``` ## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ── ``` ``` ## ✓ ggplot2 3.3.5 ✓ purrr 0.3.4 ## ✓ tibble 3.1.6 ✓ dplyr 1.0.8 ## ✓ tidyr 1.0.2 ✓ stringr 1.4.0 ## ✓ readr 1.3.1 ✓ forcats 0.5.0 ``` ``` ## Warning: package 'ggplot2' was built under R version 3.6.2 ``` ``` ## Warning: package 'tibble' was built under R version 3.6.2 ``` ``` ## Warning: package 'purrr' was built under R version 3.6.2 ``` ``` ## Warning: package 'dplyr' was built under R version 3.6.2 ``` ``` ## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ── ## x dplyr::filter() masks stats::filter() ## x dplyr::lag() masks stats::lag() ``` <!-- <img src="https://upload.wikimedia.org/wikipedia/commons/0/0e/Hinman_collator.jpg" width="150px"/> --> --- count: false .panel1-gpas-auto[ ```r *set.seed(2022) ``` ] .panel2-gpas-auto[ ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) *rnorm(n = 6000, mean = 4, sd = .7) ``` ] .panel2-gpas-auto[ ``` [1] 4.630099 3.178658 3.371760 2.988849 3.768290 1.969560 3.258521 4.194568 [9] 4.524640 4.169108 4.704330 3.870398 3.312721 4.065036 3.963051 3.943770 [17] 3.542127 3.334522 4.713693 4.601332 4.255123 4.268556 4.779384 4.848057 [25] 3.756172 3.398313 4.455019 4.229641 3.637437 3.832712 4.082445 4.582063 [33] 2.908757 3.845637 3.427964 4.753674 4.755765 4.099490 4.109886 3.881896 [41] 3.811674 4.565438 3.212698 2.998448 4.042250 3.444912 4.238193 3.818372 [49] 3.086606 4.257721 5.185233 4.697086 4.130726 4.866836 4.216561 4.445003 [57] 4.016228 4.824505 3.682517 4.291149 3.063090 3.095618 3.783648 4.109558 [65] 3.416258 3.982816 3.203854 4.750438 5.620149 4.296081 3.904143 4.929878 [73] 4.305575 4.046500 4.913262 3.853518 4.712777 4.956224 5.033687 4.621115 [81] 3.288864 5.309608 4.753339 3.247915 2.463097 4.374181 4.940613 4.969502 [89] 5.922849 3.967839 4.520160 4.182297 4.299797 3.742219 6.021196 3.575049 [97] 2.684561 4.502850 4.175998 4.326916 3.847478 3.147647 3.472145 4.133861 [105] 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2.745693 [209] 3.536958 3.739409 4.111063 3.525111 4.057742 4.870618 4.616347 4.380771 [217] 3.446366 4.299001 4.665780 4.574082 2.732338 3.804060 4.469748 5.117881 [225] 3.491988 4.672403 4.669508 4.886093 3.834131 2.935920 4.237687 4.977182 [233] 3.169756 3.716870 3.799026 4.659810 3.261683 3.539906 3.709998 4.317777 [241] 3.612232 4.247708 4.103800 4.263558 5.054891 3.350894 3.589001 5.721248 [249] 4.471619 4.234097 5.126329 3.219221 4.007091 3.263349 4.303746 4.460663 [257] 2.991949 4.331353 3.435904 3.450174 3.205255 3.362002 4.062976 3.834734 [265] 5.139305 4.353640 4.026206 4.255616 3.023779 4.444594 3.665573 3.426018 [273] 4.876669 3.077155 4.380983 3.869172 4.431175 4.369591 4.164119 3.921391 [281] 3.078592 3.764263 4.334887 3.234262 4.882984 4.025211 5.316747 3.393481 [289] 3.303607 2.937937 3.971876 2.749424 4.669372 3.803653 3.712169 3.675599 [297] 2.281544 4.219020 3.446063 4.157826 2.751335 3.041120 4.275784 4.187055 [305] 4.061065 5.086305 4.556870 4.238938 3.223133 3.270347 3.867704 4.900222 [313] 2.998167 3.728778 3.648178 4.047285 4.354583 3.102869 3.261252 3.662475 [321] 4.509972 3.847134 4.916239 3.824509 3.618042 4.861635 3.623520 4.417075 [329] 4.316374 3.535057 2.440564 3.999490 4.951201 3.070709 4.174834 3.187905 [337] 4.878210 3.805857 3.840973 3.681576 3.921108 3.976106 3.721336 3.765983 [345] 4.391426 3.829931 2.816940 3.093432 4.721278 3.458421 4.278227 3.487542 [353] 4.389609 3.631318 3.292879 3.787375 3.305071 4.401101 4.393418 3.592176 [361] 4.714265 3.774430 3.972639 4.161705 4.943907 4.928273 3.966332 3.581951 [369] 4.425416 4.574106 3.854853 3.099598 4.283785 4.402918 3.538137 3.268143 [377] 4.233421 3.488570 3.932841 5.175523 3.799663 4.675020 3.494907 4.161807 [385] 5.268505 3.573109 3.339155 4.383169 4.229477 3.724521 3.289362 3.561361 [393] 4.547635 5.885645 5.304953 4.824869 3.879044 2.616566 3.831290 3.268506 [401] 4.577739 2.494499 4.193023 4.747044 5.203911 4.209975 4.769588 4.360233 [409] 4.342616 3.293872 4.415702 3.843545 3.114641 3.868243 4.148394 3.357370 [417] 3.342279 3.770005 4.939531 3.985641 3.804310 3.535162 5.440526 3.286694 [425] 4.836514 4.208747 4.108521 4.181331 4.380839 3.259598 4.657910 3.801613 [433] 3.421095 5.373742 3.372941 5.714164 3.626631 4.062286 3.003102 3.848355 [441] 3.794187 3.717112 3.659631 3.018944 4.252600 5.325249 3.973819 3.404616 [449] 4.331116 4.115462 3.037820 5.490459 3.681241 4.118843 2.651118 4.941182 [457] 3.648600 4.065103 1.567337 3.286582 3.063713 3.789949 4.394423 1.847499 [465] 3.676934 5.523518 4.258196 4.717289 4.456185 4.372629 4.430822 3.861251 [473] 3.938891 4.442907 4.016103 3.619840 3.499450 2.594148 3.964466 3.716126 [481] 4.254601 6.635634 3.988958 4.906842 3.572174 3.929719 3.089325 5.446362 [489] 3.394816 3.638697 4.579755 3.718930 3.678020 5.077179 4.184912 3.764369 [497] 3.612047 4.636743 3.419600 4.969518 3.963011 4.358797 3.262439 3.642269 [505] 4.833970 3.083539 3.780911 3.821262 5.118724 4.389983 3.272408 3.674723 [513] 4.345609 3.960991 4.595166 2.348205 4.359514 3.633270 3.971116 3.916581 [521] 3.304252 4.169315 3.866839 5.163751 3.946283 3.518523 4.743784 3.903736 [529] 3.356821 3.930388 5.110829 3.666330 4.815478 3.899145 3.497409 4.195480 [537] 3.828971 3.748343 4.860111 3.457878 4.330267 4.157330 2.864195 3.758115 [545] 4.376326 3.580566 4.216050 4.111685 4.827331 3.203135 5.103105 2.882668 [553] 4.661970 5.462366 4.457555 4.488519 3.352222 4.089509 3.731449 3.660538 [561] 3.072225 3.687922 3.728209 3.402034 3.829411 4.899069 4.685485 3.688653 [569] 3.976036 3.526930 4.280634 3.342389 3.535636 4.180173 4.322630 3.538375 [577] 4.905919 3.586242 3.099946 4.771577 3.669858 4.394543 3.541623 3.505361 [585] 3.356359 4.273503 4.950385 3.816163 4.949933 4.104164 4.756133 4.576830 [593] 4.908161 4.838540 3.489635 3.860775 3.822882 3.747735 3.425744 4.887252 [601] 4.263015 3.896727 3.963741 3.621481 3.341945 3.687715 3.437990 3.853112 [609] 3.979649 3.628436 4.532529 3.334488 4.569444 3.287629 4.467294 5.008881 [617] 4.037318 3.842406 4.394360 4.428875 4.617852 3.832341 4.280862 3.467648 [625] 4.891682 3.688459 3.846736 4.531764 2.953548 4.404403 3.984955 4.487701 [633] 3.231404 4.088072 4.188096 2.551938 2.789831 3.782761 4.326192 3.140852 [641] 4.538290 3.839358 3.932686 4.182300 4.103756 4.305387 3.856399 3.715374 [649] 4.156525 4.340076 3.831554 3.003947 2.415961 4.476365 4.496982 4.569409 [657] 4.523806 4.379080 4.046993 4.359967 4.391100 3.232714 3.685090 4.292718 [665] 5.420544 3.845740 5.262180 3.629195 3.033008 3.794194 4.450844 3.524897 [673] 3.735900 4.510889 3.654401 4.961910 3.798471 3.640917 3.537387 3.763099 [681] 4.659821 3.342491 3.488705 4.266641 2.731558 3.980880 3.808094 4.352515 [689] 3.718183 2.515013 3.475897 3.268407 6.024485 2.049416 4.227022 4.139777 [697] 4.639051 3.414795 4.056277 3.336095 3.442515 3.183961 3.319940 3.066716 [705] 3.167412 3.958635 3.174195 4.524007 4.277731 4.305723 4.654596 3.114885 [713] 3.846277 4.340112 4.775036 3.437865 3.704085 3.380010 4.649623 4.468604 [721] 5.237352 4.418937 5.028000 5.144326 3.585861 2.151148 3.648881 4.582451 [729] 4.285254 4.564019 2.610456 3.744482 5.048811 3.521740 3.273064 4.182502 [737] 3.420909 4.469319 4.920087 4.209723 3.011202 4.055019 2.815252 3.329642 [745] 3.962370 3.271197 2.632498 5.923804 3.157432 3.540697 3.563779 3.587351 [753] 4.524375 3.456055 4.412829 5.916018 4.406621 3.737084 5.347994 4.608862 [761] 4.445715 4.748745 4.265061 4.063744 4.675789 5.115155 4.732080 4.775034 [769] 4.871311 4.208367 4.339055 4.999970 3.827214 3.747984 4.592517 4.975815 [777] 4.195655 4.711502 3.778041 3.597813 3.950784 4.541587 3.434356 3.300589 [785] 4.380135 4.551980 4.543519 3.989580 4.003833 4.653826 4.948512 3.937894 [793] 3.763320 4.720567 3.526779 4.753977 3.838552 4.242195 3.773042 4.285863 [801] 4.124827 3.425214 3.169659 3.978108 4.033213 3.908583 3.715853 2.693339 [809] 4.118603 4.723575 4.075848 4.625940 3.088471 4.052472 5.048595 4.935920 [817] 3.542141 3.721530 3.096639 3.879612 3.527579 4.584940 3.680762 3.792052 [825] 3.695004 4.442638 3.498806 3.634429 3.305442 3.931323 3.546457 5.342875 [833] 3.512385 4.457024 4.293726 3.832030 5.219751 4.942986 3.747048 4.134867 [841] 4.789032 3.336343 3.356620 4.543914 3.665211 4.748749 3.561431 3.902753 [849] 3.063749 5.036192 3.834330 3.273796 3.493796 4.254692 3.750301 5.522224 [857] 4.621021 3.772089 3.681927 5.131408 4.026055 4.095046 2.744096 3.258374 [865] 3.288172 2.847851 4.273205 4.328949 3.201555 4.983908 4.502903 3.785558 [873] 3.955315 4.111599 3.709392 3.393356 3.680602 3.169786 3.603776 3.730082 [881] 3.408015 4.426508 3.781503 3.653713 4.183675 4.200127 3.185421 2.896985 [889] 4.780675 4.726846 3.883838 4.715204 3.095238 5.131922 3.749839 3.633973 [897] 3.735791 3.236201 3.869685 4.531810 5.470323 3.043287 3.877842 4.999535 [905] 4.601907 3.591767 3.466879 3.410591 2.340709 4.371617 3.740319 3.784634 [913] 4.565476 3.882799 3.819669 4.104444 5.523479 2.616859 5.512599 3.080041 [921] 5.156489 4.376237 3.959329 3.805895 4.574644 5.936977 3.682538 3.934101 [929] 3.205493 4.415731 3.528112 4.568593 2.885561 3.349386 2.770156 3.957191 [937] 3.565231 4.813364 6.040964 4.858101 5.311689 4.190784 4.158262 4.692815 [945] 2.961162 4.863883 4.128335 4.778548 3.772923 4.048934 4.068808 5.145345 [953] 4.737208 3.014793 4.394997 3.599061 2.979746 4.547816 4.592439 5.098204 [961] 4.609206 2.924131 4.889188 4.597977 4.854381 3.171255 2.909675 3.946789 [969] 4.807557 4.807356 3.309175 3.896463 4.388467 3.562055 4.068220 3.947545 [977] 4.762935 2.425023 3.714159 4.577923 3.884460 5.144066 4.559422 4.306992 [985] 4.875471 4.109418 4.948264 4.235138 3.197127 2.997072 4.904215 3.895105 [993] 5.219055 4.977504 4.561356 3.085357 2.934235 4.300868 4.135779 4.642798 [1001] 3.241282 4.601995 4.273744 4.046712 4.363334 4.706753 5.678611 2.067567 [1009] 2.862859 5.502083 3.700090 6.150923 5.136250 3.619676 4.385601 4.009737 [1017] 4.569889 4.186206 3.445114 2.936474 4.359342 4.404334 3.409845 4.186452 [1025] 3.705518 3.805682 3.309465 4.636465 5.332780 4.004123 4.606684 4.879658 [1033] 3.651751 3.601904 4.282606 5.050097 4.768987 3.364907 4.734634 3.753334 [1041] 4.860999 3.257378 2.714795 3.543411 2.835241 4.828826 4.064070 4.579499 [1049] 3.905872 4.258372 3.591318 4.091042 4.752691 4.152648 3.653366 3.696490 [1057] 4.839800 3.985498 3.671893 4.533567 3.986166 2.786592 3.840619 3.762244 [1065] 3.933452 4.595301 3.854653 3.135278 4.505448 4.028982 5.153455 4.233214 [1073] 4.494718 3.619951 2.925429 4.122362 4.924251 3.804290 4.068356 4.487424 [1081] 4.756270 3.400385 4.106967 4.254039 3.667426 4.938096 4.631857 5.161090 [1089] 2.498123 2.629815 2.988505 4.168333 2.308354 3.666804 3.582388 4.407784 [1097] 3.424720 5.074532 4.804176 4.120360 3.538256 4.681630 3.956785 4.541546 [1105] 4.079746 2.623558 3.434937 3.715749 4.543833 4.571570 2.658163 4.275627 [1113] 3.481806 5.469381 4.469927 4.237855 4.302185 2.686064 4.478700 3.974992 [1121] 4.079419 3.800429 3.395400 3.614853 2.860055 3.559181 4.664932 3.453224 [1129] 4.301610 2.971388 4.740490 4.333950 2.481246 4.284132 4.129311 4.395836 [1137] 2.751536 3.976857 4.854607 4.411674 4.817318 3.668689 5.157549 2.921917 [1145] 4.074616 3.528930 4.925761 3.693702 5.101006 4.833283 3.635487 2.765636 [1153] 5.343617 4.676735 3.638979 3.534622 3.419007 4.066158 3.221877 3.264320 [1161] 4.078429 3.603778 3.793376 4.190081 4.846232 4.210672 4.011996 4.138609 [1169] 2.869612 3.048472 4.444744 4.802697 3.227875 4.199618 3.287751 3.695336 [1177] 4.279440 3.620212 3.178073 4.900471 3.812738 4.614709 3.226870 3.640953 [1185] 3.524474 2.820440 4.285006 4.656977 4.235063 4.516348 5.561657 4.133197 [1193] 2.487313 4.587277 3.322503 4.132987 3.680900 5.313413 4.260320 3.198896 [1201] 4.202868 4.900151 3.819039 3.889712 3.631899 2.859073 4.835012 2.972948 [1209] 4.067790 4.610932 4.161954 4.409212 4.248387 3.593515 4.259682 3.144844 [1217] 4.213079 4.683710 4.911988 2.625800 4.029529 3.883646 5.152214 3.698130 [1225] 3.879741 5.447628 4.870023 3.728679 4.002697 4.852387 4.201609 3.330161 [1233] 3.777600 3.901801 5.434203 3.309421 4.090060 3.587243 3.568975 3.794814 [1241] 4.009195 3.983233 4.275944 3.891566 3.357753 5.424449 3.329947 5.046376 [1249] 4.207034 3.909820 4.263004 5.043247 3.879689 2.123890 3.639244 3.256327 [1257] 4.225441 4.887714 3.542048 4.287097 4.086391 4.395660 1.689737 4.516286 [1265] 4.456990 3.251575 4.182695 3.573190 4.674139 4.423782 3.826724 3.442294 [1273] 3.256912 3.655976 3.458174 4.063302 3.114914 4.013515 5.198759 4.349901 [1281] 5.260041 4.232716 4.586977 2.576466 3.810437 3.556063 3.775487 2.970015 [1289] 4.717826 3.102050 4.392390 4.173646 4.354974 3.450474 3.827761 4.102904 [1297] 4.455399 3.757736 3.508694 3.949032 3.778553 3.557878 3.957916 4.342442 [1305] 5.146811 3.561363 4.298726 4.401311 3.554264 4.216387 4.986284 3.680430 [1313] 3.148215 4.566354 4.259049 3.415593 3.732673 4.211758 4.691960 3.035019 [1321] 4.616207 3.445320 3.525210 5.279539 3.246310 4.275529 3.323743 4.511509 [1329] 3.375122 4.604568 4.581300 3.812605 3.844590 3.998380 3.887772 3.890133 [1337] 4.851758 5.591223 4.836291 3.292840 3.981925 3.420106 3.586181 2.692877 [1345] 4.099591 2.462626 3.610852 4.654642 4.710784 4.727081 4.006738 3.285364 [1353] 4.430183 4.507942 4.265068 4.518542 3.574731 4.260892 5.141520 4.508302 [1361] 3.260710 3.496472 4.191097 4.367018 4.061459 4.578218 3.618192 3.967605 [1369] 4.007400 3.756020 4.092441 2.927128 3.133941 3.858285 3.453729 2.832787 [1377] 3.284200 4.528628 2.975962 4.580312 4.253085 2.851523 3.112546 4.802109 [1385] 3.157835 3.989535 4.382772 3.568602 3.675494 4.559631 3.315623 5.378849 [1393] 4.038323 2.642742 4.439928 3.285224 2.527852 4.273859 3.949173 4.058124 [1401] 4.760259 5.081748 4.415317 3.787078 3.942769 4.102889 3.914413 4.733586 [1409] 3.488467 4.659709 3.551978 2.526398 4.833592 3.851783 3.177486 3.889975 [1417] 4.483199 3.586438 5.176090 2.924150 3.739675 3.806279 4.723409 4.640625 [1425] 3.982986 4.892663 4.448264 4.347424 3.705537 3.278713 4.584423 5.870733 [1433] 3.963080 3.749345 3.180059 3.218521 3.631969 4.207071 4.555692 4.968416 [1441] 5.385588 3.926586 4.953134 3.347141 4.157542 5.729673 4.245220 2.884193 [1449] 4.517213 3.930779 4.395424 2.165905 3.908132 3.371775 3.174469 2.830671 [1457] 4.051913 3.999766 3.324226 5.318200 4.341800 4.341774 4.601812 3.048092 [1465] 4.672203 3.732841 4.071567 2.128432 2.764585 4.601270 3.983645 5.325592 [1473] 3.931733 4.488155 4.180399 3.998209 5.256771 3.611959 4.347909 3.047402 [1481] 4.667570 3.785414 3.916805 4.422175 3.992936 4.332226 4.250080 3.062838 [1489] 3.352946 4.160854 3.782886 3.498643 4.755465 3.843348 4.008387 4.420079 [1497] 4.756508 3.478307 4.763058 3.302801 3.987383 3.976281 3.934349 3.832405 [1505] 5.355673 3.866407 4.125224 4.198689 4.561111 5.009117 3.717965 5.687303 [1513] 2.349703 3.247921 3.630835 3.059444 2.596686 5.430147 4.254287 3.756048 [1521] 3.140289 4.539160 5.856092 3.583778 4.313198 4.486463 5.336638 4.034888 [1529] 3.712921 4.191142 5.157783 4.680833 3.588993 3.913240 3.328583 3.523568 [1537] 3.896397 4.048422 3.650172 4.155617 3.128604 3.539896 3.653969 3.428670 [1545] 3.486968 5.086800 3.360077 2.681030 3.925046 4.639202 4.624017 3.330700 [1553] 3.938777 3.952357 2.273260 4.248473 3.471821 4.577171 4.327436 3.977200 [1561] 4.943138 4.085443 4.447088 3.369655 2.711782 4.401692 4.507991 4.518859 [1569] 4.041867 3.490729 2.150896 4.891626 2.482517 4.530689 2.343580 4.023254 [1577] 4.526619 3.309718 3.045012 4.718750 4.250810 3.083014 3.867303 4.372314 [1585] 3.572899 3.967236 4.254058 5.420504 3.493281 3.870890 4.341720 5.326274 [1593] 5.408883 3.923266 4.639561 3.974177 3.506794 3.511346 3.725185 2.674407 [1601] 2.672490 2.950100 4.517269 4.746632 3.877953 4.007634 5.250444 5.375739 [1609] 3.348515 4.248066 3.930814 4.362678 5.723155 4.449230 3.763953 3.845520 [1617] 4.781057 4.277519 5.312193 2.738856 3.804239 3.893732 3.582095 4.278371 [1625] 4.796161 4.312953 4.888981 3.769051 3.534167 4.163388 5.384651 3.017243 [1633] 4.475128 5.136678 3.598262 4.321951 4.377031 4.263277 4.774159 3.865568 [1641] 3.040859 3.849929 3.397836 3.972801 4.063100 4.719845 4.227416 2.944157 [1649] 3.812862 3.961184 4.719884 3.873363 4.699773 3.396995 3.888399 4.745943 [1657] 3.225739 3.011078 4.822557 4.414317 5.430521 3.187047 4.372893 3.756853 [1665] 3.028996 5.116455 4.968267 3.255728 4.222283 4.749496 3.228571 4.064492 [1673] 4.258731 3.606431 3.662682 3.626734 4.316975 2.914295 3.323444 3.027354 [1681] 4.086342 2.440010 3.435236 3.681256 4.641970 4.181042 4.532075 3.735520 [1689] 3.797782 3.872504 4.504069 4.969501 3.770188 4.245225 5.038453 4.800898 [1697] 3.527028 4.263143 3.445999 2.931429 5.122222 2.981084 3.877419 3.682324 [1705] 4.827293 2.832008 2.873041 4.823664 4.365020 2.940172 4.562146 3.350525 [1713] 4.475737 5.373449 4.441676 4.290497 4.772331 3.742829 4.722658 3.951490 [1721] 3.201033 4.333695 3.963380 3.489603 4.530744 4.673541 4.600727 3.159500 [1729] 4.579299 4.007708 2.899869 4.314003 4.323035 3.947379 4.853476 3.812243 [1737] 3.602974 3.780062 4.246496 4.340119 4.334107 5.439517 3.732620 3.593815 [1745] 3.561677 3.406434 4.198663 3.638102 3.584534 2.640355 4.825453 3.377754 [1753] 4.822224 3.974702 3.741975 4.926053 4.119214 3.652086 4.562519 4.483014 [1761] 4.397671 4.762347 4.946861 2.869726 4.089144 4.135679 3.565171 4.658573 [1769] 5.401116 3.310576 3.728554 4.333697 4.052375 4.248277 4.484829 3.674179 [1777] 3.589628 3.322070 4.114134 4.930205 4.496052 4.009653 2.523868 2.530449 [1785] 2.908311 4.800920 3.587243 3.595063 3.905268 3.419449 3.836192 3.900894 [1793] 4.018366 4.182400 4.165515 3.805095 3.924971 3.781252 3.709368 4.167436 [1801] 3.734501 4.364533 4.280439 3.912082 4.348959 3.515563 3.766261 2.528277 [1809] 3.099270 5.238280 4.341249 4.497355 4.106377 5.142291 4.302076 3.381257 [1817] 5.501589 3.352519 3.494428 4.521921 5.758106 3.730629 3.304785 3.785400 [1825] 3.191887 4.047381 3.836251 4.980159 5.404892 3.505548 4.450711 3.615120 [1833] 4.128991 3.358266 3.905638 3.112533 3.269762 4.351359 5.343825 3.789949 [1841] 3.420631 3.528774 3.938050 2.819949 2.566086 4.935410 4.044310 4.134943 [1849] 3.729984 2.661924 4.131793 3.027956 4.178872 4.120639 2.958891 4.551457 [1857] 4.337275 3.978999 3.569614 3.132515 4.885980 3.335820 3.885796 4.310095 [1865] 4.372040 4.437639 4.788539 4.736900 3.616609 3.827445 4.252469 3.517655 [1873] 3.602102 4.550272 3.411938 4.713410 2.448746 3.364541 3.912896 4.527514 [1881] 3.610968 4.581732 3.389809 2.644390 3.410526 3.927129 3.985082 4.672199 [1889] 3.413951 3.835819 4.183443 4.390747 3.998241 3.934075 3.186261 5.103421 [1897] 4.009463 5.267897 4.081826 3.356844 4.269883 2.525352 4.488422 3.139257 [1905] 3.825596 3.517826 3.453964 3.758949 2.565411 4.838639 4.306459 4.390574 [1913] 5.354710 3.827556 4.163892 4.438762 4.494293 3.302017 4.932673 3.311665 [1921] 4.466756 3.700349 4.969158 5.524717 4.987629 3.684100 4.498643 4.529543 [1929] 3.704421 4.544828 4.671341 3.179319 3.271077 5.201010 3.314320 3.230120 [1937] 4.311142 2.931448 2.626735 4.326654 4.001591 4.842902 5.533077 3.398263 [1945] 5.218826 2.626019 4.115513 2.866762 4.294270 4.240257 4.992693 4.584458 [1953] 4.161455 4.076890 4.510740 2.774461 3.822497 4.259075 4.886548 3.729242 [1961] 3.071186 4.596948 3.202484 3.327348 4.354346 2.755521 3.741134 3.707482 [1969] 3.171455 4.190116 5.359147 4.336521 3.762530 2.797754 3.437520 2.930963 [1977] 4.323808 3.035146 4.328967 3.779789 3.804267 5.093502 4.914720 3.058350 [1985] 3.467940 5.011981 4.508944 3.779946 4.322247 1.450061 4.716241 3.959466 [1993] 4.685002 3.351305 5.186718 4.069985 3.593775 3.238932 3.666165 3.930144 [2001] 3.618129 4.550789 4.209126 5.063461 4.639169 4.139609 5.719529 3.631776 [2009] 3.438404 4.478827 3.398670 3.919682 2.787105 3.534549 3.626576 3.862971 [2017] 3.719750 4.601302 3.010961 3.839170 4.034918 4.074166 2.903161 4.993119 [2025] 4.969295 4.385899 5.165114 3.138994 4.872816 5.091486 4.341471 4.691404 [2033] 3.505992 4.688082 2.726433 4.684278 3.497356 4.555580 3.708121 3.726507 [2041] 5.092603 2.751593 4.751606 4.797755 5.033670 4.650510 4.904540 3.628924 [2049] 5.027769 3.233588 3.986707 3.088054 3.053471 3.895957 3.818786 3.484488 [2057] 3.725919 3.672458 4.541462 2.129923 4.416470 4.438023 3.062688 3.518056 [2065] 4.588178 4.049721 4.050529 4.105836 3.490308 3.702830 3.053689 4.902974 [2073] 3.598399 2.692080 3.099806 2.769676 4.218720 3.154018 4.868168 3.571072 [2081] 3.408502 3.463621 3.631635 3.461687 4.042172 4.536094 5.256477 2.808606 [2089] 4.540455 5.483182 5.017620 3.720541 3.311323 4.432287 4.659942 3.254666 [2097] 2.620907 4.138978 4.937477 3.722050 4.507525 4.258224 3.260433 3.631285 [2105] 6.315990 5.544323 3.586353 4.677868 3.764220 3.466803 3.078429 3.405184 [2113] 2.639093 3.180311 4.390180 4.554842 3.889936 4.084693 3.564462 3.482661 [2121] 4.023071 3.918721 2.351003 3.797261 4.397962 3.980246 3.956436 3.884710 [2129] 3.941149 3.586942 4.784624 3.720348 4.128223 4.746888 4.282446 3.723770 [2137] 3.343349 3.755812 5.422686 4.066045 2.772920 4.574894 4.014442 4.296168 [2145] 4.717640 5.293531 4.102453 3.619766 3.824209 4.692397 2.260081 4.277106 [2153] 4.776050 4.061156 4.192695 4.985520 4.494416 3.729060 3.602819 3.381986 [2161] 4.568632 4.029000 4.670574 5.127896 3.423048 4.633400 3.943267 4.285805 [2169] 3.914154 4.810097 3.918662 4.853267 4.168934 5.955413 3.089566 4.758941 [2177] 4.217727 4.587898 3.579262 4.799557 3.541060 3.285126 4.784629 4.193800 [2185] 4.215373 3.816322 2.374358 3.718758 3.552843 4.182236 2.551124 4.537402 [2193] 2.946174 4.440305 4.449842 4.839324 3.335212 3.236631 4.898638 3.122907 [2201] 3.532091 3.171904 4.607726 4.080059 3.048145 3.941678 4.084426 3.393204 [2209] 4.336024 3.718683 4.605514 3.228468 3.089175 3.345174 4.176778 3.071823 [2217] 4.177528 4.286263 4.186811 4.316409 4.188169 3.701340 3.234138 3.021600 [2225] 4.409455 4.426901 3.198019 4.227971 4.277838 4.074217 3.764790 3.842244 [2233] 3.928209 2.813641 3.028506 3.768741 3.347933 3.802633 4.421136 4.109564 [2241] 3.077210 3.776072 1.969358 4.498695 3.406865 3.402123 4.802729 3.944975 [2249] 4.032672 3.607796 4.041132 3.772122 3.422062 4.038055 3.713985 4.049259 [2257] 5.586757 4.479294 4.973807 3.469614 4.322763 4.395471 4.516466 5.231620 [2265] 4.798585 5.706376 5.611986 4.285470 3.867394 2.597505 4.114409 3.585307 [2273] 3.118326 4.805845 4.566694 4.532350 3.214301 5.051052 5.482758 4.551081 [2281] 4.626427 4.824003 4.553104 4.964681 3.880154 3.579832 2.831642 2.740474 [2289] 3.706898 2.520026 4.707401 5.259674 4.047044 3.270296 3.556109 4.119464 [2297] 3.271493 3.452981 4.092767 4.538520 3.400907 3.661954 2.862660 3.661284 [2305] 3.896395 5.530441 4.351096 4.284762 4.713066 2.544837 3.716273 3.258666 [2313] 2.815883 4.196600 4.754751 4.498361 4.793615 5.215303 4.715876 3.527627 [2321] 3.175446 1.862497 4.522572 4.876457 4.195222 4.069209 3.898645 4.292846 [2329] 4.182263 3.237416 5.579883 4.194185 4.342310 5.015207 4.242877 3.961339 [2337] 3.426941 4.666126 4.557183 2.869313 3.555400 4.191833 4.075696 2.595831 [2345] 4.746867 3.824335 4.297817 4.220732 3.709567 3.554401 4.305302 3.900088 [2353] 4.464492 3.665331 3.404226 4.607367 4.246231 3.813717 3.890765 3.762509 [2361] 3.550370 4.909977 3.486397 3.900852 4.245402 3.208278 3.367344 3.388262 [2369] 3.750885 3.845829 3.613290 5.350963 5.462773 3.535684 4.572671 4.648314 [2377] 3.581494 3.972560 3.681715 3.485700 3.613169 4.266431 3.580296 3.250069 [2385] 4.298743 3.837439 4.486467 5.768025 2.430208 5.042501 4.453755 4.155836 [2393] 4.262206 4.730512 4.403978 4.017515 4.729715 4.333351 4.784045 3.917404 [2401] 2.921883 3.593498 3.926488 4.120422 3.531751 4.433368 4.526716 3.354149 [2409] 3.481991 3.839248 4.272788 4.626287 3.777770 3.212763 3.866288 3.790113 [2417] 3.318880 4.362937 4.069950 3.506306 5.424383 5.197790 4.536474 3.972680 [2425] 4.752818 4.461225 4.500790 3.928220 3.843582 4.469431 3.099757 5.849400 [2433] 4.104106 3.895349 5.215309 4.079504 4.433914 4.548458 5.672330 4.974521 [2441] 3.449497 4.210983 3.412586 4.094450 4.530841 3.634270 3.232015 3.441209 [2449] 4.090346 4.462507 5.335150 4.936716 4.785618 3.970659 2.800854 4.621698 [2457] 5.048565 3.382441 3.560233 4.611290 2.951647 4.286542 4.123700 2.745793 [2465] 4.226378 2.762554 4.031597 5.556027 4.827889 5.483127 3.216581 3.924508 [2473] 4.239749 4.860688 4.479205 3.535404 4.390128 3.166051 3.216654 3.352540 [2481] 5.345342 3.328704 4.774124 2.718563 4.336084 4.361441 4.526455 3.122590 [2489] 3.078186 4.701925 3.765467 3.844460 4.461885 4.820893 3.192430 4.639697 [2497] 4.239417 3.955024 5.699533 4.032938 3.749886 4.556481 4.128642 4.047047 [2505] 3.848503 2.920259 4.799866 4.005868 4.882719 5.544428 3.311142 4.545028 [2513] 5.234928 3.666470 5.009880 2.893563 3.162938 3.094032 4.590235 4.432392 [2521] 2.989998 2.861606 3.346085 4.364141 3.314484 4.076295 4.662562 3.995849 [2529] 3.584163 3.769083 3.437625 2.918992 4.879132 5.000343 3.619581 4.696272 [2537] 3.003930 5.154928 3.413862 4.214698 3.468593 3.958600 4.033085 3.919882 [2545] 3.593616 4.675175 5.194317 3.202740 4.384633 3.376488 3.296933 3.295433 [2553] 4.016617 3.763039 4.306874 3.214749 3.993011 4.329343 3.164516 4.711406 [2561] 2.841152 3.609003 4.641009 4.317532 3.893659 4.410588 4.196271 2.727896 [2569] 3.845651 5.309883 4.415730 3.878268 4.251915 4.870495 5.062963 3.793503 [2577] 4.806224 4.502174 3.353477 3.148901 5.306399 3.953882 4.036691 3.953961 [2585] 4.975754 2.802701 3.927404 5.266030 4.360367 3.113790 4.739314 4.164185 [2593] 3.553736 3.509744 4.052196 4.713285 3.651550 3.919886 4.781242 3.929900 [2601] 3.753347 4.409705 4.921629 4.741215 3.840511 4.780366 3.693409 3.959329 [2609] 3.232521 4.388821 4.004698 4.413482 4.347463 3.637161 3.455360 4.075034 [2617] 3.405767 4.681745 3.990377 3.414094 5.490672 4.335666 4.171645 3.839777 [2625] 4.254279 4.691159 3.886976 4.067265 5.114227 4.148390 3.745314 3.903253 [2633] 3.524846 3.792848 3.245142 4.481378 4.198973 2.791255 4.024609 3.674752 [2641] 4.827890 4.835915 3.515534 3.865589 3.932528 2.815585 4.346447 4.044071 [2649] 3.975073 4.324505 4.920007 3.938512 3.919856 4.115971 3.620485 4.090600 [2657] 4.243778 4.040869 3.946638 4.325629 4.235785 5.883828 3.102401 4.055905 [2665] 4.464948 3.230531 5.320070 2.404636 3.713864 5.172095 4.294366 3.191393 [2673] 3.176803 2.720849 3.728141 2.970398 3.780097 3.356904 3.143467 4.450759 [2681] 3.699779 3.895391 3.638481 4.378011 3.478211 3.436249 5.533081 3.991155 [2689] 4.273001 4.581649 4.396686 2.218794 4.089227 4.512472 4.542357 4.318853 [2697] 4.671838 4.155888 4.358723 3.650019 3.505350 4.807692 3.697888 4.663357 [2705] 3.334444 4.749432 4.010168 4.814990 2.956877 3.415982 3.773811 2.608883 [2713] 3.979020 4.321350 4.683101 4.056294 3.289460 3.349656 4.056656 3.861362 [2721] 4.753676 3.678502 3.646633 2.908704 5.426426 3.283448 4.458991 4.286941 [2729] 4.857468 4.605656 4.330623 3.579702 2.691189 4.083852 3.715051 4.641522 [2737] 4.028610 4.102359 2.711883 2.989720 3.679665 3.980551 3.492213 4.316714 [2745] 2.766748 4.331936 4.336891 4.035436 4.099651 3.411974 3.133300 4.567659 [2753] 3.876786 5.002993 4.839079 3.255621 4.851176 3.878537 4.090572 4.257908 [2761] 4.105828 3.799203 3.687915 4.247571 3.972057 3.094823 5.155400 3.405338 [2769] 3.042747 3.975381 4.416665 4.049731 4.339762 4.459617 3.627261 3.885350 [2777] 5.111018 3.001581 3.963518 4.335133 2.977309 4.515804 2.874093 4.661791 [2785] 3.911695 4.659754 3.324675 4.293371 5.270110 4.640678 3.658118 3.567599 [2793] 4.154118 4.082148 4.192833 5.102456 3.306766 4.295822 4.755361 3.685533 [2801] 4.243205 4.436576 4.685074 4.105945 3.140808 4.118579 3.292341 4.544314 [2809] 4.129652 4.013281 4.214159 3.693590 3.584975 3.355330 3.822324 3.597893 [2817] 4.004369 3.976840 4.388576 3.839520 2.603238 4.526432 4.299344 3.047025 [2825] 4.270239 3.221804 3.333016 3.605338 4.145297 4.159703 4.683387 3.243153 [2833] 3.431935 5.065139 4.090493 4.107490 3.369791 3.921014 3.968974 3.281906 [2841] 3.540312 3.963577 6.065440 4.242248 3.123140 4.173999 2.517904 3.889421 [2849] 3.207944 4.874030 3.091789 4.947854 4.068090 3.509323 5.057184 4.368875 [2857] 3.812346 3.798402 3.382833 2.449035 4.522089 5.572795 3.938167 4.756059 [2865] 4.007667 3.785686 3.985000 4.228165 4.544910 4.627387 5.628483 3.933264 [2873] 3.559027 3.175917 3.297137 3.845806 5.095213 3.834148 3.250641 3.802086 [2881] 3.002572 5.009467 3.773217 4.009491 3.988465 3.309555 5.093471 4.544208 [2889] 3.082156 4.115002 4.476533 4.074500 3.147934 4.133283 4.891785 3.865348 [2897] 4.232153 4.596677 3.691360 3.578555 3.961420 4.030861 3.935549 4.509839 [2905] 4.408876 4.250139 3.580215 3.652158 2.881077 3.117186 3.425315 3.975040 [2913] 4.711492 3.928282 2.733806 2.454610 4.048991 4.577548 4.296056 3.463640 [2921] 4.362979 3.968906 3.998930 5.043686 3.249260 4.682099 3.691352 3.048242 [2929] 4.495774 5.180171 4.261962 3.935215 3.385473 4.095498 2.885309 3.390751 [2937] 3.178548 3.350331 1.873144 2.661477 3.805937 4.970393 3.757120 3.912821 [2945] 2.780176 3.910633 3.654643 4.512802 3.741538 4.769370 3.057955 3.111577 [2953] 3.433734 3.780170 4.335941 3.912968 3.922374 3.345211 5.294243 2.935535 [2961] 4.110549 4.204815 4.531653 4.126775 2.824516 4.596569 3.490697 3.308771 [2969] 4.254893 1.998815 4.181352 4.001937 4.731749 3.109355 3.034554 3.710976 [2977] 4.923418 3.718692 3.061743 3.428038 3.244488 4.259739 4.531629 3.501885 [2985] 3.016235 4.064989 3.953218 4.052665 3.886851 3.828230 3.828502 4.449026 [2993] 2.063599 2.802731 3.605909 4.411392 3.850083 4.254796 4.193839 4.424305 [3001] 4.326563 3.440476 3.783756 4.317346 3.410754 4.845767 3.463876 5.019450 [3009] 3.964444 3.698530 3.659415 3.502546 4.868954 4.323373 3.065252 4.101331 [3017] 5.219209 3.228498 3.070290 3.378819 3.501761 3.776125 3.363313 3.640369 [3025] 4.312612 2.389535 3.523831 5.061703 3.960247 2.445474 4.972998 3.543446 [3033] 4.587020 2.916326 5.176768 4.795934 5.326972 3.756061 2.763801 3.428466 [3041] 4.905688 4.397100 4.366765 4.098142 3.787643 4.360905 4.693228 4.943083 [3049] 4.977001 2.703194 4.160784 3.859000 3.094621 3.996187 4.082862 3.287943 [3057] 3.938308 3.829349 2.909039 4.976942 4.049194 4.097815 3.891527 3.554381 [3065] 3.250588 4.214093 3.497840 4.629793 4.605508 3.802558 4.188384 3.911209 [3073] 4.651394 5.279766 5.379031 4.071952 3.873720 4.967782 3.884997 3.971714 [3081] 3.647598 3.829731 4.337141 5.102109 4.357106 4.728176 3.214604 4.886892 [3089] 3.684116 5.132250 3.246221 3.519148 3.929640 5.124605 4.098787 3.704890 [3097] 3.999386 4.178990 3.776908 4.537625 3.642253 3.845688 4.770854 4.137764 [3105] 4.044601 4.067610 3.818254 4.549100 5.082500 3.890045 3.673610 3.599462 [3113] 3.812049 4.478267 3.922419 3.963825 3.387017 3.387188 3.382864 4.326913 [3121] 5.540106 3.801064 4.354175 3.106889 3.943734 4.519823 5.157029 3.844838 [3129] 3.387025 5.901746 2.749544 3.968777 4.881915 4.137213 3.813249 2.513798 [3137] 2.786967 3.007875 4.964534 4.663678 3.377125 4.804300 3.440666 3.566018 [3145] 4.893540 4.004980 3.542889 2.690306 5.006329 4.135563 3.218854 4.050748 [3153] 3.629121 4.344673 3.641205 3.716609 3.874084 3.099596 3.635284 3.079248 [3161] 5.170368 2.980432 4.656331 3.691460 5.047006 4.080344 4.696443 3.209641 [3169] 3.760857 3.950802 5.098101 3.551441 3.995592 3.766330 4.979532 4.188362 [3177] 4.354782 3.698159 3.957825 3.785264 3.911691 2.773437 2.481236 3.714505 [3185] 3.991385 4.445864 3.706797 2.954684 4.532824 3.410828 3.939249 4.941282 [3193] 3.692631 2.850070 4.141745 3.715236 3.949735 4.142528 4.551910 3.983460 [3201] 3.407178 4.123532 4.431306 3.662100 5.006517 4.390667 2.845855 5.485261 [3209] 3.553483 4.250310 3.120270 3.110820 3.609218 4.424198 4.249557 4.056581 [3217] 4.010622 4.104059 4.153298 3.536137 3.523292 3.206219 4.540644 4.304977 [3225] 4.351984 4.000082 2.223081 3.418213 4.381782 4.216015 5.031386 4.039843 [3233] 2.641226 5.528806 3.181142 4.145480 3.846558 3.689413 4.637963 3.831279 [3241] 5.151076 4.888376 5.014041 4.002462 3.367194 2.748198 3.326492 3.817417 [3249] 5.231619 4.904316 4.090717 4.007211 3.539473 2.717322 3.462649 2.711002 [3257] 4.647694 4.498878 3.642422 3.793196 4.919048 3.624487 4.940121 3.977995 [3265] 3.309015 3.627561 4.550764 4.774173 2.472656 5.125549 4.697033 4.055738 [3273] 3.717130 3.828351 4.659940 4.689177 5.239679 3.534513 3.913316 5.468144 [3281] 4.719799 4.450585 3.581072 3.094039 3.853086 4.845004 3.158894 4.516004 [3289] 3.695713 4.276966 3.248205 4.040325 4.747711 4.891915 3.822134 4.111287 [3297] 4.349878 3.801905 4.586501 4.278439 3.508914 4.907182 3.267839 4.248298 [3305] 4.234116 3.486188 3.957370 4.380482 3.861202 3.584288 3.465214 4.678891 [3313] 4.121699 4.015008 4.294934 3.896216 5.547629 3.418026 3.016678 5.088018 [3321] 5.091963 3.543583 3.656715 4.557274 2.017964 4.749560 4.323028 3.735146 [3329] 3.841972 4.399703 2.426733 5.306752 3.446993 4.416103 4.830838 4.567491 [3337] 2.801890 4.766625 4.055736 4.096371 4.887301 3.757126 5.159180 3.104407 [3345] 3.879330 4.453891 4.696956 4.259205 3.374890 3.115119 3.804297 4.224724 [3353] 4.625032 2.970249 3.863109 4.291689 4.467230 3.598640 4.533421 3.104478 [3361] 3.687806 3.939837 3.213737 4.076640 3.967609 2.132940 4.489919 4.646935 [3369] 3.388343 4.946059 4.764968 4.754185 3.877549 3.125564 4.723586 3.843757 [3377] 4.676264 4.583622 3.520333 2.809875 4.678020 3.299599 5.404233 3.978516 [3385] 3.476803 2.790229 4.421784 2.817900 4.628348 3.592541 3.415764 3.972016 [3393] 4.297466 5.138005 4.141854 4.819185 5.586986 3.623260 3.926664 5.072255 [3401] 4.655766 3.019564 3.917115 4.661702 3.520902 3.414018 5.573623 3.595091 [3409] 4.341852 4.747476 3.358012 3.141485 3.774327 3.320030 4.290315 4.462847 [3417] 3.694861 5.295718 3.990128 4.340303 4.503779 2.178194 4.723207 4.077151 [3425] 4.283787 4.320300 3.892636 3.583957 3.735630 4.524471 4.576377 4.061593 [3433] 3.182553 4.620600 3.825807 4.973297 3.747378 2.386860 5.685268 4.110057 [3441] 4.275136 2.189082 5.215783 3.220844 4.250208 4.519830 3.804572 3.024969 [3449] 4.945472 4.883306 4.663872 3.324536 4.094298 4.624902 5.065097 3.972683 [3457] 4.008926 4.738397 5.550777 3.866468 4.508359 3.269406 4.120948 4.183020 [3465] 4.972406 2.784461 3.499165 3.961842 4.197195 3.242402 2.592710 3.446804 [3473] 4.907193 2.873162 4.858805 4.564669 2.869318 3.861524 5.310013 3.992062 [3481] 4.566594 3.495929 3.550164 2.985335 2.919919 4.236977 4.370575 3.633101 [3489] 4.179682 4.671020 4.049077 3.865936 3.498140 3.440704 3.990662 2.506478 [3497] 5.432103 3.943407 4.421149 3.268847 3.514864 3.206963 3.864984 4.284453 [3505] 2.488948 3.577702 3.519307 2.934332 2.955194 4.007748 4.273976 4.921559 [3513] 4.964552 4.649346 4.929603 4.592742 4.110316 3.998970 3.164663 4.629462 [3521] 3.404792 3.685196 4.023497 3.323501 4.481820 3.378496 4.716051 4.007546 [3529] 4.219722 3.070458 3.946001 4.884003 3.782053 4.608092 4.422744 4.393277 [3537] 3.149406 5.156083 3.220509 3.504596 5.076333 4.326644 4.210683 3.830715 [3545] 4.271929 5.130598 3.355070 2.545948 5.011585 4.980208 3.377619 2.472344 [3553] 4.416734 4.414102 4.346404 4.861782 2.627176 4.754203 3.152118 3.199698 [3561] 4.581459 4.034340 4.523826 4.501828 3.921711 4.195206 3.568465 3.158420 [3569] 3.338065 2.954471 4.720975 3.052360 5.498651 4.864300 4.545183 4.253551 [3577] 4.834170 4.514201 3.549545 5.527568 3.706767 3.672425 4.069094 5.304983 [3585] 3.882635 4.569021 3.789943 3.913297 5.252948 4.318849 2.275516 3.842693 [3593] 3.663588 3.979928 5.465633 3.315403 4.311994 4.583676 3.827043 4.441797 [3601] 5.178195 4.068930 3.552584 4.522084 3.039034 3.717164 3.205264 3.669533 [3609] 5.222941 3.465466 4.761373 3.269737 4.501192 3.044478 3.290202 3.874333 [3617] 4.131714 3.658734 5.057231 3.427596 4.534132 3.815492 4.027199 3.280422 [3625] 3.236215 3.173784 4.237700 3.831537 3.880475 4.302487 3.769806 4.150785 [3633] 3.580349 3.369631 2.242521 4.030713 3.876360 3.581726 4.184945 3.252259 [3641] 3.547411 3.417363 3.744949 4.370452 3.708431 4.394654 2.060669 4.863166 [3649] 3.488943 5.572085 4.075770 3.578711 3.748293 4.000670 4.585010 3.893367 [3657] 2.557302 3.740935 4.498384 3.915740 4.644670 5.014477 4.438380 4.017391 [3665] 4.239672 3.538547 3.323706 4.287466 5.146914 3.556267 3.139706 4.571353 [3673] 4.480937 3.705175 4.278198 4.153129 4.300351 4.325911 4.823692 4.608467 [3681] 4.144861 3.726418 3.752264 4.036397 2.865511 4.480527 4.031572 3.425434 [3689] 3.260157 3.469298 4.002295 3.824097 3.869807 4.116356 3.399394 2.693918 [3697] 4.272393 3.470745 3.938981 3.669006 4.161994 4.772495 4.076217 4.376371 [3705] 3.035388 4.822433 2.017572 4.481482 4.621280 3.942623 3.992909 3.816570 [3713] 3.908504 3.531904 4.268210 4.403761 3.821498 4.560989 4.826768 4.976416 [3721] 4.612954 4.107919 3.844791 3.987342 3.332353 4.544657 4.318914 4.173980 [3729] 3.986275 3.976761 3.047420 4.316096 5.770625 3.344432 4.010837 3.489022 [3737] 3.922276 4.335069 3.981557 3.730656 5.332588 4.147990 4.078982 3.740867 [3745] 3.518188 3.226021 5.345134 2.732282 4.506902 4.658449 5.161610 4.207673 [3753] 2.430849 3.950674 4.519864 3.301143 2.860923 3.781493 4.452766 3.883327 [3761] 2.343183 3.482268 3.907796 4.332816 3.922807 3.309653 5.376516 5.048820 [3769] 3.839068 4.727715 5.173454 4.748967 4.469593 3.577540 5.154739 3.939001 [3777] 3.743788 3.198793 4.039393 4.200293 3.871617 3.874695 4.366887 3.722524 [3785] 4.192285 3.439676 3.287100 3.705701 3.524607 3.102174 3.371726 3.863832 [3793] 2.810677 2.376567 3.256967 3.237747 4.858962 4.183930 4.330186 5.087538 [3801] 5.034946 3.883741 3.581797 5.158912 3.547514 3.865991 2.568402 3.510744 [3809] 5.133079 4.253408 4.695193 3.231973 4.249818 3.821490 5.274430 4.039967 [3817] 3.483621 3.014698 3.232006 3.576230 5.359989 3.151640 3.630004 2.999222 [3825] 3.276234 3.419570 4.157217 3.489607 4.885477 4.255027 4.656947 4.240780 [3833] 3.144418 2.603572 3.281735 3.328491 3.998496 2.670246 2.399740 5.079388 [3841] 3.533242 3.244478 5.058207 4.572538 3.302486 5.552711 3.591539 3.820180 [3849] 4.366971 4.612276 3.020357 3.204976 3.187394 4.067008 3.687931 2.806496 [3857] 4.602908 3.799344 3.523634 3.877895 3.910658 2.486364 5.285507 2.583637 [3865] 4.091339 4.368905 3.623240 4.239220 2.680569 3.905395 4.984142 3.786531 [3873] 4.275570 3.747304 4.359100 3.019871 2.773053 3.662173 4.705663 3.382293 [3881] 3.853454 3.574751 3.751033 3.905406 4.344588 3.471627 4.137207 3.729064 [3889] 4.303376 4.936001 4.480886 4.467511 4.651412 4.028338 4.131856 4.262450 [3897] 4.252491 3.314654 3.145931 5.098269 4.700950 4.312600 2.787046 4.323120 [3905] 5.085197 4.357638 3.570640 3.883683 2.936455 3.508896 4.500948 5.085504 [3913] 2.511287 3.197040 4.283703 2.497198 4.111061 3.794260 4.299528 3.877954 [3921] 3.703076 3.606470 3.701712 4.150868 3.502278 4.841693 4.690581 3.988284 [3929] 3.982135 3.677637 4.319193 4.567303 3.999081 3.821669 5.303405 4.176346 [3937] 3.194982 4.505641 3.904545 3.588623 3.230869 3.902777 3.452971 4.218512 [3945] 4.400791 5.262232 4.038177 4.178187 3.468206 4.581212 4.098236 3.679142 [3953] 3.310826 3.677465 4.146678 3.917274 3.994934 4.516164 3.952656 5.380103 [3961] 3.857883 4.356525 2.769992 4.772039 4.580806 3.842587 4.308965 4.657148 [3969] 3.692098 3.626139 2.835723 3.713959 3.852272 3.166814 4.312546 4.102557 [3977] 4.515645 3.003330 5.459428 4.120739 4.430397 3.332994 3.786918 3.832182 [3985] 3.886464 4.760898 4.893968 4.476322 2.709776 4.879379 4.819613 5.149196 [3993] 2.876950 4.124201 3.881649 3.118896 3.921698 4.167544 2.867966 4.214687 [4001] 4.180884 4.042265 3.207523 3.190463 3.842315 4.389718 4.698140 3.869319 [4009] 3.565958 3.233110 4.768446 4.116283 5.169230 4.130172 4.159658 3.473060 [4017] 4.611847 4.279346 3.388059 3.783573 3.321028 3.808865 2.142472 3.540234 [4025] 4.628629 4.338717 3.967820 2.922664 3.778578 4.130599 4.869511 2.814375 [4033] 6.074286 3.727395 3.546942 4.000678 3.445792 3.723799 3.957216 4.058409 [4041] 4.741860 4.250541 4.096816 3.853888 4.686264 3.710121 2.825694 3.475039 [4049] 3.987455 4.775725 4.513201 3.693411 4.473793 3.682354 4.279604 5.350278 [4057] 3.824502 3.926321 5.585783 3.943504 3.041949 3.891296 4.001129 5.038060 [4065] 3.298708 4.167369 3.969694 3.837882 4.819286 5.307574 4.853699 4.357601 [4073] 4.304172 3.127085 5.279025 4.432745 4.346770 4.771141 3.864821 3.017833 [4081] 3.420723 5.208958 4.143317 4.039560 3.802213 3.766281 4.076411 3.786587 [4089] 4.635398 6.186232 3.764635 4.467004 3.952299 5.195388 5.016187 3.172451 [4097] 4.101882 3.626200 4.723564 4.202625 5.435073 4.299511 4.167218 3.966250 [4105] 4.701279 4.763200 4.407921 4.294031 4.052448 4.824307 4.025358 3.277120 [4113] 4.661166 3.364624 3.856382 3.702814 4.122400 3.239329 3.299456 4.970068 [4121] 3.694818 4.978515 4.041795 4.543961 3.254914 3.334666 4.166746 3.947824 [4129] 4.318643 4.312479 4.490560 4.456862 4.497009 4.013757 5.141698 3.469990 [4137] 1.923574 4.262025 2.926411 4.598099 4.088759 4.233665 3.464728 4.933057 [4145] 4.142525 4.839403 3.663982 4.038210 3.430623 5.011369 4.210748 3.964701 [4153] 5.137906 4.419041 3.996240 3.326054 3.588457 3.123657 3.961921 3.332687 [4161] 4.160451 2.577618 3.497408 4.818274 4.761268 4.244414 4.487938 2.697967 [4169] 4.303664 2.826654 3.853947 3.944690 3.932581 4.640670 3.916914 3.905836 [4177] 3.382169 4.138192 3.606030 3.196964 4.625162 3.362799 3.474687 4.374107 [4185] 3.883409 3.544031 4.500097 3.327222 3.901890 4.441244 3.962365 4.594077 [4193] 5.388709 3.938996 3.202334 2.910701 3.587427 3.592626 6.101514 3.228346 [4201] 4.818734 4.094925 3.962788 3.857858 3.926234 4.230980 3.862187 3.622408 [4209] 3.991376 3.781023 3.975860 4.600644 3.862477 3.871106 2.887893 3.470958 [4217] 4.060684 4.239538 3.429865 3.570486 4.971504 3.640516 3.383015 3.960440 [4225] 4.338144 4.130591 3.263919 4.485379 4.179978 4.572628 3.412492 4.365802 [4233] 2.873551 4.406710 3.933234 2.518403 2.952899 4.868920 4.983832 3.076425 [4241] 3.724756 4.644264 5.033631 4.020941 3.400526 3.570502 4.174172 3.316774 [4249] 4.055245 4.635869 4.401806 4.604569 3.324999 4.275025 4.476562 3.775394 [4257] 3.356602 3.412154 4.257334 4.039009 3.666965 4.011963 3.473412 4.604962 [4265] 3.624950 4.447072 2.683435 3.876793 4.967663 4.158446 3.480824 4.767328 [4273] 3.202947 3.797126 4.493470 3.853515 3.350494 3.449819 4.874943 3.791953 [4281] 3.482916 4.673371 3.294791 2.934650 5.727592 4.062663 4.071916 3.455169 [4289] 3.855051 4.901985 3.291204 4.956084 3.877338 4.904689 3.269241 3.386865 [4297] 4.011152 4.677442 5.279140 3.357085 2.744472 2.875178 4.520771 3.408781 [4305] 4.449548 5.236093 4.452626 4.761137 3.085929 2.199480 3.938965 4.720189 [4313] 3.585602 4.471141 3.948452 4.314612 4.610977 4.571649 4.215394 4.217455 [4321] 4.252591 3.197279 4.228835 4.281990 3.483817 5.205492 4.149612 4.376719 [4329] 3.052675 4.165631 3.007714 3.384861 4.907608 4.324839 2.703366 4.878765 [4337] 4.259757 4.868646 3.416552 2.781199 4.321759 4.069845 3.945097 3.446389 [4345] 3.808873 3.498614 3.337143 3.865372 4.124956 4.657823 4.149184 4.801950 [4353] 4.087268 3.567171 4.583586 3.188975 3.800101 2.873276 3.586254 4.953653 [4361] 3.084006 2.833152 4.339161 3.671960 3.411986 3.477011 4.086676 3.935855 [4369] 3.603240 3.427160 2.013812 4.537755 4.342770 5.042367 4.823481 3.694799 [4377] 3.901838 3.968502 4.065613 4.419507 3.667522 4.649330 3.983232 3.774533 [4385] 4.442673 4.407841 4.252618 2.761685 4.708443 4.043835 4.711206 3.949801 [4393] 4.434601 3.777195 4.565169 3.895613 4.268870 3.090435 3.787777 4.356076 [4401] 3.747933 4.095849 3.461804 3.175977 4.689840 3.466690 4.653442 3.298252 [4409] 4.578876 5.132200 3.470374 4.833760 4.271720 3.771284 4.435560 3.033979 [4417] 3.825165 3.873968 3.975917 4.243452 3.068284 4.086642 4.350858 6.078113 [4425] 4.227185 4.196474 4.031193 4.319897 3.734797 4.496295 2.296283 4.754824 [4433] 4.482212 5.105121 4.087835 3.564495 4.753559 4.997719 3.618337 5.470038 [4441] 3.002614 4.598486 5.040972 4.129860 4.181005 4.582050 4.548800 3.479717 [4449] 3.916825 4.213722 4.542070 3.681775 3.584470 3.972183 5.149335 2.727886 [4457] 2.512219 3.310671 3.712533 4.280039 4.336651 3.788887 3.648281 4.569853 [4465] 2.920635 3.818396 3.577212 3.386333 4.048615 3.427162 3.813611 3.857839 [4473] 4.964327 3.957182 3.201057 5.539599 3.645729 3.960257 4.051678 4.349922 [4481] 4.033764 4.167848 5.163724 2.673876 4.205140 3.557925 3.657028 4.342288 [4489] 4.022692 4.540208 5.109004 3.554960 4.196106 4.096669 4.784344 5.632745 [4497] 4.953321 4.536662 3.178675 3.392702 4.631591 3.986579 2.264124 4.228187 [4505] 4.473744 5.110832 2.846049 4.334365 4.846755 2.500042 4.356097 4.288748 [4513] 3.241489 3.271977 2.978955 4.088506 4.894605 3.345648 4.074929 4.092285 [4521] 3.587162 5.412039 4.779789 3.568462 4.119804 3.018874 4.196436 2.631643 [4529] 4.477445 3.155198 4.228881 4.362812 4.065997 4.184319 3.574575 3.410072 [4537] 3.740996 5.073651 4.963661 3.423573 5.268416 4.746715 4.651372 4.412654 [4545] 4.633962 4.800311 4.161683 3.664888 4.737270 4.409239 5.383383 3.934582 [4553] 3.962561 4.327743 2.655253 4.098032 3.140413 4.464734 4.737739 3.346405 [4561] 5.275894 3.963525 3.455951 4.548422 3.877216 3.974544 4.166903 2.873800 [4569] 3.775745 4.101481 3.665584 5.003829 4.728839 3.667609 5.263214 4.455397 [4577] 4.095974 4.034193 4.785553 4.236430 2.766000 3.887707 3.634634 3.656866 [4585] 4.896998 4.482757 3.595586 3.197411 3.736006 3.591312 4.937999 3.777664 [4593] 4.330255 2.893425 4.763254 3.081804 4.971139 4.013124 4.571335 4.259234 [4601] 4.134151 4.169139 4.564849 3.242717 6.123271 3.637404 4.211430 3.839243 [4609] 4.339503 3.588770 3.978898 4.482914 3.979994 4.362010 4.327900 2.897663 [4617] 4.022475 3.345276 4.085257 2.677244 3.349134 3.901005 5.310385 5.206288 [4625] 4.278551 3.261683 3.868954 3.968201 3.869995 3.891864 3.749763 4.192710 [4633] 3.235976 3.578723 3.684652 3.910436 5.005468 3.872725 3.881646 2.773109 [4641] 4.345683 4.449383 3.846098 3.263788 5.293245 3.494773 3.272334 4.075785 [4649] 3.444304 4.477700 4.180992 4.019765 4.945895 4.616167 4.196738 3.913829 [4657] 3.913324 4.114523 4.720278 2.864015 4.630727 3.910221 3.150012 3.675406 [4665] 3.435522 3.940836 4.171097 4.903757 4.186810 4.437089 3.857428 4.170608 [4673] 3.906549 3.846751 3.060347 4.760152 3.434358 3.529164 3.641860 1.786913 [4681] 4.149999 3.170624 3.514180 4.086356 3.576161 2.471821 4.178613 3.777183 [4689] 5.384973 4.546414 3.404255 3.670467 4.433411 4.032819 4.866429 3.728510 [4697] 4.234005 2.929564 4.084969 3.860556 3.279858 3.795120 5.261132 4.185383 [4705] 4.041694 3.548452 4.673669 3.843067 4.779291 3.460906 3.828938 4.138466 [4713] 3.497728 4.103421 4.723428 3.096048 3.550804 2.334029 4.041975 3.448863 [4721] 4.335719 3.615786 3.297189 4.295079 3.690048 4.035945 3.059487 4.059027 [4729] 4.347466 4.001317 3.810264 3.359507 3.022063 3.924493 3.660285 4.202033 [4737] 4.725138 4.723127 3.583859 4.793011 4.006457 4.886267 3.847763 4.607323 [4745] 4.132846 4.177681 3.920053 3.580796 4.436092 2.928524 4.441497 4.072157 [4753] 3.373805 4.360546 4.552434 4.768222 4.366507 3.759897 3.913142 4.644793 [4761] 4.165084 3.470889 3.472929 3.626657 3.045130 5.365825 4.086092 4.014879 [4769] 4.103040 3.922162 3.774600 4.143172 3.599320 4.572811 4.925106 5.284079 [4777] 4.592582 4.970223 4.119879 4.417827 4.627083 4.956551 4.365532 5.644372 [4785] 4.179298 3.984209 3.311474 4.660160 3.538879 2.909663 4.317719 4.410013 [4793] 4.043544 3.511762 4.032863 3.379716 4.047602 3.978889 4.898448 3.992773 [4801] 4.103954 4.750464 4.128589 3.587698 4.266122 3.592117 2.893650 3.762869 [4809] 3.736127 5.012580 3.828644 3.604003 3.445078 4.037462 5.331506 4.217333 [4817] 5.106792 3.885514 4.511388 3.591612 4.339230 4.768531 4.023224 4.054987 [4825] 2.460069 3.599728 4.111318 4.453658 4.452265 4.344485 4.123420 4.892387 [4833] 3.484438 4.217326 3.334566 4.448379 4.440740 2.964988 4.848976 4.242146 [4841] 3.680673 4.283991 4.348469 4.120507 3.937899 3.841612 4.127128 4.206275 [4849] 3.432797 4.127592 4.272525 4.055254 3.014149 4.954884 4.460402 3.359944 [4857] 4.650283 4.066696 3.169554 4.276580 3.577213 5.303263 3.262185 3.509755 [4865] 3.774406 3.331119 5.317301 3.063570 4.732440 4.215700 3.003055 2.844313 [4873] 4.230665 2.789995 5.417745 2.955994 5.012049 4.810591 3.884262 3.074300 [4881] 4.347047 3.674938 3.902000 3.582671 3.215077 3.205162 3.126232 3.742736 [4889] 4.601029 4.201805 3.508844 3.821481 5.086466 3.134082 3.449160 4.180986 [4897] 3.300658 3.505713 3.927354 4.093023 3.834013 2.773037 3.073127 3.236143 [4905] 3.869504 4.100808 4.124551 3.930855 3.265755 4.120407 2.775705 3.253530 [4913] 3.652605 3.876757 4.366254 3.803543 4.108737 3.596753 3.734589 4.022982 [4921] 3.821862 3.405128 3.923376 3.921168 4.545310 5.435496 5.103118 4.288983 [4929] 4.150211 4.589622 5.150974 4.185044 5.291465 4.699440 4.943712 4.120253 [4937] 4.042478 4.349621 3.981637 4.268338 3.771745 3.870007 4.094693 3.340620 [4945] 4.495287 4.708345 3.390139 4.471884 4.913314 4.046434 4.002637 4.442803 [4953] 3.202585 4.038977 3.278381 5.207297 4.639277 4.440066 3.633967 2.271324 [4961] 3.188493 4.679258 3.996289 4.052971 2.784417 3.478492 4.284468 4.057137 [4969] 4.912872 2.665741 4.688983 4.809197 4.169908 2.845400 2.168624 3.657462 [4977] 2.303746 3.468574 4.877533 3.824841 3.773719 3.073456 3.335326 4.563155 [4985] 3.639809 3.187694 4.889300 3.489176 4.572274 4.409559 3.482388 3.678538 [4993] 5.364401 5.447219 4.190570 4.283750 4.040036 2.812235 3.579864 4.037549 [5001] 5.269514 4.019584 3.304182 3.277064 3.888446 2.508798 3.443243 3.480012 [5009] 4.363923 3.987240 3.244290 3.462831 4.280861 3.923331 4.516776 4.181221 [5017] 4.557114 2.580363 4.881039 4.599419 4.320223 3.328142 3.035888 4.209623 [5025] 4.524976 3.687955 4.495346 4.064310 2.985787 3.659062 3.597026 3.592965 [5033] 3.233999 3.982984 3.173891 3.205207 2.248948 4.669864 4.129002 4.510077 [5041] 4.669691 3.879219 4.622143 3.046579 3.192302 4.542437 3.375350 4.182285 [5049] 4.434519 4.648207 2.874819 3.581451 3.276435 4.314914 4.449551 4.748623 [5057] 3.475376 3.476625 3.239044 4.225705 4.461599 5.240804 3.030245 4.666517 [5065] 5.304392 3.520802 4.177091 5.398945 5.140429 3.568852 3.552429 4.462385 [5073] 2.890254 4.126392 3.226777 3.162424 4.650322 4.566166 4.445792 4.543822 [5081] 4.039817 3.664322 4.203018 4.273614 3.871718 5.509971 4.609815 3.356105 [5089] 4.456856 4.319260 3.676424 3.690212 4.321883 4.576601 3.725241 4.037401 [5097] 3.444339 3.628802 3.816502 4.740078 3.601049 2.963252 4.696708 4.391200 [5105] 4.253927 4.023587 3.431030 4.180867 5.386322 3.485192 3.755214 3.428297 [5113] 3.956178 3.802175 4.082769 3.784819 3.585230 4.161384 3.123868 4.639993 [5121] 4.468003 4.298452 3.950458 2.747249 3.749936 3.325025 4.015716 3.942996 [5129] 3.526107 3.836825 2.708311 4.311671 3.991624 3.628400 2.624697 4.029088 [5137] 3.261109 2.955372 3.761310 4.184698 4.558079 3.478434 4.762101 3.460216 [5145] 5.153647 2.820028 2.985862 3.423731 4.007526 5.096145 3.817257 3.497160 [5153] 4.471815 3.785757 4.133582 2.830572 3.686022 4.566795 3.908166 3.930055 [5161] 3.129567 4.314403 2.241978 4.207697 3.304543 4.856198 4.326321 5.009300 [5169] 5.346853 3.723067 3.782463 4.244892 3.969440 4.493913 2.751592 3.942464 [5177] 4.707555 5.456590 5.012314 3.914683 5.062977 4.369073 3.662507 3.541427 [5185] 2.334499 4.850694 2.334415 3.861645 3.101423 3.137050 3.264842 4.913836 [5193] 3.379962 4.032273 3.181417 5.133687 4.451239 3.208751 3.476343 3.388677 [5201] 4.655427 2.667285 3.159067 5.114143 3.868052 3.972959 4.203320 5.174206 [5209] 4.393308 3.632408 4.071537 3.396115 4.491014 4.323971 4.385108 4.268781 [5217] 3.572649 4.930824 4.594000 4.588160 4.978997 4.117438 4.740295 3.931134 [5225] 3.651737 3.326637 4.164710 4.006957 3.016761 3.239991 3.069374 3.440572 [5233] 4.413712 3.641222 4.656700 4.382834 4.223236 3.066116 4.791064 4.282329 [5241] 4.739927 4.905741 4.592810 4.894669 4.885423 4.694600 4.126591 3.379234 [5249] 3.952606 4.379006 4.049831 4.691790 3.989152 3.979014 2.940252 4.402858 [5257] 4.487736 3.422263 3.302014 4.421041 4.159122 3.984712 3.886185 3.670615 [5265] 2.595679 4.761401 3.205035 3.043129 3.672853 3.985135 3.855508 3.456111 [5273] 4.895536 3.312982 4.084405 3.447263 3.388452 3.816452 3.890722 3.711429 [5281] 4.246773 4.256899 3.504459 4.565017 2.941466 4.600047 4.216075 3.158200 [5289] 3.764275 3.705110 5.203896 4.157929 3.447244 2.942230 4.155232 4.015217 [5297] 3.986925 4.056513 4.702857 3.120893 2.939734 3.536196 4.036843 4.254742 [5305] 3.778420 4.119876 3.953070 4.446286 3.395143 3.552623 3.113508 4.726735 [5313] 4.658231 4.322722 4.169868 4.422149 4.727452 4.830678 4.706584 3.642643 [5321] 3.763744 3.233128 4.696350 2.982238 3.634149 3.611974 4.071703 4.287568 [5329] 2.997054 3.643768 4.110135 3.286120 4.233047 2.957415 4.390512 4.584781 [5337] 4.328985 4.943621 6.065445 4.487394 4.913127 2.689345 4.639579 3.764972 [5345] 3.901042 4.428304 4.214847 5.278620 4.158910 4.396296 4.417787 3.538017 [5353] 3.364488 4.011645 3.247549 4.114289 3.192595 3.414149 3.931185 2.442577 [5361] 2.646452 5.012097 3.664282 4.161175 3.335591 5.731014 4.549387 4.189440 [5369] 2.864065 3.500392 5.297806 2.880154 4.317465 3.583839 4.836008 4.283970 [5377] 4.378349 3.692550 3.647147 4.078340 4.845840 4.322691 4.610936 3.677471 [5385] 3.693771 4.927146 4.215472 4.638287 4.004920 4.383599 2.914316 3.756339 [5393] 3.599147 3.990278 4.937611 3.218812 3.740789 5.182795 3.417067 5.379620 [5401] 4.167944 4.354640 4.639368 4.211709 4.506872 5.327396 3.187730 3.930368 [5409] 3.957000 4.072081 3.006559 4.022003 3.436989 3.133012 3.729732 3.167769 [5417] 4.373325 4.128252 3.318201 4.568689 4.020929 4.294562 4.199748 4.010901 [5425] 4.550531 5.539583 3.652127 3.979880 3.651613 3.948094 5.000447 4.970901 [5433] 2.849964 3.560955 3.631259 4.325835 4.582015 4.719388 3.785806 4.975032 [5441] 3.802329 3.178196 3.713256 3.190813 4.109688 4.724500 2.958690 3.836656 [5449] 3.476620 4.337164 4.199665 4.561503 3.843581 4.852130 4.573257 4.023234 [5457] 5.059532 4.655519 2.798739 4.144192 3.356526 4.252771 4.063452 4.124256 [5465] 5.272415 3.327418 5.334175 4.567309 4.111120 4.391951 3.682301 3.728828 [5473] 3.307847 3.722737 4.212900 4.615658 4.841885 4.133228 4.092949 1.957569 [5481] 3.872168 4.542689 3.600821 3.765816 2.455570 3.295400 3.110102 4.395538 [5489] 3.760404 3.665412 4.007881 3.802637 4.352151 3.112553 3.896398 5.001567 [5497] 4.249403 4.612712 4.201730 3.629611 4.032895 3.516815 3.048171 3.904604 [5505] 4.361587 4.138242 3.689426 4.302433 4.490372 3.200791 4.232931 4.529322 [5513] 4.564745 3.424885 5.410943 3.249848 4.834013 3.841072 3.742518 4.819763 [5521] 4.591903 4.092684 2.410739 4.198363 5.073639 4.323770 4.187234 3.734815 [5529] 2.670024 4.054755 3.184509 3.125485 3.156592 3.139606 3.132341 3.478517 [5537] 4.192048 3.301220 2.916158 4.867482 3.971583 3.713344 4.186447 4.567642 [5545] 3.757598 4.280856 3.554771 3.465070 4.022647 4.136184 4.397135 4.042081 [5553] 3.942328 3.540254 5.440694 3.692494 3.150252 3.978687 3.614374 3.699955 [5561] 3.241331 4.075890 3.913848 4.506873 3.256400 5.156748 3.376599 4.917456 [5569] 5.461279 3.789265 3.126340 3.649080 5.084796 4.069474 3.158485 4.379694 [5577] 3.873538 4.255865 3.384009 3.189619 4.135546 4.570326 3.737085 4.390622 [5585] 2.859876 4.280896 3.453756 3.179164 3.429897 4.846868 4.024010 3.558482 [5593] 4.425282 4.035763 4.196118 5.080995 3.720245 4.115180 3.303585 3.231113 [5601] 4.153405 3.655422 3.410993 3.138245 4.501637 4.251640 3.712444 3.485536 [5609] 3.558025 3.458311 3.256012 3.506584 3.262387 5.151382 4.660449 5.167080 [5617] 4.711550 3.550653 4.610610 4.138514 3.702593 4.122940 3.174922 3.959283 [5625] 3.597958 3.222387 5.367204 4.720987 3.297584 4.474279 4.056503 3.530521 [5633] 3.788228 3.750976 4.465189 4.333634 5.525975 3.468307 3.899400 4.026607 [5641] 4.876171 3.238518 4.970643 2.875724 4.351197 4.311398 4.631135 4.870412 [5649] 3.440480 3.510976 4.937832 5.538922 2.965903 4.839381 4.185297 3.981422 [5657] 3.881048 2.973313 3.550088 3.977540 3.754229 4.380440 5.052389 3.904679 [5665] 3.713648 3.747091 4.277605 3.780965 3.936245 3.326483 3.414345 3.979681 [5673] 5.406092 4.544300 3.086185 4.309150 4.302224 4.055054 3.805200 4.243508 [5681] 3.722461 4.505364 3.669391 4.114371 3.110293 3.954685 4.897215 3.713740 [5689] 2.341867 4.547775 3.246695 3.777771 5.337782 3.855811 3.550678 4.111382 [5697] 4.620048 3.687840 3.275526 2.974186 4.440138 3.697588 4.309263 3.871380 [5705] 4.445600 5.901075 2.842366 4.224638 4.365277 4.005899 5.093247 2.867483 [5713] 3.770702 4.932496 4.024357 3.195761 4.886248 5.109621 4.577117 4.615028 [5721] 4.865132 3.355578 4.439311 4.881531 3.157550 3.512925 4.863203 3.103597 [5729] 4.189925 4.733188 3.942469 4.965231 3.093950 4.027770 4.892845 4.429633 [5737] 3.593941 3.628915 3.582660 3.974295 3.849436 4.412797 4.168864 5.643609 [5745] 3.165496 4.170986 3.095794 4.004304 3.420575 4.002447 3.453316 3.931854 [5753] 3.386329 4.187256 4.001512 4.111201 5.069231 3.975869 4.234176 4.380049 [5761] 3.287996 3.894653 4.160759 4.436208 2.669769 3.592212 3.635316 4.921794 [5769] 3.077089 3.774589 5.129967 3.429603 3.315918 3.770028 3.320906 4.990645 [5777] 3.256730 3.544925 3.037967 3.697398 3.980447 3.465220 4.666731 3.431693 [5785] 4.512064 3.950834 4.231199 3.969391 4.599244 3.684895 4.951091 3.173393 [5793] 3.645901 4.604428 4.162149 5.616849 3.450593 5.341839 3.322954 3.466876 [5801] 3.576190 3.427063 4.347587 4.428805 3.217411 4.633180 4.245959 4.031234 [5809] 3.802756 4.197301 4.213576 5.080355 4.096949 3.955927 4.455227 3.735303 [5817] 4.646921 3.123859 3.754193 3.340773 3.746865 4.159605 3.880978 4.271648 [5825] 2.488543 3.802786 3.599180 3.637316 4.172158 5.139205 2.892570 2.364727 [5833] 4.207943 4.256307 3.467744 3.196653 4.519473 3.319375 2.344526 4.785133 [5841] 3.895412 3.944601 4.314204 5.242420 3.968286 3.390589 3.631164 4.914812 [5849] 4.581234 4.828608 3.599331 4.413935 5.014970 3.078745 4.764113 4.157622 [5857] 3.012036 3.280770 3.857140 3.936607 2.676129 4.247898 3.579370 3.542736 [5865] 4.482381 3.734207 4.579371 4.237434 4.163733 4.837151 4.787406 4.137585 [5873] 4.393293 4.124837 3.672295 4.424284 3.712342 4.020242 3.681164 3.767266 [5881] 4.868675 3.118717 4.346208 4.446594 4.406078 3.577661 3.789054 5.180712 [5889] 4.749393 4.294313 3.342098 4.862268 3.997996 4.266956 4.386063 3.984576 [5897] 5.156276 3.413837 4.213673 4.146830 3.478270 3.351854 4.219662 1.847433 [5905] 2.449326 3.782710 3.042703 3.694579 3.644770 3.070702 3.617009 4.097816 [5913] 4.652884 4.504899 5.364194 3.809905 4.493884 3.707103 3.828338 3.428042 [5921] 3.063839 3.027011 4.404477 3.402308 3.939166 3.492039 4.589158 4.621827 [5929] 4.086302 4.446745 3.854335 3.687536 2.972371 3.843529 3.650395 5.029576 [5937] 4.458863 5.014627 3.175358 2.441624 4.935079 3.657407 3.719439 4.288285 [5945] 3.292619 3.741571 3.178707 3.685679 3.134851 2.617208 4.624728 3.681792 [5953] 4.435500 3.960154 3.026442 3.938928 3.645711 3.832453 3.146440 3.227341 [5961] 4.511426 4.089620 4.480091 3.695679 3.959940 3.252058 3.643400 3.967664 [5969] 4.450447 3.930301 5.509000 2.976201 3.547791 3.887766 4.580081 3.088510 [5977] 3.605081 3.700235 4.687222 4.548658 5.015143 4.652250 5.277091 4.415913 [5985] 5.053294 3.299570 4.686716 3.473600 2.299193 4.981583 4.433232 4.133381 [5993] 3.044545 4.297736 4.871718 3.532519 4.345808 2.789449 4.455478 2.977042 ``` ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% * tibble(gpa = .) ``` ] .panel2-gpas-auto[ ``` # A tibble: 6,000 × 1 gpa <dbl> 1 4.63 2 3.18 3 3.37 4 2.99 5 3.77 6 1.97 7 3.26 8 4.19 9 4.52 10 4.17 # … with 5,990 more rows ``` ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% * filter(gpa < 4.0 & gpa > 0) ``` ] .panel2-gpas-auto[ ``` # A tibble: 3,030 × 1 gpa <dbl> 1 3.18 2 3.37 3 2.99 4 3.77 5 1.97 6 3.26 7 3.87 8 3.31 9 3.96 10 3.94 # … with 3,020 more rows ``` ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> *campus_gpas ``` ] .panel2-gpas-auto[ ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas *campus_gpas ``` ] .panel2-gpas-auto[ ``` # A tibble: 3,030 × 1 gpa <dbl> 1 3.18 2 3.37 3 2.99 4 3.77 5 1.97 6 3.26 7 3.87 8 3.31 9 3.96 10 3.94 # … with 3,020 more rows ``` ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% * ggplot() ``` ] .panel2-gpas-auto[ <!-- --> ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% ggplot() + * scale_x_continuous(limits = c(0,4)) ``` ] .panel2-gpas-auto[ <!-- --> ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% ggplot() + scale_x_continuous(limits = c(0,4)) + * aes(x = gpa) ``` ] .panel2-gpas-auto[ <!-- --> ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% ggplot() + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + * geom_rug(alpha = .3) ``` ] .panel2-gpas-auto[ <!-- --> ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% ggplot() + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug(alpha = .3) + * geom_histogram() ``` ] .panel2-gpas-auto[ <!-- --> ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% ggplot() + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug(alpha = .3) + geom_histogram() + * ggxmean::geom_x_mean() ``` ] .panel2-gpas-auto[ <!-- --> ] --- count: false .panel1-gpas-auto[ ```r set.seed(2022) rnorm(n = 6000, mean = 4, sd = .7) %>% tibble(gpa = .) %>% filter(gpa < 4.0 & gpa > 0) -> campus_gpas campus_gpas %>% ggplot() + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug(alpha = .3) + geom_histogram() + ggxmean::geom_x_mean() + * ggxmean::geom_x_mean_label() ``` ] .panel2-gpas-auto[ <!-- --> ] <style> .panel1-gpas-auto { color: black; width: 38.6060606060606%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel2-gpas-auto { color: black; width: 59.3939393939394%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel3-gpas-auto { color: black; width: NA%; hight: 33%; float: left; padding-left: 1%; font-size: 80% } </style> --- count: false .panel1-gpas_sample-auto[ ```r *set.seed(2022) ``` ] .panel2-gpas_sample-auto[ ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) *campus_gpas ``` ] .panel2-gpas_sample-auto[ ``` # A tibble: 3,030 × 1 gpa <dbl> 1 3.18 2 3.37 3 2.99 4 3.77 5 1.97 6 3.26 7 3.87 8 3.31 9 3.96 10 3.94 # … with 3,020 more rows ``` ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% * sample_n(size = 30) ``` ] .panel2-gpas_sample-auto[ ``` # A tibble: 30 × 1 gpa <dbl> 1 3.40 2 3.94 3 3.28 4 3.29 5 3.14 6 3.72 7 3.59 8 3.45 9 3.18 10 2.73 # … with 20 more rows ``` ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% * ggplot() ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + * labs(title = "A single sample of 30 observations") ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + labs(title = "A single sample of 30 observations") + * scale_x_continuous(limits = c(0,4)) ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + labs(title = "A single sample of 30 observations") + scale_x_continuous(limits = c(0,4)) + * aes(x = gpa) ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + labs(title = "A single sample of 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + * geom_rug() ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + labs(title = "A single sample of 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug() + * geom_dotplot() ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + labs(title = "A single sample of 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug() + geom_dotplot() + * ggxmean::geom_x_mean() ``` ] .panel2-gpas_sample-auto[ <!-- --> ] --- count: false .panel1-gpas_sample-auto[ ```r set.seed(2022) campus_gpas %>% sample_n(size = 30) %>% ggplot() + labs(title = "A single sample of 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug() + geom_dotplot() + ggxmean::geom_x_mean() + * ggxmean::geom_x_mean_label() ``` ] .panel2-gpas_sample-auto[ <!-- --> ] <style> .panel1-gpas_sample-auto { color: black; width: 38.6060606060606%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel2-gpas_sample-auto { color: black; width: 59.3939393939394%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel3-gpas_sample-auto { color: black; width: NA%; hight: 33%; float: left; padding-left: 1%; font-size: 80% } </style> --- count: false .panel1-gpas_sample16-auto[ ```r *set.seed(1234) ``` ] .panel2-gpas_sample16-auto[ ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) *campus_gpas ``` ] .panel2-gpas_sample16-auto[ ``` # A tibble: 3,030 × 1 gpa <dbl> 1 3.18 2 3.37 3 2.99 4 3.77 5 1.97 6 3.26 7 3.87 8 3.31 9 3.96 10 3.94 # … with 3,020 more rows ``` ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% * ggplot() ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + * ggsample::facet_sample(n_facets = 16, n_sampled = 30) ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + * labs(title = "Different hypothetical outcomes for sampling 30 observations") ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + labs(title = "Different hypothetical outcomes for sampling 30 observations") + * scale_x_continuous(limits = c(0,4)) ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + labs(title = "Different hypothetical outcomes for sampling 30 observations") + scale_x_continuous(limits = c(0,4)) + * aes(x = gpa) ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + labs(title = "Different hypothetical outcomes for sampling 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + * geom_rug() ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + labs(title = "Different hypothetical outcomes for sampling 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug() + * geom_dotplot() ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + labs(title = "Different hypothetical outcomes for sampling 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug() + geom_dotplot() + * ggxmean::geom_x_mean() ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] --- count: false .panel1-gpas_sample16-auto[ ```r set.seed(1234) campus_gpas %>% ggplot() + ggsample::facet_sample(n_facets = 16, n_sampled = 30) + labs(title = "Different hypothetical outcomes for sampling 30 observations") + scale_x_continuous(limits = c(0,4)) + aes(x = gpa) + geom_rug() + geom_dotplot() + ggxmean::geom_x_mean() + * ggxmean::geom_x_mean_label(size = 3, alpha = .6) ``` ] .panel2-gpas_sample16-auto[ <!-- --> ] <style> .panel1-gpas_sample16-auto { color: black; width: 38.6060606060606%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel2-gpas_sample16-auto { color: black; width: 59.3939393939394%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel3-gpas_sample16-auto { color: black; width: NA%; hight: 33%; float: left; padding-left: 1%; font-size: 80% } </style> --- count: false .panel1-gpas_sample1000-auto[ ```r *set.seed(1243) ``` ] .panel2-gpas_sample1000-auto[ ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) *campus_gpas ``` ] .panel2-gpas_sample1000-auto[ ``` # A tibble: 3,030 × 1 gpa <dbl> 1 3.18 2 3.37 3 2.99 4 3.77 5 1.97 6 3.26 7 3.87 8 3.31 9 3.96 10 3.94 # … with 3,020 more rows ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% * pull(gpa) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.178658 3.371760 2.988849 3.768290 1.969560 3.258521 3.870398 3.312721 [9] 3.963051 3.943770 3.542127 3.334522 3.756172 3.398313 3.637437 3.832712 [17] 2.908757 3.845637 3.427964 3.881896 3.811674 3.212698 2.998448 3.444912 [25] 3.818372 3.086606 3.682517 3.063090 3.095618 3.783648 3.416258 3.982816 [33] 3.203854 3.904143 3.853518 3.288864 3.247915 2.463097 3.967839 3.742219 [41] 3.575049 2.684561 3.847478 3.147647 3.472145 3.632942 3.302266 2.598391 [49] 3.666913 3.033205 3.351266 3.775690 3.114059 3.637035 3.778816 2.769191 [57] 2.835233 2.639316 2.901264 3.808692 3.007123 3.938486 3.248617 2.681788 [65] 3.135042 3.115374 3.199995 3.526226 3.248263 3.317039 3.211608 2.621481 [73] 3.592608 2.766245 3.630522 3.037971 2.646401 2.953017 3.019282 3.660876 [81] 3.148675 3.830224 3.008953 3.265378 3.664899 3.790386 2.619827 3.101669 [89] 3.660731 3.444683 3.830987 3.591758 3.861449 3.577739 3.237946 3.882202 [97] 3.863822 2.519265 3.360853 2.745693 3.536958 3.739409 3.525111 3.446366 [105] 2.732338 3.804060 3.491988 3.834131 2.935920 3.169756 3.716870 3.799026 [113] 3.261683 3.539906 3.709998 3.612232 3.350894 3.589001 3.219221 3.263349 [121] 2.991949 3.435904 3.450174 3.205255 3.362002 3.834734 3.023779 3.665573 [129] 3.426018 3.077155 3.869172 3.921391 3.078592 3.764263 3.234262 3.393481 [137] 3.303607 2.937937 3.971876 2.749424 3.803653 3.712169 3.675599 2.281544 [145] 3.446063 2.751335 3.041120 3.223133 3.270347 3.867704 2.998167 3.728778 [153] 3.648178 3.102869 3.261252 3.662475 3.847134 3.824509 3.618042 3.623520 [161] 3.535057 2.440564 3.999490 3.070709 3.187905 3.805857 3.840973 3.681576 [169] 3.921108 3.976106 3.721336 3.765983 3.829931 2.816940 3.093432 3.458421 [177] 3.487542 3.631318 3.292879 3.787375 3.305071 3.592176 3.774430 3.972639 [185] 3.966332 3.581951 3.854853 3.099598 3.538137 3.268143 3.488570 3.932841 [193] 3.799663 3.494907 3.573109 3.339155 3.724521 3.289362 3.561361 3.879044 [201] 2.616566 3.831290 3.268506 2.494499 3.293872 3.843545 3.114641 3.868243 [209] 3.357370 3.342279 3.770005 3.985641 3.804310 3.535162 3.286694 3.259598 [217] 3.801613 3.421095 3.372941 3.626631 3.003102 3.848355 3.794187 3.717112 [225] 3.659631 3.018944 3.973819 3.404616 3.037820 3.681241 2.651118 3.648600 [233] 1.567337 3.286582 3.063713 3.789949 1.847499 3.676934 3.861251 3.938891 [241] 3.619840 3.499450 2.594148 3.964466 3.716126 3.988958 3.572174 3.929719 [249] 3.089325 3.394816 3.638697 3.718930 3.678020 3.764369 3.612047 3.419600 [257] 3.963011 3.262439 3.642269 3.083539 3.780911 3.821262 3.272408 3.674723 [265] 3.960991 2.348205 3.633270 3.971116 3.916581 3.304252 3.866839 3.946283 [273] 3.518523 3.903736 3.356821 3.930388 3.666330 3.899145 3.497409 3.828971 [281] 3.748343 3.457878 2.864195 3.758115 3.580566 3.203135 2.882668 3.352222 [289] 3.731449 3.660538 3.072225 3.687922 3.728209 3.402034 3.829411 3.688653 [297] 3.976036 3.526930 3.342389 3.535636 3.538375 3.586242 3.099946 3.669858 [305] 3.541623 3.505361 3.356359 3.816163 3.489635 3.860775 3.822882 3.747735 [313] 3.425744 3.896727 3.963741 3.621481 3.341945 3.687715 3.437990 3.853112 [321] 3.979649 3.628436 3.334488 3.287629 3.842406 3.832341 3.467648 3.688459 [329] 3.846736 2.953548 3.984955 3.231404 2.551938 2.789831 3.782761 3.140852 [337] 3.839358 3.932686 3.856399 3.715374 3.831554 3.003947 2.415961 3.232714 [345] 3.685090 3.845740 3.629195 3.033008 3.794194 3.524897 3.735900 3.654401 [353] 3.798471 3.640917 3.537387 3.763099 3.342491 3.488705 2.731558 3.980880 [361] 3.808094 3.718183 2.515013 3.475897 3.268407 2.049416 3.414795 3.336095 [369] 3.442515 3.183961 3.319940 3.066716 3.167412 3.958635 3.174195 3.114885 [377] 3.846277 3.437865 3.704085 3.380010 3.585861 2.151148 3.648881 2.610456 [385] 3.744482 3.521740 3.273064 3.420909 3.011202 2.815252 3.329642 3.962370 [393] 3.271197 2.632498 3.157432 3.540697 3.563779 3.587351 3.456055 3.737084 [401] 3.827214 3.747984 3.778041 3.597813 3.950784 3.434356 3.300589 3.989580 [409] 3.937894 3.763320 3.526779 3.838552 3.773042 3.425214 3.169659 3.978108 [417] 3.908583 3.715853 2.693339 3.088471 3.542141 3.721530 3.096639 3.879612 [425] 3.527579 3.680762 3.792052 3.695004 3.498806 3.634429 3.305442 3.931323 [433] 3.546457 3.512385 3.832030 3.747048 3.336343 3.356620 3.665211 3.561431 [441] 3.902753 3.063749 3.834330 3.273796 3.493796 3.750301 3.772089 3.681927 [449] 2.744096 3.258374 3.288172 2.847851 3.201555 3.785558 3.955315 3.709392 [457] 3.393356 3.680602 3.169786 3.603776 3.730082 3.408015 3.781503 3.653713 [465] 3.185421 2.896985 3.883838 3.095238 3.749839 3.633973 3.735791 3.236201 [473] 3.869685 3.043287 3.877842 3.591767 3.466879 3.410591 2.340709 3.740319 [481] 3.784634 3.882799 3.819669 2.616859 3.080041 3.959329 3.805895 3.682538 [489] 3.934101 3.205493 3.528112 2.885561 3.349386 2.770156 3.957191 3.565231 [497] 2.961162 3.772923 3.014793 3.599061 2.979746 2.924131 3.171255 2.909675 [505] 3.946789 3.309175 3.896463 3.562055 3.947545 2.425023 3.714159 3.884460 [513] 3.197127 2.997072 3.895105 3.085357 2.934235 3.241282 2.067567 2.862859 [521] 3.700090 3.619676 3.445114 2.936474 3.409845 3.705518 3.805682 3.309465 [529] 3.651751 3.601904 3.364907 3.753334 3.257378 2.714795 3.543411 2.835241 [537] 3.905872 3.591318 3.653366 3.696490 3.985498 3.671893 3.986166 2.786592 [545] 3.840619 3.762244 3.933452 3.854653 3.135278 3.619951 2.925429 3.804290 [553] 3.400385 3.667426 2.498123 2.629815 2.988505 2.308354 3.666804 3.582388 [561] 3.424720 3.538256 3.956785 2.623558 3.434937 3.715749 2.658163 3.481806 [569] 2.686064 3.974992 3.800429 3.395400 3.614853 2.860055 3.559181 3.453224 [577] 2.971388 2.481246 2.751536 3.976857 3.668689 2.921917 3.528930 3.693702 [585] 3.635487 2.765636 3.638979 3.534622 3.419007 3.221877 3.264320 3.603778 [593] 3.793376 2.869612 3.048472 3.227875 3.287751 3.695336 3.620212 3.178073 [601] 3.812738 3.226870 3.640953 3.524474 2.820440 2.487313 3.322503 3.680900 [609] 3.198896 3.819039 3.889712 3.631899 2.859073 2.972948 3.593515 3.144844 [617] 2.625800 3.883646 3.698130 3.879741 3.728679 3.330161 3.777600 3.901801 [625] 3.309421 3.587243 3.568975 3.794814 3.983233 3.891566 3.357753 3.329947 [633] 3.909820 3.879689 2.123890 3.639244 3.256327 3.542048 1.689737 3.251575 [641] 3.573190 3.826724 3.442294 3.256912 3.655976 3.458174 3.114914 2.576466 [649] 3.810437 3.556063 3.775487 2.970015 3.102050 3.450474 3.827761 3.757736 [657] 3.508694 3.949032 3.778553 3.557878 3.957916 3.561363 3.554264 3.680430 [665] 3.148215 3.415593 3.732673 3.035019 3.445320 3.525210 3.246310 3.323743 [673] 3.375122 3.812605 3.844590 3.998380 3.887772 3.890133 3.292840 3.981925 [681] 3.420106 3.586181 2.692877 2.462626 3.610852 3.285364 3.574731 3.260710 [689] 3.496472 3.618192 3.967605 3.756020 2.927128 3.133941 3.858285 3.453729 [697] 2.832787 3.284200 2.975962 2.851523 3.112546 3.157835 3.989535 3.568602 [705] 3.675494 3.315623 2.642742 3.285224 2.527852 3.949173 3.787078 3.942769 [713] 3.914413 3.488467 3.551978 2.526398 3.851783 3.177486 3.889975 3.586438 [721] 2.924150 3.739675 3.806279 3.982986 3.705537 3.278713 3.963080 3.749345 [729] 3.180059 3.218521 3.631969 3.926586 3.347141 2.884193 3.930779 2.165905 [737] 3.908132 3.371775 3.174469 2.830671 3.999766 3.324226 3.048092 3.732841 [745] 2.128432 2.764585 3.983645 3.931733 3.998209 3.611959 3.047402 3.785414 [753] 3.916805 3.992936 3.062838 3.352946 3.782886 3.498643 3.843348 3.478307 [761] 3.302801 3.987383 3.976281 3.934349 3.832405 3.866407 3.717965 2.349703 [769] 3.247921 3.630835 3.059444 2.596686 3.756048 3.140289 3.583778 3.712921 [777] 3.588993 3.913240 3.328583 3.523568 3.896397 3.650172 3.128604 3.539896 [785] 3.653969 3.428670 3.486968 3.360077 2.681030 3.925046 3.330700 3.938777 [793] 3.952357 2.273260 3.471821 3.977200 3.369655 2.711782 3.490729 2.150896 [801] 2.482517 2.343580 3.309718 3.045012 3.083014 3.867303 3.572899 3.967236 [809] 3.493281 3.870890 3.923266 3.974177 3.506794 3.511346 3.725185 2.674407 [817] 2.672490 2.950100 3.877953 3.348515 3.930814 3.763953 3.845520 2.738856 [825] 3.804239 3.893732 3.582095 3.769051 3.534167 3.017243 3.598262 3.865568 [833] 3.040859 3.849929 3.397836 3.972801 2.944157 3.812862 3.961184 3.873363 [841] 3.396995 3.888399 3.225739 3.011078 3.187047 3.756853 3.028996 3.255728 [849] 3.228571 3.606431 3.662682 3.626734 2.914295 3.323444 3.027354 2.440010 [857] 3.435236 3.681256 3.735520 3.797782 3.872504 3.770188 3.527028 3.445999 [865] 2.931429 2.981084 3.877419 3.682324 2.832008 2.873041 2.940172 3.350525 [873] 3.742829 3.951490 3.201033 3.963380 3.489603 3.159500 2.899869 3.947379 [881] 3.812243 3.602974 3.780062 3.732620 3.593815 3.561677 3.406434 3.638102 [889] 3.584534 2.640355 3.377754 3.974702 3.741975 3.652086 2.869726 3.565171 [897] 3.310576 3.728554 3.674179 3.589628 3.322070 2.523868 2.530449 2.908311 [905] 3.587243 3.595063 3.905268 3.419449 3.836192 3.900894 3.805095 3.924971 [913] 3.781252 3.709368 3.734501 3.912082 3.515563 3.766261 2.528277 3.099270 [921] 3.381257 3.352519 3.494428 3.730629 3.304785 3.785400 3.191887 3.836251 [929] 3.505548 3.615120 3.358266 3.905638 3.112533 3.269762 3.789949 3.420631 [937] 3.528774 3.938050 2.819949 2.566086 3.729984 2.661924 3.027956 2.958891 [945] 3.978999 3.569614 3.132515 3.335820 3.885796 3.616609 3.827445 3.517655 [953] 3.602102 3.411938 2.448746 3.364541 3.912896 3.610968 3.389809 2.644390 [961] 3.410526 3.927129 3.985082 3.413951 3.835819 3.998241 3.934075 3.186261 [969] 3.356844 2.525352 3.139257 3.825596 3.517826 3.453964 3.758949 2.565411 [977] 3.827556 3.302017 3.311665 3.700349 3.684100 3.704421 3.179319 3.271077 [985] 3.314320 3.230120 2.931448 2.626735 3.398263 2.626019 2.866762 2.774461 [993] 3.822497 3.729242 3.071186 3.202484 3.327348 2.755521 3.741134 3.707482 [1001] 3.171455 3.762530 2.797754 3.437520 2.930963 3.035146 3.779789 3.804267 [1009] 3.058350 3.467940 3.779946 1.450061 3.959466 3.351305 3.593775 3.238932 [1017] 3.666165 3.930144 3.618129 3.631776 3.438404 3.398670 3.919682 2.787105 [1025] 3.534549 3.626576 3.862971 3.719750 3.010961 3.839170 2.903161 3.138994 [1033] 3.505992 2.726433 3.497356 3.708121 3.726507 2.751593 3.628924 3.233588 [1041] 3.986707 3.088054 3.053471 3.895957 3.818786 3.484488 3.725919 3.672458 [1049] 2.129923 3.062688 3.518056 3.490308 3.702830 3.053689 3.598399 2.692080 [1057] 3.099806 2.769676 3.154018 3.571072 3.408502 3.463621 3.631635 3.461687 [1065] 2.808606 3.720541 3.311323 3.254666 2.620907 3.722050 3.260433 3.631285 [1073] 3.586353 3.764220 3.466803 3.078429 3.405184 2.639093 3.180311 3.889936 [1081] 3.564462 3.482661 3.918721 2.351003 3.797261 3.980246 3.956436 3.884710 [1089] 3.941149 3.586942 3.720348 3.723770 3.343349 3.755812 2.772920 3.619766 [1097] 3.824209 2.260081 3.729060 3.602819 3.381986 3.423048 3.943267 3.914154 [1105] 3.918662 3.089566 3.579262 3.541060 3.285126 3.816322 2.374358 3.718758 [1113] 3.552843 2.551124 2.946174 3.335212 3.236631 3.122907 3.532091 3.171904 [1121] 3.048145 3.941678 3.393204 3.718683 3.228468 3.089175 3.345174 3.071823 [1129] 3.701340 3.234138 3.021600 3.198019 3.764790 3.842244 3.928209 2.813641 [1137] 3.028506 3.768741 3.347933 3.802633 3.077210 3.776072 1.969358 3.406865 [1145] 3.402123 3.944975 3.607796 3.772122 3.422062 3.713985 3.469614 3.867394 [1153] 2.597505 3.585307 3.118326 3.214301 3.880154 3.579832 2.831642 2.740474 [1161] 3.706898 2.520026 3.270296 3.556109 3.271493 3.452981 3.400907 3.661954 [1169] 2.862660 3.661284 3.896395 2.544837 3.716273 3.258666 2.815883 3.527627 [1177] 3.175446 1.862497 3.898645 3.237416 3.961339 3.426941 2.869313 3.555400 [1185] 2.595831 3.824335 3.709567 3.554401 3.900088 3.665331 3.404226 3.813717 [1193] 3.890765 3.762509 3.550370 3.486397 3.900852 3.208278 3.367344 3.388262 [1201] 3.750885 3.845829 3.613290 3.535684 3.581494 3.972560 3.681715 3.485700 [1209] 3.613169 3.580296 3.250069 3.837439 2.430208 3.917404 2.921883 3.593498 [1217] 3.926488 3.531751 3.354149 3.481991 3.839248 3.777770 3.212763 3.866288 [1225] 3.790113 3.318880 3.506306 3.972680 3.928220 3.843582 3.099757 3.895349 [1233] 3.449497 3.412586 3.634270 3.232015 3.441209 3.970659 2.800854 3.382441 [1241] 3.560233 2.951647 2.745793 2.762554 3.216581 3.924508 3.535404 3.166051 [1249] 3.216654 3.352540 3.328704 2.718563 3.122590 3.078186 3.765467 3.844460 [1257] 3.192430 3.955024 3.749886 3.848503 2.920259 3.311142 3.666470 2.893563 [1265] 3.162938 3.094032 2.989998 2.861606 3.346085 3.314484 3.995849 3.584163 [1273] 3.769083 3.437625 2.918992 3.619581 3.003930 3.413862 3.468593 3.958600 [1281] 3.919882 3.593616 3.202740 3.376488 3.296933 3.295433 3.763039 3.214749 [1289] 3.993011 3.164516 2.841152 3.609003 3.893659 2.727896 3.845651 3.878268 [1297] 3.793503 3.353477 3.148901 3.953882 3.953961 2.802701 3.927404 3.113790 [1305] 3.553736 3.509744 3.651550 3.919886 3.929900 3.753347 3.840511 3.693409 [1313] 3.959329 3.232521 3.637161 3.455360 3.405767 3.990377 3.414094 3.839777 [1321] 3.886976 3.745314 3.903253 3.524846 3.792848 3.245142 2.791255 3.674752 [1329] 3.515534 3.865589 3.932528 2.815585 3.975073 3.938512 3.919856 3.620485 [1337] 3.946638 3.102401 3.230531 2.404636 3.713864 3.191393 3.176803 2.720849 [1345] 3.728141 2.970398 3.780097 3.356904 3.143467 3.699779 3.895391 3.638481 [1353] 3.478211 3.436249 3.991155 2.218794 3.650019 3.505350 3.697888 3.334444 [1361] 2.956877 3.415982 3.773811 2.608883 3.979020 3.289460 3.349656 3.861362 [1369] 3.678502 3.646633 2.908704 3.283448 3.579702 2.691189 3.715051 2.711883 [1377] 2.989720 3.679665 3.980551 3.492213 2.766748 3.411974 3.133300 3.876786 [1385] 3.255621 3.878537 3.799203 3.687915 3.972057 3.094823 3.405338 3.042747 [1393] 3.975381 3.627261 3.885350 3.001581 3.963518 2.977309 2.874093 3.911695 [1401] 3.324675 3.658118 3.567599 3.306766 3.685533 3.140808 3.292341 3.693590 [1409] 3.584975 3.355330 3.822324 3.597893 3.976840 3.839520 2.603238 3.047025 [1417] 3.221804 3.333016 3.605338 3.243153 3.431935 3.369791 3.921014 3.968974 [1425] 3.281906 3.540312 3.963577 3.123140 2.517904 3.889421 3.207944 3.091789 [1433] 3.509323 3.812346 3.798402 3.382833 2.449035 3.938167 3.785686 3.985000 [1441] 3.933264 3.559027 3.175917 3.297137 3.845806 3.834148 3.250641 3.802086 [1449] 3.002572 3.773217 3.988465 3.309555 3.082156 3.147934 3.865348 3.691360 [1457] 3.578555 3.961420 3.935549 3.580215 3.652158 2.881077 3.117186 3.425315 [1465] 3.975040 3.928282 2.733806 2.454610 3.463640 3.968906 3.998930 3.249260 [1473] 3.691352 3.048242 3.935215 3.385473 2.885309 3.390751 3.178548 3.350331 [1481] 1.873144 2.661477 3.805937 3.757120 3.912821 2.780176 3.910633 3.654643 [1489] 3.741538 3.057955 3.111577 3.433734 3.780170 3.912968 3.922374 3.345211 [1497] 2.935535 2.824516 3.490697 3.308771 1.998815 3.109355 3.034554 3.710976 [1505] 3.718692 3.061743 3.428038 3.244488 3.501885 3.016235 3.953218 3.886851 [1513] 3.828230 3.828502 2.063599 2.802731 3.605909 3.850083 3.440476 3.783756 [1521] 3.410754 3.463876 3.964444 3.698530 3.659415 3.502546 3.065252 3.228498 [1529] 3.070290 3.378819 3.501761 3.776125 3.363313 3.640369 2.389535 3.523831 [1537] 3.960247 2.445474 3.543446 2.916326 3.756061 2.763801 3.428466 3.787643 [1545] 2.703194 3.859000 3.094621 3.996187 3.287943 3.938308 3.829349 2.909039 [1553] 3.891527 3.554381 3.250588 3.497840 3.802558 3.911209 3.873720 3.884997 [1561] 3.971714 3.647598 3.829731 3.214604 3.684116 3.246221 3.519148 3.929640 [1569] 3.704890 3.999386 3.776908 3.642253 3.845688 3.818254 3.890045 3.673610 [1577] 3.599462 3.812049 3.922419 3.963825 3.387017 3.387188 3.382864 3.801064 [1585] 3.106889 3.943734 3.844838 3.387025 2.749544 3.968777 3.813249 2.513798 [1593] 2.786967 3.007875 3.377125 3.440666 3.566018 3.542889 2.690306 3.218854 [1601] 3.629121 3.641205 3.716609 3.874084 3.099596 3.635284 3.079248 2.980432 [1609] 3.691460 3.209641 3.760857 3.950802 3.551441 3.995592 3.766330 3.698159 [1617] 3.957825 3.785264 3.911691 2.773437 2.481236 3.714505 3.991385 3.706797 [1625] 2.954684 3.410828 3.939249 3.692631 2.850070 3.715236 3.949735 3.983460 [1633] 3.407178 3.662100 2.845855 3.553483 3.120270 3.110820 3.609218 3.536137 [1641] 3.523292 3.206219 2.223081 3.418213 2.641226 3.181142 3.846558 3.689413 [1649] 3.831279 3.367194 2.748198 3.326492 3.817417 3.539473 2.717322 3.462649 [1657] 2.711002 3.642422 3.793196 3.624487 3.977995 3.309015 3.627561 2.472656 [1665] 3.717130 3.828351 3.534513 3.913316 3.581072 3.094039 3.853086 3.158894 [1673] 3.695713 3.248205 3.822134 3.801905 3.508914 3.267839 3.486188 3.957370 [1681] 3.861202 3.584288 3.465214 3.896216 3.418026 3.016678 3.543583 3.656715 [1689] 2.017964 3.735146 3.841972 2.426733 3.446993 2.801890 3.757126 3.104407 [1697] 3.879330 3.374890 3.115119 3.804297 2.970249 3.863109 3.598640 3.104478 [1705] 3.687806 3.939837 3.213737 3.967609 2.132940 3.388343 3.877549 3.125564 [1713] 3.843757 3.520333 2.809875 3.299599 3.978516 3.476803 2.790229 2.817900 [1721] 3.592541 3.415764 3.972016 3.623260 3.926664 3.019564 3.917115 3.520902 [1729] 3.414018 3.595091 3.358012 3.141485 3.774327 3.320030 3.694861 3.990128 [1737] 2.178194 3.892636 3.583957 3.735630 3.182553 3.825807 3.747378 2.386860 [1745] 2.189082 3.220844 3.804572 3.024969 3.324536 3.972683 3.866468 3.269406 [1753] 2.784461 3.499165 3.961842 3.242402 2.592710 3.446804 2.873162 2.869318 [1761] 3.861524 3.992062 3.495929 3.550164 2.985335 2.919919 3.633101 3.865936 [1769] 3.498140 3.440704 3.990662 2.506478 3.943407 3.268847 3.514864 3.206963 [1777] 3.864984 2.488948 3.577702 3.519307 2.934332 2.955194 3.998970 3.164663 [1785] 3.404792 3.685196 3.323501 3.378496 3.070458 3.946001 3.782053 3.149406 [1793] 3.220509 3.504596 3.830715 3.355070 2.545948 3.377619 2.472344 2.627176 [1801] 3.152118 3.199698 3.921711 3.568465 3.158420 3.338065 2.954471 3.052360 [1809] 3.549545 3.706767 3.672425 3.882635 3.789943 3.913297 2.275516 3.842693 [1817] 3.663588 3.979928 3.315403 3.827043 3.552584 3.039034 3.717164 3.205264 [1825] 3.669533 3.465466 3.269737 3.044478 3.290202 3.874333 3.658734 3.427596 [1833] 3.815492 3.280422 3.236215 3.173784 3.831537 3.880475 3.769806 3.580349 [1841] 3.369631 2.242521 3.876360 3.581726 3.252259 3.547411 3.417363 3.744949 [1849] 3.708431 2.060669 3.488943 3.578711 3.748293 3.893367 2.557302 3.740935 [1857] 3.915740 3.538547 3.323706 3.556267 3.139706 3.705175 3.726418 3.752264 [1865] 2.865511 3.425434 3.260157 3.469298 3.824097 3.869807 3.399394 2.693918 [1873] 3.470745 3.938981 3.669006 3.035388 2.017572 3.942623 3.992909 3.816570 [1881] 3.908504 3.531904 3.821498 3.844791 3.987342 3.332353 3.986275 3.976761 [1889] 3.047420 3.344432 3.489022 3.922276 3.981557 3.730656 3.740867 3.518188 [1897] 3.226021 2.732282 2.430849 3.950674 3.301143 2.860923 3.781493 3.883327 [1905] 2.343183 3.482268 3.907796 3.922807 3.309653 3.839068 3.577540 3.939001 [1913] 3.743788 3.198793 3.871617 3.874695 3.722524 3.439676 3.287100 3.705701 [1921] 3.524607 3.102174 3.371726 3.863832 2.810677 2.376567 3.256967 3.237747 [1929] 3.883741 3.581797 3.547514 3.865991 2.568402 3.510744 3.231973 3.821490 [1937] 3.483621 3.014698 3.232006 3.576230 3.151640 3.630004 2.999222 3.276234 [1945] 3.419570 3.489607 3.144418 2.603572 3.281735 3.328491 3.998496 2.670246 [1953] 2.399740 3.533242 3.244478 3.302486 3.591539 3.820180 3.020357 3.204976 [1961] 3.187394 3.687931 2.806496 3.799344 3.523634 3.877895 3.910658 2.486364 [1969] 2.583637 3.623240 2.680569 3.905395 3.786531 3.747304 3.019871 2.773053 [1977] 3.662173 3.382293 3.853454 3.574751 3.751033 3.905406 3.471627 3.729064 [1985] 3.314654 3.145931 2.787046 3.570640 3.883683 2.936455 3.508896 2.511287 [1993] 3.197040 2.497198 3.794260 3.877954 3.703076 3.606470 3.701712 3.502278 [2001] 3.988284 3.982135 3.677637 3.999081 3.821669 3.194982 3.904545 3.588623 [2009] 3.230869 3.902777 3.452971 3.468206 3.679142 3.310826 3.677465 3.917274 [2017] 3.994934 3.952656 3.857883 2.769992 3.842587 3.692098 3.626139 2.835723 [2025] 3.713959 3.852272 3.166814 3.003330 3.332994 3.786918 3.832182 3.886464 [2033] 2.709776 2.876950 3.881649 3.118896 3.921698 2.867966 3.207523 3.190463 [2041] 3.842315 3.869319 3.565958 3.233110 3.473060 3.388059 3.783573 3.321028 [2049] 3.808865 2.142472 3.540234 3.967820 2.922664 3.778578 2.814375 3.727395 [2057] 3.546942 3.445792 3.723799 3.957216 3.853888 3.710121 2.825694 3.475039 [2065] 3.987455 3.693411 3.682354 3.824502 3.926321 3.943504 3.041949 3.891296 [2073] 3.298708 3.969694 3.837882 3.127085 3.864821 3.017833 3.420723 3.802213 [2081] 3.766281 3.786587 3.764635 3.952299 3.172451 3.626200 3.966250 3.277120 [2089] 3.364624 3.856382 3.702814 3.239329 3.299456 3.694818 3.254914 3.334666 [2097] 3.947824 3.469990 1.923574 2.926411 3.464728 3.663982 3.430623 3.964701 [2105] 3.996240 3.326054 3.588457 3.123657 3.961921 3.332687 2.577618 3.497408 [2113] 2.697967 2.826654 3.853947 3.944690 3.932581 3.916914 3.905836 3.382169 [2121] 3.606030 3.196964 3.362799 3.474687 3.883409 3.544031 3.327222 3.901890 [2129] 3.962365 3.938996 3.202334 2.910701 3.587427 3.592626 3.228346 3.962788 [2137] 3.857858 3.926234 3.862187 3.622408 3.991376 3.781023 3.975860 3.862477 [2145] 3.871106 2.887893 3.470958 3.429865 3.570486 3.640516 3.383015 3.960440 [2153] 3.263919 3.412492 2.873551 3.933234 2.518403 2.952899 3.076425 3.724756 [2161] 3.400526 3.570502 3.316774 3.324999 3.775394 3.356602 3.412154 3.666965 [2169] 3.473412 3.624950 2.683435 3.876793 3.480824 3.202947 3.797126 3.853515 [2177] 3.350494 3.449819 3.791953 3.482916 3.294791 2.934650 3.455169 3.855051 [2185] 3.291204 3.877338 3.269241 3.386865 3.357085 2.744472 2.875178 3.408781 [2193] 3.085929 2.199480 3.938965 3.585602 3.948452 3.197279 3.483817 3.052675 [2201] 3.007714 3.384861 2.703366 3.416552 2.781199 3.945097 3.446389 3.808873 [2209] 3.498614 3.337143 3.865372 3.567171 3.188975 3.800101 2.873276 3.586254 [2217] 3.084006 2.833152 3.671960 3.411986 3.477011 3.935855 3.603240 3.427160 [2225] 2.013812 3.694799 3.901838 3.968502 3.667522 3.983232 3.774533 2.761685 [2233] 3.949801 3.777195 3.895613 3.090435 3.787777 3.747933 3.461804 3.175977 [2241] 3.466690 3.298252 3.470374 3.771284 3.033979 3.825165 3.873968 3.975917 [2249] 3.068284 3.734797 2.296283 3.564495 3.618337 3.002614 3.479717 3.916825 [2257] 3.681775 3.584470 3.972183 2.727886 2.512219 3.310671 3.712533 3.788887 [2265] 3.648281 2.920635 3.818396 3.577212 3.386333 3.427162 3.813611 3.857839 [2273] 3.957182 3.201057 3.645729 3.960257 2.673876 3.557925 3.657028 3.554960 [2281] 3.178675 3.392702 3.986579 2.264124 2.846049 2.500042 3.241489 3.271977 [2289] 2.978955 3.345648 3.587162 3.568462 3.018874 2.631643 3.155198 3.574575 [2297] 3.410072 3.740996 3.423573 3.664888 3.934582 3.962561 2.655253 3.140413 [2305] 3.346405 3.963525 3.455951 3.877216 3.974544 2.873800 3.775745 3.665584 [2313] 3.667609 2.766000 3.887707 3.634634 3.656866 3.595586 3.197411 3.736006 [2321] 3.591312 3.777664 2.893425 3.081804 3.242717 3.637404 3.839243 3.588770 [2329] 3.978898 3.979994 2.897663 3.345276 2.677244 3.349134 3.901005 3.261683 [2337] 3.868954 3.968201 3.869995 3.891864 3.749763 3.235976 3.578723 3.684652 [2345] 3.910436 3.872725 3.881646 2.773109 3.846098 3.263788 3.494773 3.272334 [2353] 3.444304 3.913829 3.913324 2.864015 3.910221 3.150012 3.675406 3.435522 [2361] 3.940836 3.857428 3.906549 3.846751 3.060347 3.434358 3.529164 3.641860 [2369] 1.786913 3.170624 3.514180 3.576161 2.471821 3.777183 3.404255 3.670467 [2377] 3.728510 2.929564 3.860556 3.279858 3.795120 3.548452 3.843067 3.460906 [2385] 3.828938 3.497728 3.096048 3.550804 2.334029 3.448863 3.615786 3.297189 [2393] 3.690048 3.059487 3.810264 3.359507 3.022063 3.924493 3.660285 3.583859 [2401] 3.847763 3.920053 3.580796 2.928524 3.373805 3.759897 3.913142 3.470889 [2409] 3.472929 3.626657 3.045130 3.922162 3.774600 3.599320 3.984209 3.311474 [2417] 3.538879 2.909663 3.511762 3.379716 3.978889 3.992773 3.587698 3.592117 [2425] 2.893650 3.762869 3.736127 3.828644 3.604003 3.445078 3.885514 3.591612 [2433] 2.460069 3.599728 3.484438 3.334566 2.964988 3.680673 3.937899 3.841612 [2441] 3.432797 3.014149 3.359944 3.169554 3.577213 3.262185 3.509755 3.774406 [2449] 3.331119 3.063570 3.003055 2.844313 2.789995 2.955994 3.884262 3.074300 [2457] 3.674938 3.902000 3.582671 3.215077 3.205162 3.126232 3.742736 3.508844 [2465] 3.821481 3.134082 3.449160 3.300658 3.505713 3.927354 3.834013 2.773037 [2473] 3.073127 3.236143 3.869504 3.930855 3.265755 2.775705 3.253530 3.652605 [2481] 3.876757 3.803543 3.596753 3.734589 3.821862 3.405128 3.923376 3.921168 [2489] 3.981637 3.771745 3.870007 3.340620 3.390139 3.202585 3.278381 3.633967 [2497] 2.271324 3.188493 3.996289 2.784417 3.478492 2.665741 2.845400 2.168624 [2505] 3.657462 2.303746 3.468574 3.824841 3.773719 3.073456 3.335326 3.639809 [2513] 3.187694 3.489176 3.482388 3.678538 2.812235 3.579864 3.304182 3.277064 [2521] 3.888446 2.508798 3.443243 3.480012 3.987240 3.244290 3.462831 3.923331 [2529] 2.580363 3.328142 3.035888 3.687955 2.985787 3.659062 3.597026 3.592965 [2537] 3.233999 3.982984 3.173891 3.205207 2.248948 3.879219 3.046579 3.192302 [2545] 3.375350 2.874819 3.581451 3.276435 3.475376 3.476625 3.239044 3.030245 [2553] 3.520802 3.568852 3.552429 2.890254 3.226777 3.162424 3.664322 3.871718 [2561] 3.356105 3.676424 3.690212 3.725241 3.444339 3.628802 3.816502 3.601049 [2569] 2.963252 3.431030 3.485192 3.755214 3.428297 3.956178 3.802175 3.784819 [2577] 3.585230 3.123868 3.950458 2.747249 3.749936 3.325025 3.942996 3.526107 [2585] 3.836825 2.708311 3.991624 3.628400 2.624697 3.261109 2.955372 3.761310 [2593] 3.478434 3.460216 2.820028 2.985862 3.423731 3.817257 3.497160 3.785757 [2601] 2.830572 3.686022 3.908166 3.930055 3.129567 2.241978 3.304543 3.723067 [2609] 3.782463 3.969440 2.751592 3.942464 3.914683 3.662507 3.541427 2.334499 [2617] 2.334415 3.861645 3.101423 3.137050 3.264842 3.379962 3.181417 3.208751 [2625] 3.476343 3.388677 2.667285 3.159067 3.868052 3.972959 3.632408 3.396115 [2633] 3.572649 3.931134 3.651737 3.326637 3.016761 3.239991 3.069374 3.440572 [2641] 3.641222 3.066116 3.379234 3.952606 3.989152 3.979014 2.940252 3.422263 [2649] 3.302014 3.984712 3.886185 3.670615 2.595679 3.205035 3.043129 3.672853 [2657] 3.985135 3.855508 3.456111 3.312982 3.447263 3.388452 3.816452 3.890722 [2665] 3.711429 3.504459 2.941466 3.158200 3.764275 3.705110 3.447244 2.942230 [2673] 3.986925 3.120893 2.939734 3.536196 3.778420 3.953070 3.395143 3.552623 [2681] 3.113508 3.642643 3.763744 3.233128 2.982238 3.634149 3.611974 2.997054 [2689] 3.643768 3.286120 2.957415 2.689345 3.764972 3.901042 3.538017 3.364488 [2697] 3.247549 3.192595 3.414149 3.931185 2.442577 2.646452 3.664282 3.335591 [2705] 2.864065 3.500392 2.880154 3.583839 3.692550 3.647147 3.677471 3.693771 [2713] 2.914316 3.756339 3.599147 3.990278 3.218812 3.740789 3.417067 3.187730 [2721] 3.930368 3.957000 3.006559 3.436989 3.133012 3.729732 3.167769 3.318201 [2729] 3.652127 3.979880 3.651613 3.948094 2.849964 3.560955 3.631259 3.785806 [2737] 3.802329 3.178196 3.713256 3.190813 2.958690 3.836656 3.476620 3.843581 [2745] 2.798739 3.356526 3.327418 3.682301 3.728828 3.307847 3.722737 1.957569 [2753] 3.872168 3.600821 3.765816 2.455570 3.295400 3.110102 3.760404 3.665412 [2761] 3.802637 3.112553 3.896398 3.629611 3.516815 3.048171 3.904604 3.689426 [2769] 3.200791 3.424885 3.249848 3.841072 3.742518 2.410739 3.734815 2.670024 [2777] 3.184509 3.125485 3.156592 3.139606 3.132341 3.478517 3.301220 2.916158 [2785] 3.971583 3.713344 3.757598 3.554771 3.465070 3.942328 3.540254 3.692494 [2793] 3.150252 3.978687 3.614374 3.699955 3.241331 3.913848 3.256400 3.376599 [2801] 3.789265 3.126340 3.649080 3.158485 3.873538 3.384009 3.189619 3.737085 [2809] 2.859876 3.453756 3.179164 3.429897 3.558482 3.720245 3.303585 3.231113 [2817] 3.655422 3.410993 3.138245 3.712444 3.485536 3.558025 3.458311 3.256012 [2825] 3.506584 3.262387 3.550653 3.702593 3.174922 3.959283 3.597958 3.222387 [2833] 3.297584 3.530521 3.788228 3.750976 3.468307 3.899400 3.238518 2.875724 [2841] 3.440480 3.510976 2.965903 3.981422 3.881048 2.973313 3.550088 3.977540 [2849] 3.754229 3.904679 3.713648 3.747091 3.780965 3.936245 3.326483 3.414345 [2857] 3.979681 3.086185 3.805200 3.722461 3.669391 3.110293 3.954685 3.713740 [2865] 2.341867 3.246695 3.777771 3.855811 3.550678 3.687840 3.275526 2.974186 [2873] 3.697588 3.871380 2.842366 2.867483 3.770702 3.195761 3.355578 3.157550 [2881] 3.512925 3.103597 3.942469 3.093950 3.593941 3.628915 3.582660 3.974295 [2889] 3.849436 3.165496 3.095794 3.420575 3.453316 3.931854 3.386329 3.975869 [2897] 3.287996 3.894653 2.669769 3.592212 3.635316 3.077089 3.774589 3.429603 [2905] 3.315918 3.770028 3.320906 3.256730 3.544925 3.037967 3.697398 3.980447 [2913] 3.465220 3.431693 3.950834 3.969391 3.684895 3.173393 3.645901 3.450593 [2921] 3.322954 3.466876 3.576190 3.427063 3.217411 3.802756 3.955927 3.735303 [2929] 3.123859 3.754193 3.340773 3.746865 3.880978 2.488543 3.802786 3.599180 [2937] 3.637316 2.892570 2.364727 3.467744 3.196653 3.319375 2.344526 3.895412 [2945] 3.944601 3.968286 3.390589 3.631164 3.599331 3.078745 3.012036 3.280770 [2953] 3.857140 3.936607 2.676129 3.579370 3.542736 3.734207 3.672295 3.712342 [2961] 3.681164 3.767266 3.118717 3.577661 3.789054 3.342098 3.997996 3.984576 [2969] 3.413837 3.478270 3.351854 1.847433 2.449326 3.782710 3.042703 3.694579 [2977] 3.644770 3.070702 3.617009 3.809905 3.707103 3.828338 3.428042 3.063839 [2985] 3.027011 3.402308 3.939166 3.492039 3.854335 3.687536 2.972371 3.843529 [2993] 3.650395 3.175358 2.441624 3.657407 3.719439 3.292619 3.741571 3.178707 [3001] 3.685679 3.134851 2.617208 3.681792 3.960154 3.026442 3.938928 3.645711 [3009] 3.832453 3.146440 3.227341 3.695679 3.959940 3.252058 3.643400 3.967664 [3017] 3.930301 2.976201 3.547791 3.887766 3.088510 3.605081 3.700235 3.299570 [3025] 3.473600 2.299193 3.044545 3.532519 2.789449 2.977042 ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% * sample(30) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) *sample_30_gpas <- function(x){ * campus_gpas %>% * pull(gpa) %>% * sample(30) *} ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } *1:1000 ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` ``` [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 [15] 15 16 17 18 19 20 21 22 23 24 25 26 27 28 [29] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 [43] 43 44 45 46 47 48 49 50 51 52 53 54 55 56 [57] 57 58 59 60 61 62 63 64 65 66 67 68 69 70 [71] 71 72 73 74 75 76 77 78 79 80 81 82 83 84 [85] 85 86 87 88 89 90 91 92 93 94 95 96 97 98 [99] 99 100 101 102 103 104 105 106 107 108 109 110 111 112 [113] 113 114 115 116 117 118 119 120 121 122 123 124 125 126 [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 [141] 141 142 143 144 145 146 147 148 149 150 151 152 153 154 [155] 155 156 157 158 159 160 161 162 163 164 165 166 167 168 [169] 169 170 171 172 173 174 175 176 177 178 179 180 181 182 [183] 183 184 185 186 187 188 189 190 191 192 193 194 195 196 [197] 197 198 199 200 201 202 203 204 205 206 207 208 209 210 [211] 211 212 213 214 215 216 217 218 219 220 221 222 223 224 [225] 225 226 227 228 229 230 231 232 233 234 235 236 237 238 [239] 239 240 241 242 243 244 245 246 247 248 249 250 251 252 [253] 253 254 255 256 257 258 259 260 261 262 263 264 265 266 [267] 267 268 269 270 271 272 273 274 275 276 277 278 279 280 [281] 281 282 283 284 285 286 287 288 289 290 291 292 293 294 [295] 295 296 297 298 299 300 301 302 303 304 305 306 307 308 [309] 309 310 311 312 313 314 315 316 317 318 319 320 321 322 [323] 323 324 325 326 327 328 329 330 331 332 333 334 335 336 [337] 337 338 339 340 341 342 343 344 345 346 347 348 349 350 [351] 351 352 353 354 355 356 357 358 359 360 361 362 363 364 [365] 365 366 367 368 369 370 371 372 373 374 375 376 377 378 [379] 379 380 381 382 383 384 385 386 387 388 389 390 391 392 [393] 393 394 395 396 397 398 399 400 401 402 403 404 405 406 [407] 407 408 409 410 411 412 413 414 415 416 417 418 419 420 [421] 421 422 423 424 425 426 427 428 429 430 431 432 433 434 [435] 435 436 437 438 439 440 441 442 443 444 445 446 447 448 [449] 449 450 451 452 453 454 455 456 457 458 459 460 461 462 [463] 463 464 465 466 467 468 469 470 471 472 473 474 475 476 [477] 477 478 479 480 481 482 483 484 485 486 487 488 489 490 [491] 491 492 493 494 495 496 497 498 499 500 501 502 503 504 [505] 505 506 507 508 509 510 511 512 513 514 515 516 517 518 [519] 519 520 521 522 523 524 525 526 527 528 529 530 531 532 [533] 533 534 535 536 537 538 539 540 541 542 543 544 545 546 [547] 547 548 549 550 551 552 553 554 555 556 557 558 559 560 [561] 561 562 563 564 565 566 567 568 569 570 571 572 573 574 [575] 575 576 577 578 579 580 581 582 583 584 585 586 587 588 [589] 589 590 591 592 593 594 595 596 597 598 599 600 601 602 [603] 603 604 605 606 607 608 609 610 611 612 613 614 615 616 [617] 617 618 619 620 621 622 623 624 625 626 627 628 629 630 [631] 631 632 633 634 635 636 637 638 639 640 641 642 643 644 [645] 645 646 647 648 649 650 651 652 653 654 655 656 657 658 [659] 659 660 661 662 663 664 665 666 667 668 669 670 671 672 [673] 673 674 675 676 677 678 679 680 681 682 683 684 685 686 [687] 687 688 689 690 691 692 693 694 695 696 697 698 699 700 [701] 701 702 703 704 705 706 707 708 709 710 711 712 713 714 [715] 715 716 717 718 719 720 721 722 723 724 725 726 727 728 [729] 729 730 731 732 733 734 735 736 737 738 739 740 741 742 [743] 743 744 745 746 747 748 749 750 751 752 753 754 755 756 [757] 757 758 759 760 761 762 763 764 765 766 767 768 769 770 [771] 771 772 773 774 775 776 777 778 779 780 781 782 783 784 [785] 785 786 787 788 789 790 791 792 793 794 795 796 797 798 [799] 799 800 801 802 803 804 805 806 807 808 809 810 811 812 [813] 813 814 815 816 817 818 819 820 821 822 823 824 825 826 [827] 827 828 829 830 831 832 833 834 835 836 837 838 839 840 [841] 841 842 843 844 845 846 847 848 849 850 851 852 853 854 [855] 855 856 857 858 859 860 861 862 863 864 865 866 867 868 [869] 869 870 871 872 873 874 875 876 877 878 879 880 881 882 [883] 883 884 885 886 887 888 889 890 891 892 893 894 895 896 [897] 897 898 899 900 901 902 903 904 905 906 907 908 909 910 [911] 911 912 913 914 915 916 917 918 919 920 921 922 923 924 [925] 925 926 927 928 929 930 931 932 933 934 935 936 937 938 [939] 939 940 941 942 943 944 945 946 947 948 949 950 951 952 [953] 953 954 955 956 957 958 959 960 961 962 963 964 965 966 [967] 967 968 969 970 971 972 973 974 975 976 977 978 979 980 [981] 981 982 983 984 985 986 987 988 989 990 991 992 993 994 [995] 995 996 997 998 999 1000 ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% * tibble(trial = .) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` ``` # A tibble: 1,000 × 1 trial <int> 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 # … with 990 more rows ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% * mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` ``` # A tibble: 1,000 × 2 trial thirty_gpas_sampled <int> <list> 1 1 <dbl [30]> 2 2 <dbl [30]> 3 3 <dbl [30]> 4 4 <dbl [30]> 5 5 <dbl [30]> 6 6 <dbl [30]> 7 7 <dbl [30]> 8 8 <dbl [30]> 9 9 <dbl [30]> 10 10 <dbl [30]> # … with 990 more rows ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% * mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` ``` # A tibble: 1,000 × 3 trial thirty_gpas_sampled sample_mean <int> <list> <dbl> 1 1 <dbl [30]> 3.47 2 2 <dbl [30]> 3.39 3 3 <dbl [30]> 3.43 4 4 <dbl [30]> 3.49 5 5 <dbl [30]> 3.49 6 6 <dbl [30]> 3.55 7 7 <dbl [30]> 3.36 8 8 <dbl [30]> 3.45 9 9 <dbl [30]> 3.37 10 10 <dbl [30]> 3.38 # … with 990 more rows ``` ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% * ggplot() ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + * aes(x = sample_mean) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + aes(x = sample_mean) + * geom_rug(alpha = .2) ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + aes(x = sample_mean) + geom_rug(alpha = .2) + * geom_histogram() ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + aes(x = sample_mean) + geom_rug(alpha = .2) + geom_histogram() + * ggxmean::geom_x_mean() ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + aes(x = sample_mean) + geom_rug(alpha = .2) + geom_histogram() + ggxmean::geom_x_mean() + * ggxmean::geom_x_mean_label() ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + aes(x = sample_mean) + geom_rug(alpha = .2) + geom_histogram() + ggxmean::geom_x_mean() + ggxmean::geom_x_mean_label() + * ggxmean:::geom_x1sd(linetype = "dashed") ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] --- count: false .panel1-gpas_sample1000-auto[ ```r set.seed(1243) campus_gpas %>% pull(gpa) %>% sample(30) sample_30_gpas <- function(x){ campus_gpas %>% pull(gpa) %>% sample(30) } 1:1000 %>% tibble(trial = .) %>% mutate(thirty_gpas_sampled = map(trial, sample_30_gpas)) %>% mutate(sample_mean = map_dbl(thirty_gpas_sampled, mean)) %>% ggplot() + aes(x = sample_mean) + geom_rug(alpha = .2) + geom_histogram() + ggxmean::geom_x_mean() + ggxmean::geom_x_mean_label() + ggxmean:::geom_x1sd(linetype = "dashed") ``` ] .panel2-gpas_sample1000-auto[ ``` [1] 3.388677 1.969560 3.538547 3.606431 2.976201 3.261683 3.890722 3.052360 [9] 3.716126 3.877953 3.650019 3.434358 3.595063 3.856399 2.646452 3.778816 [17] 3.873720 2.486364 3.122907 3.881048 3.999081 3.967839 3.737085 3.734207 [25] 3.246310 3.756172 3.094039 3.674179 2.979746 3.535162 ``` <!-- --> ] <style> .panel1-gpas_sample1000-auto { color: black; width: 38.6060606060606%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel2-gpas_sample1000-auto { color: black; width: 59.3939393939394%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel3-gpas_sample1000-auto { color: black; width: NA%; hight: 33%; float: left; padding-left: 1%; font-size: 80% } </style> --- # Central Limit Theorem for Sample Means -- ## Distribution of sample means is approximately normal when the sample size is large. ( $ >=20 $) -- ## Sample distribution should not be strongly skewed. -- ## The mean for the sampling distribution of the sample mean will be equal to the population mean -- ## Have $$ SD(\bar(X)) = \frac{population.standard.deviation}{\sqrt(n)} $$ --- <!-- --> --- count: false .panel1-time_snippet_length-auto[ ```r *ma206data::chap2_SnippetEstimate ``` ] .panel2-time_snippet_length-auto[ ``` # A tibble: 48 × 1 estimate <dbl> 1 10 2 12 3 6 4 13 5 15 6 10 7 15 8 21 9 10 10 15 # … with 38 more rows ``` ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% * ggplot() ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + * aes(x = estimate) ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + * geom_rug(alpha = .2) ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + * geom_dotplot() ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + * scale_x_continuous(breaks = 1:6*5) ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + * labs(title = "'How long do you think we played that song for you?'") ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + * labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + * labs(x = "Seconds guessed") ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + * ggxmean::geom_x_mean() ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + ggxmean::geom_x_mean() + * geom_vline(xintercept = 10, * color = "red") ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + ggxmean::geom_x_mean() + geom_vline(xintercept = 10, color = "red") + * ggxmean::geom_x_mean_label() ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + ggxmean::geom_x_mean() + geom_vline(xintercept = 10, color = "red") + ggxmean::geom_x_mean_label() + * ggstamp::stamp_label(label = "'Are you willing to generalize the results of this study to all college students in the population? That is, if we performed this same study on all college students, they would, on average, overestimate the acutal lenght of the snippet (10 seconds)'" %>% str_wrap(30), * x = 22, y = .65, alpha = .8) ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + ggxmean::geom_x_mean() + geom_vline(xintercept = 10, color = "red") + ggxmean::geom_x_mean_label() + ggstamp::stamp_label(label = "'Are you willing to generalize the results of this study to all college students in the population? That is, if we performed this same study on all college students, they would, on average, overestimate the acutal lenght of the snippet (10 seconds)'" %>% str_wrap(30), x = 22, y = .65, alpha = .8) + * ggxmean:::stamp_t_dist(mean = 10, * sd = 6.49/sqrt(48), # sd for sampling distribution * fill = "cadetblue", * alpha = .7, height = 2 * ) ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + ggxmean::geom_x_mean() + geom_vline(xintercept = 10, color = "red") + ggxmean::geom_x_mean_label() + ggstamp::stamp_label(label = "'Are you willing to generalize the results of this study to all college students in the population? That is, if we performed this same study on all college students, they would, on average, overestimate the acutal lenght of the snippet (10 seconds)'" %>% str_wrap(30), x = 22, y = .65, alpha = .8) + ggxmean:::stamp_t_dist(mean = 10, sd = 6.49/sqrt(48), # sd for sampling distribution fill = "cadetblue", alpha = .7, height = 2 ) + * ggxmean:::geom_tdist(height = 12, alpha = .8, * fill = "magenta") ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] --- count: false .panel1-time_snippet_length-auto[ ```r ma206data::chap2_SnippetEstimate %>% ggplot() + aes(x = estimate) + geom_rug(alpha = .2) + geom_dotplot() + scale_x_continuous(breaks = 1:6*5) + labs(title = "'How long do you think we played that song for you?'") + labs(subtitle = "Snippit length estimates by 48 Students. Actual length was 10 seconds") + labs(x = "Seconds guessed") + ggxmean::geom_x_mean() + geom_vline(xintercept = 10, color = "red") + ggxmean::geom_x_mean_label() + ggstamp::stamp_label(label = "'Are you willing to generalize the results of this study to all college students in the population? That is, if we performed this same study on all college students, they would, on average, overestimate the acutal lenght of the snippet (10 seconds)'" %>% str_wrap(30), x = 22, y = .65, alpha = .8) + ggxmean:::stamp_t_dist(mean = 10, sd = 6.49/sqrt(48), # sd for sampling distribution fill = "cadetblue", alpha = .7, height = 2 ) + ggxmean:::geom_tdist(height = 12, alpha = .8, fill = "magenta") + * ggxmean:::geom_ttestconf( * size = 2, * color = "magenta", * alpha = 1 * ) ``` ] .panel2-time_snippet_length-auto[ <!-- --> ] <style> .panel1-time_snippet_length-auto { color: black; width: 38.6060606060606%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel2-time_snippet_length-auto { color: black; width: 59.3939393939394%; hight: 32%; float: left; padding-left: 1%; font-size: 80% } .panel3-time_snippet_length-auto { color: black; width: NA%; hight: 33%; float: left; padding-left: 1%; font-size: 80% } </style> --- $$ H_0: \mu = 10 $$ $$ H_A: \mu \ 10 $$