176.98506493
[956] 174.55013553 112.18447423 79.23428368 -1.75863811 67.83210511
[961] 102.69107405 80.52190580 193.89127767 27.11966366 136.19276892
[966] 39.09618692 84.71205651 101.21988583 117.61330506 141.18948778
[971] 129.88932805 164.78187322 71.09669104 108.64874902 70.94018770
[976] 60.87047018 16.65853979 64.32633758 74.66620861 65.24080279
[981] 127.08039056 70.94613518 121.54160255 133.58505948 78.32463472
[986] 60.95082856 120.81490912 58.91897002 110.55379452 137.74115849
[991] 189.00548763 133.29738410 99.46330902 39.94726968 67.83011078
[996] 139.86461552 126.41241372 114.18348694 99.39303476 90.40431113Estatística e Probabilidade
Aula 03 - Coleta, organização e apresentação de dados
Filosofia de publicação (Selo DC)
Livro de Apoio
Usaremos Batista (2023):
Motivação inicial
- Dados (Primeiro tipo)
Motivação inicial
- Dados (Segundo tipo)
[1] -50.60818918 -50.07156532 -32.19248839 -25.91675268 -21.83078022
[6] -20.00012703 -17.05280013 -16.49397725 -16.05085152 -14.83662617
[11] -13.02391316 -10.27358754 -10.19665626 -9.26434191 -7.91348400
[16] -6.25342905 -5.95305960 -1.75863811 -0.42615289 -0.03711965
[21] 0.15921912 1.83737554 2.17566485 2.49771492 2.61908443
[26] 3.71782162 3.83328288 4.78287139 7.31297728 7.79916211
[31] 8.86437052 11.38475446 11.40072085 12.04566231 12.86026324
[36] 13.16571211 13.41482444 13.43113246 14.52733922 14.81702537
[41] 14.93286561 15.13046492 16.23339104 16.65603627 16.65853979
[46] 17.09745713 18.11403129 18.65802251 18.66636591 18.94730415
[51] 19.05997391 19.17885731 19.37639531 19.66613773 19.74572794
[56] 20.99996227 21.50899203 21.95136136 21.99607744 22.37743370
[61] 22.94487224 23.83077015 24.27649323 25.32699108 25.50318816
[66] 25.71519208 25.96406386 26.00864892 26.56511251 26.59133353
[71] 26.74996614 26.96030665 27.11966366 27.32803478 27.51197319
[76] 27.68842215 28.22428188 28.24264087 28.47863736 29.01774458
[81] 29.82484891 29.87946839 30.01714317 30.40949940 30.45919292
[86] 30.70616275 30.76569845 31.00282108 31.11024570 31.43347250
[91] 31.98469282 32.16226445 32.47426719 32.50785575 32.57742793
[96] 32.79680974 32.93450206 33.50982643 35.22674076 35.24581787
[101] 35.37074860 35.49700071 35.61024184 35.88148437 35.99226983
[106] 36.14713767 36.26750249 36.66342279 36.74009892 37.52170724
[111] 37.68401441 38.12027656 38.29610367 38.58311869 39.09618692
[116] 39.32032183 39.43880916 39.49388119 39.59619123 39.65025733
[121] 39.74073038 39.94726968 40.02011641 40.22098498 40.32774640
[126] 40.56900863 40.58723635 40.61999543 40.79410450 40.80274630
[131] 41.04052379 41.19766102 41.58804313 42.52641395 43.02195300
[136] 43.13000509 43.31858674 43.33766227 43.46484080 43.59720045
[141] 44.89531614 45.02284927 45.26922831 45.95914887 46.34765780
[146] 46.86886034 46.89580248 47.36424078 47.40017859 47.41806790
[151] 47.57772476 47.94218492 48.00283177 48.27810205 48.44480401
[156] 48.57163169 49.27559756 49.35481906 49.57863186 49.70345300
[161] 49.78986365 50.21679785 50.76701755 50.84654029 51.57922612
[166] 51.61740066 52.25280719 52.69890010 52.92872484 52.95010922
[171] 53.62442549 54.16512009 54.25977582 54.52767189 54.57108759
[176] 54.69622119 54.82237523 54.88940279 54.90148678 55.37538244
[181] 55.39834764 55.65093022 55.66060172 56.07354935 56.39205866
[186] 56.43624609 56.58502463 56.66608288 56.70897791 56.76363801
[191] 56.86467543 57.35696156 57.81844571 57.96612915 58.02081751
[196] 58.48386726 58.50127365 58.56687325 58.91757911 58.91897002
[201] 59.28293291 59.57220683 59.65816295 59.99338579 60.82317452
[206] 60.87047018 60.95082856 61.30546109 61.34753224 61.87275600
[211] 61.90978304 62.03183745 62.05234457 62.45075262 62.71212459
[216] 62.81527889 62.86333017 63.02684207 63.08204477 63.15177877
[221] 63.26960968 63.33421857 63.51574630 63.55228647 63.63119134
[226] 63.67642620 63.80024542 64.11955719 64.13958986 64.32633758
[231] 64.53948940 64.62353847 64.75803251 64.85216193 65.02984668
[236] 65.06123497 65.20156862 65.24080279 65.37934239 65.45783182
[241] 65.46113128 65.46722481 65.62222848 65.74688274 65.85806906
[246] 65.90839135 65.94243193 65.98260843 65.99952011 66.11927084
[251] 66.13403519 66.15713891 66.25670311 66.30658974 66.41428051
[256] 67.42185057 67.70528732 67.83011078 67.83210511 68.02881397
[261] 68.09006292 68.12437255 68.33757667 68.33934925 68.46572743
[266] 68.54507487 68.78803048 69.16632949 69.18736511 69.35294107
[271] 69.36596579 69.61018826 69.95066635 70.00865342 70.04161421
[276] 70.04861544 70.18446816 70.34356716 70.61387890 70.67828451
[281] 70.73365181 70.94018770 70.94613518 71.09669104 71.46030486
[286] 71.57177624 71.81074627 71.96401200 72.16749200 72.16879175
[291] 72.34568263 72.52957574 73.00201553 73.04891834 73.09992525
[296] 73.10287920 73.15307754 73.59681587 73.85448259 74.49678629
[301] 74.66620861 75.29868637 75.39986469 75.57194652 75.70705565
[306] 75.93171964 75.93956913 75.94226009 76.20820912 76.64730499
[311] 76.79327364 76.99722603 77.01853589 77.06035361 77.19118624
[316] 77.59608842 77.60867049 77.63140706 77.69774100 77.72083953
[321] 77.84166053 78.05453426 78.23458443 78.32463472 78.42498360
[326] 78.48060920 78.54280824 78.55822842 78.59450172 78.83705599
[331] 79.05798484 79.15147911 79.17427808 79.18226626 79.23428368
[336] 79.26773366 79.44119774 79.45545316 79.48650255 79.69816862
[341] 79.77831785 79.96812265 80.07014859 80.12405924 80.44478963
[346] 80.52190580 80.67913388 81.29653636 81.31692224 81.36773747
[351] 81.42612936 81.66243970 81.71610990 81.75803886 81.80088764
[356] 81.80414574 81.81619913 81.91376211 82.00257996 82.01723878
[361] 82.02314677 82.10600428 82.20737696 82.47646913 82.55101143
[366] 82.76349312 82.78741085 82.84606146 83.08508479 83.16704397
[371] 83.18728871 83.21266510 83.27217175 83.43982803 83.53876419
[376] 83.74266282 83.77279952 83.92952265 84.21198952 84.29776668
[381] 84.32123791 84.32629667 84.39326695 84.51602589 84.55934677
[386] 84.61964525 84.71205651 84.73576229 84.77526660 84.79109488
[391] 84.86661072 84.93956592 85.10591176 85.62835586 85.65191192
[396] 85.66874127 85.75332475 85.85891879 85.97629824 85.99130404
[401] 86.03826016 86.05882522 86.07249293 86.79312555 86.81119190
[406] 87.13377028 87.17608029 87.22457133 87.24985535 87.27659671
[411] 87.31097349 87.41285465 87.50662577 87.54258030 87.84293312
[416] 87.92820917 88.08832220 88.40627464 88.56713174 88.65946156
[421] 88.86692455 89.06540697 89.07482247 89.38287462 89.41334996
[426] 89.62643730 89.65363880 89.79291696 89.81074668 89.86025254
[431] 89.93555229 90.07469468 90.24248077 90.24891691 90.31666358
[436] 90.38933117 90.40431113 90.42588281 90.58830433 90.78737290
[441] 91.07908949 91.18837096 91.53622150 91.64151269 92.02809805
[446] 92.31500856 92.72947332 93.23052016 93.24559579 93.35651724
[451] 93.46774053 93.81542355 93.87249371 93.99642789 94.08502737
[456] 94.13888128 94.69844180 94.72100771 94.91194969 95.08999052
[461] 95.50639492 95.58302652 95.59487419 95.69807049 95.98088177
[466] 96.02714914 96.10269670 96.30220828 96.36550187 96.61152958
[471] 96.86106542 97.02028269 97.03593614 97.09802709 97.16818461
[476] 97.26250210 97.37935880 97.53768225 97.67885500 97.68142953
[481] 98.03445580 98.21340765 98.33824214 98.39591342 98.40112863
[486] 98.41301281 98.44005416 98.44393375 98.46340099 98.55923323
[491] 98.83598475 98.85111389 98.90342691 98.95410962 99.04110814
[496] 99.13895389 99.39303476 99.46330902 99.71750317 99.75088638
[501] 99.94898030 100.81277326 100.89942073 100.93730855 100.97484228
[506] 101.11553983 101.13170354 101.17150126 101.21988583 101.47183716
[511] 101.55112381 101.73730469 101.89998830 102.06942385 102.22336486
[516] 102.31807191 102.32581184 102.69107405 102.82738605 102.86304012
[521] 103.19317408 103.30351513 103.47723907 103.65978883 103.85723620
[526] 104.14774456 104.36173842 104.46736332 104.62923236 104.80619603
[531] 104.86558098 104.91114693 104.93517972 105.09917229 105.30529197
[536] 105.65146808 105.78516882 105.96756087 105.98004444 106.26922851
[541] 106.56394370 106.66621267 106.77145202 106.84781854 106.97553698
[546] 107.09401423 107.19671441 107.36548184 107.40839776 107.83852306
[551] 107.94153107 108.23996494 108.31089923 108.51762850 108.64874902
[556] 108.66072694 108.99692271 109.18819463 109.24629800 109.42632364
[561] 109.61227986 109.65398175 110.03859877 110.14408890 110.31526330
[566] 110.37948520 110.45208250 110.50808438 110.51468167 110.55379452
[571] 110.62864338 110.64701215 110.78243793 111.13677339 111.27428778
[576] 111.33979785 111.38383521 111.41446603 111.62625763 111.81662963
[581] 112.07470199 112.18447423 112.23485634 112.43790039 112.45131058
[586] 112.78740072 112.85793197 112.90766390 113.09603313 113.15130638
[591] 113.19488345 113.28047105 113.32035266 113.34032055 113.71074582
[596] 113.82416540 114.06228061 114.18348694 114.25666907 114.54937442
[601] 114.72725633 114.78007869 115.25546238 115.34631566 115.42863177
[606] 115.65783948 115.71349040 115.86152886 115.99356887 116.13460992
[611] 116.13774856 116.24377974 116.37550706 116.54382426 116.69300999
[616] 116.91947958 117.00578218 117.13959392 117.61330506 117.62719794
[621] 118.10436143 118.35949933 118.62361693 118.72668903 118.84041640
[626] 118.85363636 119.04611063 119.22705287 119.24338053 119.48971504
[631] 119.51390559 119.54994457 119.62866408 119.68486560 119.75779077
[636] 120.01808643 120.27003020 120.30874654 120.51386629 120.76492965
[641] 120.81490912 120.87016586 120.96877029 121.03686231 121.27565469
[646] 121.41233065 121.54160255 121.62145627 122.01209322 122.15609143
[651] 122.56331391 122.62827021 122.71590665 122.80886720 122.94811033
[656] 123.39148560 123.44329828 123.65725515 123.74467110 123.88702210
[661] 124.03605826 124.14892624 124.57951279 124.74120783 124.76658564
[666] 124.79107957 124.90168675 124.95317984 125.20474454 125.26883443
[671] 125.29096323 125.33236787 125.35899284 125.45593482 125.54565517
[676] 125.57982346 125.86167111 125.90248343 126.05272627 126.05893332
[681] 126.08986042 126.41241372 126.53249342 126.64484962 126.95358403
[686] 127.08039056 127.11739129 127.24163623 127.44111874 127.59770740
[691] 127.73967376 128.03053495 128.13723814 128.15873322 128.39782055
[696] 128.40526295 128.42852151 128.55947237 129.40111631 129.52047336
[701] 129.61583113 129.64140273 129.74786735 129.75813305 129.88932805
[706] 130.22745607 130.44150845 130.60227534 130.81171468 130.96513384
[711] 131.17390109 131.18406184 131.39611236 131.46691539 131.67179455
[716] 131.78099276 132.17500176 132.20620619 132.22187856 132.40894452
[721] 132.65830968 132.68700994 132.69371264 132.76138181 132.98820692
[726] 133.01595988 133.04933429 133.14617264 133.29738410 133.36493659
[731] 133.55952177 133.56401236 133.58505948 133.88456724 134.21088496
[736] 134.56586684 134.68288481 134.79108481 134.81145345 135.38441590
[741] 135.54327616 135.57869830 135.64471381 135.83004169 136.14035118
[746] 136.19276892 136.21377136 136.26708232 136.29087501 136.32046770
[751] 136.53109686 136.67577101 136.67905179 136.78453288 137.06950642
[756] 137.07553713 137.09431034 137.18428079 137.22118642 137.29196144
[761] 137.61312197 137.73042439 137.74115849 137.78907540 137.82455370
[766] 137.85068541 138.23712856 138.34219672 138.37075271 139.26650163
[771] 139.28138023 139.31711921 139.59446358 139.61747686 139.67497163
[776] 139.80042788 139.86461552 140.29128484 140.31741324 140.64130544
[781] 140.78511634 141.18948778 141.25111884 141.27469559 141.54260549
[786] 141.58486790 141.69395288 141.72369515 141.90944961 141.93450603
[791] 142.06695095 142.74452052 143.10411030 143.20225391 143.37542982
[796] 143.47375225 143.60234925 144.21382145 144.22239604 144.23460730
[801] 144.33846460 144.34208453 144.34829939 144.51988810 144.64629498
[806] 145.01930952 145.04528192 145.14403643 145.59881155 145.85714430
[811] 146.05323738 146.06083510 146.21465734 146.27606310 146.32847054
[816] 146.58906076 146.67223643 146.69512268 147.54594832 147.57601168
[821] 147.70322782 147.73932182 147.89724477 147.95705974 147.99145653
[826] 148.05588708 148.42831703 148.79150434 149.01767616 149.34961674
[831] 149.37223517 149.65667487 149.66414684 149.76659371 150.02229981
[836] 150.33963287 150.36983487 150.39156881 150.39837961 151.18338045
[841] 151.24637129 151.40839885 151.42853604 151.58450581 151.73606100
[846] 151.99618026 152.55223329 152.63137781 152.76725961 153.10121653
[851] 153.12787266 153.15830184 153.25974905 153.29396670 153.31881978
[856] 153.75741193 153.89462962 154.03926551 154.14782627 154.32756997
[861] 154.66255042 154.73149209 154.99238361 155.08897515 155.10043589
[866] 155.31815079 155.46546909 155.87393524 156.11366915 156.39768070
[871] 156.44341137 156.50483626 156.56115701 157.50030241 157.75523729
[876] 157.76098120 157.76741590 157.78987423 157.94499424 157.97614951
[881] 157.99268036 158.19837525 158.63531406 158.67381249 158.77510367
[886] 158.80845447 158.81253634 159.02051018 159.08757749 159.20765628
[891] 159.25499001 159.88933843 160.05893452 160.10039479 160.28459417
[896] 160.77568881 160.80629190 160.88130280 161.35141951 161.47580236
[901] 161.65287285 161.77229393 161.92011423 161.99843432 161.99911798
[906] 162.22232293 162.42455639 162.77724291 162.81845628 163.08575260
[911] 163.55730007 163.68421330 163.85906882 164.17628321 164.22433254
[916] 164.34432952 164.36170155 164.48041528 164.48052662 164.69213597
[921] 164.70632806 164.78187322 164.92505411 165.05135387 165.83826319
[926] 165.90890477 166.23705613 166.35791194 166.47823822 166.88912329
[931] 167.25470902 168.39769766 169.38621629 169.42444890 169.51375596
[936] 169.78595597 170.21720101 170.27228110 171.31824247 171.46063907
[941] 172.15402788 173.01297609 173.53761549 173.64683953 174.55013553
[946] 174.59445413 174.81490594 175.12723195 175.92575649 176.12931720
[951] 176.30304223 176.98506493 176.99908030 177.16088972 177.33736369
[956] 177.74727930 178.95744228 180.25570214 180.97093517 181.54458683
[961] 182.86072495 183.92153640 184.71752457 184.88603695 186.86727140
[966] 187.20081912 187.58728096 189.00548763 189.26951134 193.89127767
[971] 194.53900175 195.53953888 199.82172261 200.60408866 201.32352362
[976] 202.76175928 203.08370797 203.41048025 204.26100961 205.72606564
[981] 206.74828192 206.88835518 207.75385005 207.92193209 208.46598063
[986] 209.30720313 209.67933805 210.98881244 211.02598315 215.00884455
[991] 219.64564735 219.95774326 220.53732134 221.49551593 224.15813357
[996] 232.22439961 235.00377654 235.03183115 250.64528733 277.05701388Motivação inicial
- Dados (Terceiro tipo)
Table of frequency
Type of variable: continuous
Classes Fi PM Fr Fac1 Fac2 Fp Fac1p Fac2p
1 -62.31 |--- -38.91 2 -50.61 0.00 2 1000 0 0.2 100.0
2 -38.91 |--- -15.51 7 -27.21 0.01 9 998 1 0.9 99.8
3 -15.51 |--- 7.89 21 -3.81 0.02 30 991 2 3.0 99.1
4 7.89 |--- 31.29 59 19.59 0.06 89 970 6 8.9 97.0
5 31.29 |--- 54.69 86 42.99 0.09 175 911 9 17.5 91.1
6 54.69 |--- 78.09 147 66.39 0.15 322 825 15 32.2 82.5
7 78.09 |--- 101.49 188 89.79 0.19 510 678 19 51.0 67.8
8 101.49 |--- 124.89 156 113.19 0.16 666 490 16 66.6 49.0
9 124.89 |--- 148.29 160 136.59 0.16 826 334 16 82.6 33.4
10 148.29 |--- 171.69 114 159.99 0.11 940 174 11 94.0 17.4
11 171.69 |--- 195.09 31 183.39 0.03 971 60 3 97.1 6.0
12 195.09 |--- 218.49 19 206.79 0.02 990 29 2 99.0 2.9
13 218.49 |--- 241.89 8 230.19 0.01 998 10 1 99.8 1.0
14 241.89 |--- 265.29 1 253.59 0.00 999 2 0 99.9 0.2
15 265.29 |--- 288.69 1 276.99 0.00 1000 1 0 100.0 0.1
==============================================
Classes: Grouping of classes
Fi: Absolute frequency
PM: Midpoint
Fr: Relative frequency
Fac1: Cumulative frequency (below)
Fac2: Cumulative frequency (above)
Fp: Percentage frequency
Fac1p: Cumulative percentage frequency (below)
Fac2p: Cumulative percentage frequency (above) Motivação inicial
- Dados (Quarto tipo)
Coleta (Dados brutos)
Dados elaborados sobre o número de erros encontrados em 20 conjunto de caracteres monitorado em um canal de comunicação:
| 3 | 0 | 3 | 4 | 3 | 1 | 2 | 3 | 0 | 0 |
| 1 | 1 | 2 | 1 | 1 | 1 | 3 | 2 | 2 | 1 |
Dados em rol ou elaborados
Dados elaborados sobre o número de erros encontrados em 20 conjunto de caracteres monitorado em um canal de comunicação:
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 4 |
Distribuição de frequência
- Frequência absoluta
| Número de erros \((x_i)\) | Frequência simples (\(f_i\)) |
|---|---|
| 0 | 3 |
| 1 | 7 |
| 2 | 4 |
| 3 | 5 |
| 4 | 1 |
| Total | 20 |
Distribuição de frequência
- Frequência relativa
| Número de erros \((x_i)\) | Frequência simples (\(f_i\)) | Frequência relativa (\(f_{r_i}\)) |
|---|---|---|
| 0 | 3 | \(3/20 = 0,15\) |
| 1 | 7 | \(7/20 = 0,35\) |
| 2 | 4 | \(4/20 = 0,20\) |
| 3 | 5 | \(5/20 = 0,25\) |
| 4 | 1 | \(1/20 = 0,05\) |
| Total | 20 | 1 |
Distribuição de frequência
- Frequência percentual
| Número de erros \((x_i)\) | Frequência simples (\(f_i\)) | Frequência relativa (\(f_{r_i}\)) | Frequência percentual \((f_{\%_i})\) |
|---|---|---|---|
| 0 | 3 | \(0,15\) | \(0,15 \times 100 = 15\) |
| 1 | 7 | \(0,35\) | \(0,35 \times 100 = 35\) |
| 2 | 4 | \(0,20\) | \(0,20 \times 100 = 20\) |
| 3 | 5 | \(0,25\) | \(0,25 \times 100 = 25\) |
| 4 | 1 | \(0,05\) | \(0,05 \times 100 = 5\) |
| Total | 20 | 1 | \(100\) |
Distribuição de frequência
- Frequência acumulada (abaixo de)
| Número de erros \((x_i)\) | \(f_i\) | \(f_{r_i}\) | \(f_{\%_i}\) | \(f_{ac\downarrow_i}\) |
|---|---|---|---|---|
| 0 | 3 | \(0,15\) | \(15\) | \(3\) |
| 1 | 7 | \(0,35\) | \(35\) | \(3+7 = 10\) |
| 2 | 4 | \(0,20\) | \(20\) | \(3 + 7 + 4 = 14\) |
| 3 | 5 | \(0,25\) | \(25\) | \(3 + 7 + 4 + 5 = 19\) |
| 4 | 1 | \(0,05\) | \(5\) | \(3 + 7 + 4 + 5 + 1 = 20\) |
| Total | 20 | 1 | \(100\) | - |
Distribuição de frequência
- Frequência acumulada (acima de)
| Número de erros \((x_i)\) | \(f_i\) | \(f_{r_i}\) | \(f_{\%_i}\) | \(f_{ac\downarrow_i}\) | \(f_{ac\uparrow_i}\) |
|---|---|---|---|---|---|
| 0 | 3 | \(0,15\) | \(15\) | \(3\) | \(3 + 7 + 4 + 5 + 1 = 20\) |
| 1 | 7 | \(0,35\) | \(35\) | \(3+7 = 10\) | \(7 + 4 + 5 + 1 = 20 - 3 = 17\) |
| 2 | 4 | \(0,20\) | \(20\) | \(3 + 7 + 4 = 14\) | \(4 + 5 + 1 = 17 - 7 = 10\) |
| 3 | 5 | \(0,25\) | \(25\) | \(3 + 7 + 4 + 5 = 19\) | \(5 + 1 = 10 - 4 = 6\) |
| 4 | 1 | \(0,05\) | \(5\) | \(3 + 7 + 4 + 5 + 1 = 20\) | \(1 = 6 - 5 = 1\) |
| Total | 20 | 1 | \(100\) | - | - |
Tabela para V. contínua (Algoritmo)
1º Passo - Número de classes
\[\begin{align} k & \approx \left\{\begin{array}{ll} \sqrt{\textrm{número de elementos}}, & n \leq 100 \\ 5log_{10}(\textrm{número de elementos}), & n > 100 \end{array}\right. \end{align}\]
2º Passo - Amplitude total\[\begin{align} A_t & = \max_i(X_i) - \min_i(X_i),~\textrm{para } i \in \mathbb{N}^{+}. \end{align}\]
3º Passo - Amplitude de classe\[\begin{align} c & = \left\{\begin{array}{ll} \frac{A_t}{k - 1}, & \textrm{Amostra} \\ \frac{A_t}{k}, & \textrm{População}. \end{array}\right. \end{align}\]
4º Passo - LI da primeira classe\[\begin{align} Li_{1a} & = \left\{\begin{array}{ll} X_{(1)} - c / 2, & \textrm{Amostra} \\ X_{(1)}, & \textrm{População}. \end{array}\right. \end{align}\]
| Classe | \(F_i\) |
|---|---|
| \(Li_{1a} \vdash Ls_{1a}\) | \(f_1\) |
| \(Li_{2a} \vdash Ls_{2a}\) | \(f_2\) |
| \(\vdots\) | \(\vdots\) |
| \(Li_{ka} \vdash Ls_{ka}\) | \(f_k\) |
Em resumo…
- Calcular \(k\),
- Calcular \(A_t\),
- Calcular \(c\),
- Calcular \(Li_{1a}\),
- Determinar as classes,
- Calcular o ponto médio, e
- Calcular as frequências como apresentadas anteriormente.
Gráficos
- Gráfico de Haste ou bastão
- Gráfico de barras
- Gráfico de Pizza
- Histograma de frequências
- Ogivas
Uso do pacote leem
- Instalação (Github)
Funções leem
| Função | Finalidade |
|---|---|
base::sort()
|
Dados em rol |
new_leem()
|
Construtor da classe leem |
tabfreq()
|
Distribuição de frequência |
hist()
|
Hitograma de frequência |
ogive()
|
Ogivas |
polyfreq()
|
Polígono de frequências |
stickchart()
|
Gráfico de hastes ou bastão |
piechart()
|
Gráfico pizza ou de setores |
Exemplos
- Considere a distribuição de frequência do número de erros encontrados em 20 conjunto de caracteres monitorado em um canal de comunicação:
| 3 | 0 | 3 | 4 | 3 | 1 | 2 | 3 | 0 | 0 |
| 1 | 1 | 2 | 1 | 1 | 1 | 3 | 2 | 2 | 1 |
- Os dados representam a temperatura (°F) do anel de vedação de cada teste de acionamento ou lançamento real do motor do foguete Challenger.
| 84 | 40 | 45 | 69 | 68 | 72 | 57 | 78 | 53 | 61 | 76 | 76 |
| 49 | 83 | 66 | 80 | 60 | 73 | 63 | 52 | 67 | 70 | 79 | 58 |
| 61 | 67 | 70 | 58 | 67 | 70 | 70 | 67 | 75 | 81 | 75 | 31 |
leem em ação
- Importando os dados
# Numero de erros
d1 <- read.table("https://raw.githubusercontent.com/bendeivide/book-epaec/master/dados/cap02/tabela2.1.txt", h = TRUE)
(d1 <- d1$erros) [1] 3 1 0 1 3 2 4 1 3 1 1 1 2 3 3 2 0 2 0 1# Temperatura do foguete Challenger
d2 <- read.table("https://raw.githubusercontent.com/bendeivide/book-epaec/master/dados/cap02/dados_exem2.1.txt", h = TRUE)
(d2 <- d2$chal) [1] 84 49 61 40 83 67 45 66 70 69 80 58 68 60 67 72 73 70 57 63 70 78 52 67 53
[26] 67 75 61 70 81 76 79 75 76 58 31leem em ação
- Dados em rol
leem em ação
- Distribuição de frequência (Código)
leem em ação
- Distribuição de frequência (Saída de
d1)
Table of frequency
Type of variable: discrete
Groups Fi Fr Fac1 Fac2 Fp Fac1p Fac2p
1 0 3 0.15 3 20 15 15 100
2 1 7 0.35 10 17 35 50 85
3 2 4 0.20 14 10 20 70 50
4 3 5 0.25 19 6 25 95 30
5 4 1 0.05 20 1 5 100 5
==============================================
Groups: Discretized grouping
Fi: Absolute frequency
Fr: Relative frequency
Fac1: Cumulative frequency (below)
Fac2: Cumulative frequency (above)
Fp: Percentage frequency
Fac1p: Cumulative percentage frequency (below)
Fac2p: Cumulative percentage frequency (above) leem em ação
- Distribuição de frequência (Saída de
d2)
Table of frequency
Type of variable: continuous
Classes Fi PM Fr Fac1 Fac2 Fp Fac1p Fac2p
1 25.7 |--- 36.3 1 31.0 0.03 1 36 3 2.78 100.00
2 36.3 |--- 46.9 2 41.6 0.06 3 35 6 8.33 97.22
3 46.9 |--- 57.5 4 52.2 0.11 7 33 11 19.44 91.67
4 57.5 |--- 68.1 12 62.8 0.33 19 29 33 52.78 80.56
5 68.1 |--- 78.7 12 73.4 0.33 31 17 33 86.11 47.22
6 78.7 |--- 89.3 5 84.0 0.14 36 5 14 100.00 13.89
==============================================
Classes: Grouping of classes
Fi: Absolute frequency
PM: Midpoint
Fr: Relative frequency
Fac1: Cumulative frequency (below)
Fac2: Cumulative frequency (above)
Fp: Percentage frequency
Fac1p: Cumulative percentage frequency (below)
Fac2p: Cumulative percentage frequency (above) leem em ação
- Apresentação gráfica: Hastes ou bastão
# Forma convencional:
aux1 <- new_leem(d1, variable = "discrete")
aux2 <- tabfreq(aux1)
stickchart(aux2,
lwd=3, # largura da linha
pcol = "red", # cor da linha
bgcol = "lightgray", # cor do fundo
panel.first = grid(col = "white") # inserindo grid e sua cor
)
# Usando o pipe
d1 |>
new_leem(variable = "discrete") |>
tabfreq() |>
stickchart(lwd=3, # largura da linha
pcol = "red", # cor da linha
bgcol = "lightgray", # cor do fundo
panel.first = grid(col = "white") # inserindo grid e sua cor
)
leem em ação
- Apresentação gráfica: Barras
leem em ação
- Apresentação gráfica: Histograma de frequências
leem em ação
- Apresentação gráfica: Polígono
- Dados discretos
leem em ação
- Apresentação gráfica: Polígono
- Dados contínuos
leem em ação
- Apresentação gráfica: Polígono sem as barras
leem em ação
- Apresentação gráfica: Ogiva (crescente)
- Dados discretos
leem em ação
- Apresentação gráfica: Ogiva (decrescente)
- Dados discretos
leem em ação
- Apresentação gráfica: Ogiva (ambos)
- Dados discretos
leem em ação
- Apresentação gráfica: Ogiva (crescente)
- Dados contínuos
leem em ação
- Apresentação gráfica: Ogiva (decrescente)
- Dados contínuos
leem em ação
- Apresentação gráfica: Ogiva (Ambos)
- Dados contínuos
leem em ação
- Apresentação gráfica: Ogiva (Ambos + Histograma)
- Dados contínuos
# Usando o pipe:
d2 |>
new_leem(variable = 2) |>
tabfreq() |>
ogive(both = TRUE, # ambas ogivas
bars = FALSE, # barras
barcol = c("red", "yellow"), # cor da barra das duas ogivas
histogram = TRUE, # incluindo o histograma
histcol = gray.colors(6), # cor do histograma
bgcol = "purple") # cor do fundo
leem em ação
- Apresentação gráfica: Pizza ou setores
- Dados discretos
leem em ação
- Apresentação gráfica: Pizza ou setores
- Dados contínuos
Questões?
Próximas aulas
Referências
BATISTA, B. D. O. Estatística e Probabilidade: Aplicada às Engenharias e Ciências. Ouro Branco, MG, Brasil: [s.n.], 2023.