Loading required package: ggplot2Επιπτώσεις των γραμμικών μετασχηματισμών στα μέτρα θέσης και διασποράς
⚠️️ΥΠΟ ΚΑΤΑΣΚΕΥΗ⚠️
1 Παρουσίαση αρχικών δεδομένων
| xx |
|---|
| 5.150232 |
| 5.765711 |
| 3.261138 |
| 2.696714 |
| 4.509085 |
| 4.567265 |
| 4.433070 |
| 4.493653 |
| 2.613701 |
| 4.838545 |
| 3.935407 |
| 4.432776 |
| 4.646230 |
| 2.907187 |
| 2.723106 |
| 4.839040 |
| 4.659102 |
| 4.413193 |
| 4.919173 |
| 3.336579 |
| 4.154780 |
| 5.390422 |
| 3.939744 |
| 2.435161 |
| 4.779007 |
| 5.300906 |
| 3.953853 |
| 3.202607 |
| 3.705465 |
| 5.803623 |
| 3.774583 |
| 4.944862 |
| 3.047474 |
| 3.713975 |
| 3.905172 |
| 5.110860 |
| 5.047414 |
| 4.000312 |
| 6.055730 |
| 4.967587 |
| 5.155701 |
| 5.319607 |
| 5.444561 |
| 4.970835 |
| 3.298654 |
| 4.001028 |
| 5.742954 |
| 3.394648 |
| 2.182896 |
| 3.012809 |
| 3.402937 |
| 3.740005 |
| 3.196218 |
| 3.820185 |
| 4.692354 |
| 1.942136 |
| 5.006047 |
| 4.935042 |
| 4.335435 |
| 4.173629 |
| 4.838742 |
| 5.074197 |
| 3.457846 |
| 4.279191 |
| 4.647702 |
| 4.136739 |
| 3.696026 |
| 5.348789 |
| 4.374016 |
| 6.029206 |
| 3.207579 |
| 5.651845 |
| 3.692674 |
| 4.139354 |
| 3.751767 |
| 5.682899 |
| 3.053433 |
| 4.087683 |
| 5.875262 |
| 4.512434 |
| 3.554464 |
| 4.506821 |
| 5.302745 |
| 4.561771 |
| 4.459406 |
| 3.159137 |
| 4.621624 |
| 2.463788 |
| 4.642841 |
| 2.992855 |
| 2.445916 |
| 2.992256 |
| 3.370626 |
| 4.029448 |
| 4.745299 |
| 3.112958 |
| 4.335139 |
| 3.422261 |
| 2.771187 |
| 4.225377 |
dataPloth <- ggplot(myDatax, aes(x=xx))
dataPloth +
geom_histogram(aes(y = after_stat(density))) +
geom_density(linewidth = 1, alpha = 0.6, fill = "green")`stat_bin()` using `bins = 30`. Pick better value `binwidth`.
2 Προσθέσεις - αφαιρέσεις
| x | xSYN3 |
|---|---|
| 5.150232 | 8.150232 |
| 5.765711 | 8.765711 |
| 3.261138 | 6.261138 |
| 2.696714 | 5.696714 |
| 4.509085 | 7.509085 |
| 4.567265 | 7.567265 |
| 4.433070 | 7.433070 |
| 4.493653 | 7.493653 |
| 2.613701 | 5.613701 |
| 4.838545 | 7.838545 |
| 3.935407 | 6.935407 |
| 4.432776 | 7.432776 |
| 4.646230 | 7.646230 |
| 2.907187 | 5.907187 |
| 2.723106 | 5.723106 |
| 4.839040 | 7.839040 |
| 4.659102 | 7.659102 |
| 4.413193 | 7.413193 |
| 4.919173 | 7.919173 |
| 3.336579 | 6.336579 |
| 4.154780 | 7.154780 |
| 5.390422 | 8.390422 |
| 3.939744 | 6.939744 |
| 2.435161 | 5.435161 |
| 4.779007 | 7.779007 |
| 5.300906 | 8.300906 |
| 3.953853 | 6.953853 |
| 3.202607 | 6.202607 |
| 3.705465 | 6.705465 |
| 5.803623 | 8.803623 |
| 3.774583 | 6.774583 |
| 4.944862 | 7.944862 |
| 3.047474 | 6.047473 |
| 3.713975 | 6.713975 |
| 3.905172 | 6.905172 |
| 5.110860 | 8.110860 |
| 5.047414 | 8.047413 |
| 4.000312 | 7.000312 |
| 6.055730 | 9.055730 |
| 4.967587 | 7.967587 |
| 5.155701 | 8.155701 |
| 5.319607 | 8.319607 |
| 5.444561 | 8.444561 |
| 4.970835 | 7.970835 |
| 3.298654 | 6.298654 |
| 4.001028 | 7.001028 |
| 5.742954 | 8.742954 |
| 3.394648 | 6.394648 |
| 2.182896 | 5.182896 |
| 3.012809 | 6.012809 |
| 3.402937 | 6.402937 |
| 3.740005 | 6.740005 |
| 3.196218 | 6.196218 |
| 3.820185 | 6.820185 |
| 4.692354 | 7.692354 |
| 1.942136 | 4.942136 |
| 5.006047 | 8.006047 |
| 4.935042 | 7.935042 |
| 4.335435 | 7.335435 |
| 4.173629 | 7.173629 |
| 4.838742 | 7.838742 |
| 5.074197 | 8.074197 |
| 3.457846 | 6.457846 |
| 4.279191 | 7.279191 |
| 4.647702 | 7.647702 |
| 4.136739 | 7.136739 |
| 3.696026 | 6.696026 |
| 5.348789 | 8.348789 |
| 4.374016 | 7.374016 |
| 6.029206 | 9.029206 |
| 3.207579 | 6.207579 |
| 5.651845 | 8.651845 |
| 3.692674 | 6.692674 |
| 4.139354 | 7.139354 |
| 3.751767 | 6.751767 |
| 5.682899 | 8.682899 |
| 3.053433 | 6.053433 |
| 4.087683 | 7.087683 |
| 5.875262 | 8.875262 |
| 4.512434 | 7.512434 |
| 3.554464 | 6.554464 |
| 4.506821 | 7.506821 |
| 5.302745 | 8.302745 |
| 4.561771 | 7.561771 |
| 4.459406 | 7.459406 |
| 3.159137 | 6.159137 |
| 4.621624 | 7.621624 |
| 2.463788 | 5.463788 |
| 4.642841 | 7.642841 |
| 2.992855 | 5.992855 |
| 2.445916 | 5.445916 |
| 2.992256 | 5.992256 |
| 3.370626 | 6.370626 |
| 4.029448 | 7.029448 |
| 4.745299 | 7.745299 |
| 3.112958 | 6.112959 |
| 4.335139 | 7.335139 |
| 3.422261 | 6.422261 |
| 2.771187 | 5.771187 |
| 4.225377 | 7.225377 |
| x | xPLIN1 |
|---|---|
| 5.150232 | 4.1502324 |
| 5.765711 | 4.7657113 |
| 3.261138 | 2.2611384 |
| 2.696714 | 1.6967143 |
| 4.509085 | 3.5090852 |
| 4.567265 | 3.5672652 |
| 4.433070 | 3.4330696 |
| 4.493653 | 3.4936526 |
| 2.613701 | 1.6137012 |
| 4.838545 | 3.8385453 |
| 3.935407 | 2.9354070 |
| 4.432776 | 3.4327757 |
| 4.646230 | 3.6462300 |
| 2.907187 | 1.9071866 |
| 2.723106 | 1.7231061 |
| 4.839040 | 3.8390404 |
| 4.659102 | 3.6591023 |
| 4.413193 | 3.4131934 |
| 4.919173 | 3.9191726 |
| 3.336579 | 2.3365789 |
| 4.154780 | 3.1547797 |
| 5.390422 | 4.3904223 |
| 3.939744 | 2.9397441 |
| 2.435161 | 1.4351613 |
| 4.779007 | 3.7790068 |
| 5.300906 | 4.3009058 |
| 3.953853 | 2.9538528 |
| 3.202607 | 2.2026068 |
| 3.705465 | 2.7054650 |
| 5.803623 | 4.8036226 |
| 3.774583 | 2.7745827 |
| 4.944862 | 3.9448615 |
| 3.047474 | 2.0474735 |
| 3.713975 | 2.7139753 |
| 3.905172 | 2.9051723 |
| 5.110860 | 4.1108598 |
| 5.047414 | 4.0474135 |
| 4.000312 | 3.0003122 |
| 6.055730 | 5.0557301 |
| 4.967587 | 3.9675871 |
| 5.155701 | 4.1557014 |
| 5.319607 | 4.3196068 |
| 5.444561 | 4.4445612 |
| 4.970835 | 3.9708351 |
| 3.298654 | 2.2986537 |
| 4.001028 | 3.0010284 |
| 5.742954 | 4.7429536 |
| 3.394648 | 2.3946483 |
| 2.182896 | 1.1828962 |
| 3.012809 | 2.0128088 |
| 3.402937 | 2.4029370 |
| 3.740005 | 2.7400048 |
| 3.196218 | 2.1962181 |
| 3.820185 | 2.8201854 |
| 4.692354 | 3.6923536 |
| 1.942136 | 0.9421357 |
| 5.006047 | 4.0060474 |
| 4.935042 | 3.9350420 |
| 4.335435 | 3.3354347 |
| 4.173629 | 3.1736294 |
| 4.838742 | 3.8387424 |
| 5.074197 | 4.0741971 |
| 3.457846 | 2.4578456 |
| 4.279191 | 3.2791909 |
| 4.647702 | 3.6477022 |
| 4.136739 | 3.1367390 |
| 3.696026 | 2.6960262 |
| 5.348789 | 4.3487889 |
| 4.374016 | 3.3740161 |
| 6.029206 | 5.0292061 |
| 3.207579 | 2.2075792 |
| 5.651845 | 4.6518448 |
| 3.692674 | 2.6926744 |
| 4.139354 | 3.1393542 |
| 3.751767 | 2.7517672 |
| 5.682899 | 4.6828992 |
| 3.053433 | 2.0534333 |
| 4.087683 | 3.0876834 |
| 5.875262 | 4.8752620 |
| 4.512434 | 3.5124342 |
| 3.554464 | 2.5544638 |
| 4.506821 | 3.5068209 |
| 5.302745 | 4.3027452 |
| 4.561771 | 3.5617708 |
| 4.459406 | 3.4594062 |
| 3.159137 | 2.1591374 |
| 4.621624 | 3.6216240 |
| 2.463788 | 1.4637878 |
| 4.642841 | 3.6428408 |
| 2.992855 | 1.9928550 |
| 2.445916 | 1.4459162 |
| 2.992256 | 1.9922557 |
| 3.370626 | 2.3706259 |
| 4.029448 | 3.0294476 |
| 4.745299 | 3.7452992 |
| 3.112958 | 2.1129585 |
| 4.335139 | 3.3351389 |
| 3.422261 | 2.4222607 |
| 2.771187 | 1.7711866 |
| 4.225377 | 3.2253772 |
3 Πολλαπλασιασμοί - διαιρέσεις
| x | xEPI2 |
|---|---|
| 5.150232 | 10.300465 |
| 5.765711 | 11.531423 |
| 3.261138 | 6.522277 |
| 2.696714 | 5.393428 |
| 4.509085 | 9.018170 |
| 4.567265 | 9.134530 |
| 4.433070 | 8.866139 |
| 4.493653 | 8.987305 |
| 2.613701 | 5.227402 |
| 4.838545 | 9.677091 |
| 3.935407 | 7.870814 |
| 4.432776 | 8.865551 |
| 4.646230 | 9.292460 |
| 2.907187 | 5.814373 |
| 2.723106 | 5.446212 |
| 4.839040 | 9.678081 |
| 4.659102 | 9.318205 |
| 4.413193 | 8.826387 |
| 4.919173 | 9.838345 |
| 3.336579 | 6.673158 |
| 4.154780 | 8.309560 |
| 5.390422 | 10.780845 |
| 3.939744 | 7.879488 |
| 2.435161 | 4.870323 |
| 4.779007 | 9.558013 |
| 5.300906 | 10.601812 |
| 3.953853 | 7.907705 |
| 3.202607 | 6.405214 |
| 3.705465 | 7.410930 |
| 5.803623 | 11.607245 |
| 3.774583 | 7.549165 |
| 4.944862 | 9.889723 |
| 3.047474 | 6.094947 |
| 3.713975 | 7.427951 |
| 3.905172 | 7.810345 |
| 5.110860 | 10.221720 |
| 5.047414 | 10.094827 |
| 4.000312 | 8.000624 |
| 6.055730 | 12.111460 |
| 4.967587 | 9.935174 |
| 5.155701 | 10.311403 |
| 5.319607 | 10.639214 |
| 5.444561 | 10.889122 |
| 4.970835 | 9.941670 |
| 3.298654 | 6.597307 |
| 4.001028 | 8.002057 |
| 5.742954 | 11.485907 |
| 3.394648 | 6.789297 |
| 2.182896 | 4.365792 |
| 3.012809 | 6.025618 |
| 3.402937 | 6.805874 |
| 3.740005 | 7.480010 |
| 3.196218 | 6.392436 |
| 3.820185 | 7.640371 |
| 4.692354 | 9.384707 |
| 1.942136 | 3.884271 |
| 5.006047 | 10.012095 |
| 4.935042 | 9.870084 |
| 4.335435 | 8.670869 |
| 4.173629 | 8.347259 |
| 4.838742 | 9.677485 |
| 5.074197 | 10.148394 |
| 3.457846 | 6.915691 |
| 4.279191 | 8.558382 |
| 4.647702 | 9.295404 |
| 4.136739 | 8.273478 |
| 3.696026 | 7.392053 |
| 5.348789 | 10.697578 |
| 4.374016 | 8.748032 |
| 6.029206 | 12.058412 |
| 3.207579 | 6.415159 |
| 5.651845 | 11.303690 |
| 3.692674 | 7.385349 |
| 4.139354 | 8.278709 |
| 3.751767 | 7.503534 |
| 5.682899 | 11.365798 |
| 3.053433 | 6.106867 |
| 4.087683 | 8.175367 |
| 5.875262 | 11.750524 |
| 4.512434 | 9.024868 |
| 3.554464 | 7.108928 |
| 4.506821 | 9.013642 |
| 5.302745 | 10.605490 |
| 4.561771 | 9.123541 |
| 4.459406 | 8.918812 |
| 3.159137 | 6.318275 |
| 4.621624 | 9.243248 |
| 2.463788 | 4.927575 |
| 4.642841 | 9.285682 |
| 2.992855 | 5.985710 |
| 2.445916 | 4.891832 |
| 2.992256 | 5.984511 |
| 3.370626 | 6.741252 |
| 4.029448 | 8.058895 |
| 4.745299 | 9.490598 |
| 3.112958 | 6.225917 |
| 4.335139 | 8.670278 |
| 3.422261 | 6.844521 |
| 2.771187 | 5.542373 |
| 4.225377 | 8.450754 |
| x | xDIA3 |
|---|---|
| 5.150232 | 1.7167441 |
| 5.765711 | 1.9219038 |
| 3.261138 | 1.0870461 |
| 2.696714 | 0.8989048 |
| 4.509085 | 1.5030284 |
| 4.567265 | 1.5224217 |
| 4.433070 | 1.4776899 |
| 4.493653 | 1.4978842 |
| 2.613701 | 0.8712337 |
| 4.838545 | 1.6128484 |
| 3.935407 | 1.3118023 |
| 4.432776 | 1.4775919 |
| 4.646230 | 1.5487433 |
| 2.907187 | 0.9690622 |
| 2.723106 | 0.9077020 |
| 4.839040 | 1.6130135 |
| 4.659102 | 1.5530341 |
| 4.413193 | 1.4710645 |
| 4.919173 | 1.6397242 |
| 3.336579 | 1.1121930 |
| 4.154780 | 1.3849266 |
| 5.390422 | 1.7968074 |
| 3.939744 | 1.3132480 |
| 2.435161 | 0.8117204 |
| 4.779007 | 1.5930023 |
| 5.300906 | 1.7669686 |
| 3.953853 | 1.3179509 |
| 3.202607 | 1.0675356 |
| 3.705465 | 1.2351550 |
| 5.803623 | 1.9345409 |
| 3.774583 | 1.2581942 |
| 4.944862 | 1.6482872 |
| 3.047474 | 1.0158245 |
| 3.713975 | 1.2379918 |
| 3.905172 | 1.3017241 |
| 5.110860 | 1.7036199 |
| 5.047414 | 1.6824712 |
| 4.000312 | 1.3334374 |
| 6.055730 | 2.0185767 |
| 4.967587 | 1.6558624 |
| 5.155701 | 1.7185671 |
| 5.319607 | 1.7732023 |
| 5.444561 | 1.8148537 |
| 4.970835 | 1.6569450 |
| 3.298654 | 1.0995512 |
| 4.001028 | 1.3336761 |
| 5.742954 | 1.9143179 |
| 3.394648 | 1.1315494 |
| 2.182896 | 0.7276321 |
| 3.012809 | 1.0042696 |
| 3.402937 | 1.1343123 |
| 3.740005 | 1.2466683 |
| 3.196218 | 1.0654060 |
| 3.820185 | 1.2733951 |
| 4.692354 | 1.5641179 |
| 1.942136 | 0.6473786 |
| 5.006047 | 1.6686825 |
| 4.935042 | 1.6450140 |
| 4.335435 | 1.4451449 |
| 4.173629 | 1.3912098 |
| 4.838742 | 1.6129141 |
| 5.074197 | 1.6913990 |
| 3.457846 | 1.1526152 |
| 4.279191 | 1.4263970 |
| 4.647702 | 1.5492341 |
| 4.136739 | 1.3789130 |
| 3.696026 | 1.2320087 |
| 5.348789 | 1.7829296 |
| 4.374016 | 1.4580054 |
| 6.029206 | 2.0097354 |
| 3.207579 | 1.0691931 |
| 5.651845 | 1.8839483 |
| 3.692674 | 1.2308915 |
| 4.139354 | 1.3797847 |
| 3.751767 | 1.2505891 |
| 5.682899 | 1.8942997 |
| 3.053433 | 1.0178111 |
| 4.087683 | 1.3625611 |
| 5.875262 | 1.9584207 |
| 4.512434 | 1.5041447 |
| 3.554464 | 1.1848213 |
| 4.506821 | 1.5022736 |
| 5.302745 | 1.7675817 |
| 4.561771 | 1.5205903 |
| 4.459406 | 1.4864687 |
| 3.159137 | 1.0530458 |
| 4.621624 | 1.5405413 |
| 2.463788 | 0.8212626 |
| 4.642841 | 1.5476136 |
| 2.992855 | 0.9976183 |
| 2.445916 | 0.8153054 |
| 2.992256 | 0.9974186 |
| 3.370626 | 1.1235420 |
| 4.029448 | 1.3431492 |
| 4.745299 | 1.5817664 |
| 3.112958 | 1.0376528 |
| 4.335139 | 1.4450463 |
| 3.422261 | 1.1407536 |
| 2.771187 | 0.9237289 |
| 4.225377 | 1.4084591 |
| x | xEPIplin2 |
|---|---|
| 5.150232 | -10.300465 |
| 5.765711 | -11.531423 |
| 3.261138 | -6.522277 |
| 2.696714 | -5.393428 |
| 4.509085 | -9.018170 |
| 4.567265 | -9.134530 |
| 4.433070 | -8.866139 |
| 4.493653 | -8.987305 |
| 2.613701 | -5.227402 |
| 4.838545 | -9.677091 |
| 3.935407 | -7.870814 |
| 4.432776 | -8.865551 |
| 4.646230 | -9.292460 |
| 2.907187 | -5.814373 |
| 2.723106 | -5.446212 |
| 4.839040 | -9.678081 |
| 4.659102 | -9.318205 |
| 4.413193 | -8.826387 |
| 4.919173 | -9.838345 |
| 3.336579 | -6.673158 |
| 4.154780 | -8.309560 |
| 5.390422 | -10.780845 |
| 3.939744 | -7.879488 |
| 2.435161 | -4.870323 |
| 4.779007 | -9.558013 |
| 5.300906 | -10.601812 |
| 3.953853 | -7.907705 |
| 3.202607 | -6.405214 |
| 3.705465 | -7.410930 |
| 5.803623 | -11.607245 |
| 3.774583 | -7.549165 |
| 4.944862 | -9.889723 |
| 3.047474 | -6.094947 |
| 3.713975 | -7.427951 |
| 3.905172 | -7.810345 |
| 5.110860 | -10.221720 |
| 5.047414 | -10.094827 |
| 4.000312 | -8.000624 |
| 6.055730 | -12.111460 |
| 4.967587 | -9.935174 |
| 5.155701 | -10.311403 |
| 5.319607 | -10.639214 |
| 5.444561 | -10.889122 |
| 4.970835 | -9.941670 |
| 3.298654 | -6.597307 |
| 4.001028 | -8.002057 |
| 5.742954 | -11.485907 |
| 3.394648 | -6.789297 |
| 2.182896 | -4.365792 |
| 3.012809 | -6.025618 |
| 3.402937 | -6.805874 |
| 3.740005 | -7.480010 |
| 3.196218 | -6.392436 |
| 3.820185 | -7.640371 |
| 4.692354 | -9.384707 |
| 1.942136 | -3.884271 |
| 5.006047 | -10.012095 |
| 4.935042 | -9.870084 |
| 4.335435 | -8.670869 |
| 4.173629 | -8.347259 |
| 4.838742 | -9.677485 |
| 5.074197 | -10.148394 |
| 3.457846 | -6.915691 |
| 4.279191 | -8.558382 |
| 4.647702 | -9.295404 |
| 4.136739 | -8.273478 |
| 3.696026 | -7.392053 |
| 5.348789 | -10.697578 |
| 4.374016 | -8.748032 |
| 6.029206 | -12.058412 |
| 3.207579 | -6.415159 |
| 5.651845 | -11.303690 |
| 3.692674 | -7.385349 |
| 4.139354 | -8.278709 |
| 3.751767 | -7.503534 |
| 5.682899 | -11.365798 |
| 3.053433 | -6.106867 |
| 4.087683 | -8.175367 |
| 5.875262 | -11.750524 |
| 4.512434 | -9.024868 |
| 3.554464 | -7.108928 |
| 4.506821 | -9.013642 |
| 5.302745 | -10.605490 |
| 4.561771 | -9.123541 |
| 4.459406 | -8.918812 |
| 3.159137 | -6.318275 |
| 4.621624 | -9.243248 |
| 2.463788 | -4.927575 |
| 4.642841 | -9.285682 |
| 2.992855 | -5.985710 |
| 2.445916 | -4.891832 |
| 2.992256 | -5.984511 |
| 3.370626 | -6.741252 |
| 4.029448 | -8.058895 |
| 4.745299 | -9.490598 |
| 3.112958 | -6.225917 |
| 4.335139 | -8.670278 |
| 3.422261 | -6.844521 |
| 2.771187 | -5.542373 |
| 4.225377 | -8.450754 |