DM: Étude de données
LECORPS Germain
Octobre 2015
On récupère tout d’abord les données à étudier qu’on affiche sous forme de “tableau” pour voir à quel type de données on a à faire.
data<-read.csv("data.csv",header=F)$V1
str(data);## num [1:8382] 1 0.748 0.813 0.942 0.695 0.764 0.753 0.854 0.736 0.697 ...Première visualisation
plot(data, type ='l', xlab = "Frequency", ylab = "Time (ms)");
On voit que la majorité des données se trouve à moins d’une ms mais que certaines valeurs dépassent largement cette ms. Sacahnt qu’on étudie des ping réguliers vers une machine, on peut supposer que ces valeurs abérantes résultent d’un problème de réponse venant de la machine sur laquelle les ping sont effectués.
En affichant les points et les lignes, on peut se rendre compte que les pics de valeurs sont atteints ponctuelement.
plot(data, type ='b', xlab = "Frequency", ylab = "Time (ms)");
La bande noire nous informe que outre les quelques valeurs abérantes, le régime semble sationnaire.
Histogrammes
Pour confirmer les suppositions précédentes, on va tracer un histogramme des données.
hist(data, xlab = "Time (ms)");
On observe bien que la grande majorité des données à l’air d’être très “petite” (temps petits). On va donc essayer d’affiner cet histogramme pour mieux observer ce qu’il se passe.
hist(data, xaxp = c(0, 20, 1), xlim = c(0, 20), breaks = 2000, xlab = "Time (ms)");
On voit que les données sont encore plus proches de 0 on va donc affiner l’histogramme encore plus.
histinfo <- hist(data, xaxp = c(0, 4, 1), xlim = c(0, 4), breaks = 2000, xlab = "Time (ms)");
On observe alors bien que la grande majorité des données se situe entre 0.6 et 0.8 (voir annexe).
Résumé
summary(data)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.6140 0.7030 0.7315 0.8922 0.7880 169.0000var(data)## [1] 6.897606sd(data)## [1] 2.626329boxplot(data, ylab = "Time (ms)")
Avec ces informations, on conclue plusieurs choses. Premièrement, la moyenne des valeurs est un peu plus élevée que l’intervalle dans lequel on a observé le maximum de données mais cela s’explique du fait que les valeurs “abérantes” qu’on observe sont bien plus élevées que la moyenne.
La variance ne nous donne pas beaucoup d’informations ici si ce n’est qu’elle confirme que certaines valeurs sont bien plus élevées que la moyenne (variance assez haute). On va donc regarder l’écart type qui lui est assez faible et conforte l’idée que les valeurs plus élevées sont bien des problèmes matériels (typiquement retard de la réponse parce que le réseau était trop encombré au moment de la requête).
Au final, le boxplot nous confirme bien que le régime général est stationnaire autour de 0.7ms et que les quelques valeurs extrèmes sont bien des erreurs. Ce qui coincide bien avec la réalité. C’est à dire que des pings réguliers vers une même machine vont avoir environ le même temps de réponse à chaque fois sauf si le réseau est encombré par trop de requêtes au moment du ping (valeurs abérantes du jeu de données).
Annexe
L’affichage de histinfo nous permet de voir que les 2000 breaks affinent le tracé à 0.1 près sur l’axe du temps ce qui nous permet d’affirmer que la plus grande partie des données se trouve entre 0.6ms et 0.8ms.
histinfo;## $breaks
## [1] 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [12] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7
## [23] 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8
## [34] 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
## [45] 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0
## [56] 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1
## [67] 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2
## [78] 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3
## [89] 9.4 9.5 9.6 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4
## [100] 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.4 11.5
## [111] 11.6 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5 12.6
## [122] 12.7 12.8 12.9 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7
## [133] 13.8 13.9 14.0 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8
## [144] 14.9 15.0 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
## [155] 16.0 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17.0
## [166] 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18.0 18.1
## [177] 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19.0 19.1 19.2
## [188] 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20.0 20.1 20.2 20.3
## [199] 20.4 20.5 20.6 20.7 20.8 20.9 21.0 21.1 21.2 21.3 21.4
## [210] 21.5 21.6 21.7 21.8 21.9 22.0 22.1 22.2 22.3 22.4 22.5
## [221] 22.6 22.7 22.8 22.9 23.0 23.1 23.2 23.3 23.4 23.5 23.6
## [232] 23.7 23.8 23.9 24.0 24.1 24.2 24.3 24.4 24.5 24.6 24.7
## [243] 24.8 24.9 25.0 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8
## [254] 25.9 26.0 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9
## [265] 27.0 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28.0
## [276] 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29.0 29.1
## [287] 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 30.0 30.1 30.2
## [298] 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31.0 31.1 31.2 31.3
## [309] 31.4 31.5 31.6 31.7 31.8 31.9 32.0 32.1 32.2 32.3 32.4
## [320] 32.5 32.6 32.7 32.8 32.9 33.0 33.1 33.2 33.3 33.4 33.5
## [331] 33.6 33.7 33.8 33.9 34.0 34.1 34.2 34.3 34.4 34.5 34.6
## [342] 34.7 34.8 34.9 35.0 35.1 35.2 35.3 35.4 35.5 35.6 35.7
## [353] 35.8 35.9 36.0 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8
## [364] 36.9 37.0 37.1 37.2 37.3 37.4 37.5 37.6 37.7 37.8 37.9
## [375] 38.0 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.9 39.0
## [386] 39.1 39.2 39.3 39.4 39.5 39.6 39.7 39.8 39.9 40.0 40.1
## [397] 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 41.0 41.1 41.2
## [408] 41.3 41.4 41.5 41.6 41.7 41.8 41.9 42.0 42.1 42.2 42.3
## [419] 42.4 42.5 42.6 42.7 42.8 42.9 43.0 43.1 43.2 43.3 43.4
## [430] 43.5 43.6 43.7 43.8 43.9 44.0 44.1 44.2 44.3 44.4 44.5
## [441] 44.6 44.7 44.8 44.9 45.0 45.1 45.2 45.3 45.4 45.5 45.6
## [452] 45.7 45.8 45.9 46.0 46.1 46.2 46.3 46.4 46.5 46.6 46.7
## [463] 46.8 46.9 47.0 47.1 47.2 47.3 47.4 47.5 47.6 47.7 47.8
## [474] 47.9 48.0 48.1 48.2 48.3 48.4 48.5 48.6 48.7 48.8 48.9
## [485] 49.0 49.1 49.2 49.3 49.4 49.5 49.6 49.7 49.8 49.9 50.0
## [496] 50.1 50.2 50.3 50.4 50.5 50.6 50.7 50.8 50.9 51.0 51.1
## [507] 51.2 51.3 51.4 51.5 51.6 51.7 51.8 51.9 52.0 52.1 52.2
## [518] 52.3 52.4 52.5 52.6 52.7 52.8 52.9 53.0 53.1 53.2 53.3
## [529] 53.4 53.5 53.6 53.7 53.8 53.9 54.0 54.1 54.2 54.3 54.4
## [540] 54.5 54.6 54.7 54.8 54.9 55.0 55.1 55.2 55.3 55.4 55.5
## [551] 55.6 55.7 55.8 55.9 56.0 56.1 56.2 56.3 56.4 56.5 56.6
## [562] 56.7 56.8 56.9 57.0 57.1 57.2 57.3 57.4 57.5 57.6 57.7
## [573] 57.8 57.9 58.0 58.1 58.2 58.3 58.4 58.5 58.6 58.7 58.8
## [584] 58.9 59.0 59.1 59.2 59.3 59.4 59.5 59.6 59.7 59.8 59.9
## [595] 60.0 60.1 60.2 60.3 60.4 60.5 60.6 60.7 60.8 60.9 61.0
## [606] 61.1 61.2 61.3 61.4 61.5 61.6 61.7 61.8 61.9 62.0 62.1
## [617] 62.2 62.3 62.4 62.5 62.6 62.7 62.8 62.9 63.0 63.1 63.2
## [628] 63.3 63.4 63.5 63.6 63.7 63.8 63.9 64.0 64.1 64.2 64.3
## [639] 64.4 64.5 64.6 64.7 64.8 64.9 65.0 65.1 65.2 65.3 65.4
## [650] 65.5 65.6 65.7 65.8 65.9 66.0 66.1 66.2 66.3 66.4 66.5
## [661] 66.6 66.7 66.8 66.9 67.0 67.1 67.2 67.3 67.4 67.5 67.6
## [672] 67.7 67.8 67.9 68.0 68.1 68.2 68.3 68.4 68.5 68.6 68.7
## [683] 68.8 68.9 69.0 69.1 69.2 69.3 69.4 69.5 69.6 69.7 69.8
## [694] 69.9 70.0 70.1 70.2 70.3 70.4 70.5 70.6 70.7 70.8 70.9
## [705] 71.0 71.1 71.2 71.3 71.4 71.5 71.6 71.7 71.8 71.9 72.0
## [716] 72.1 72.2 72.3 72.4 72.5 72.6 72.7 72.8 72.9 73.0 73.1
## [727] 73.2 73.3 73.4 73.5 73.6 73.7 73.8 73.9 74.0 74.1 74.2
## [738] 74.3 74.4 74.5 74.6 74.7 74.8 74.9 75.0 75.1 75.2 75.3
## [749] 75.4 75.5 75.6 75.7 75.8 75.9 76.0 76.1 76.2 76.3 76.4
## [760] 76.5 76.6 76.7 76.8 76.9 77.0 77.1 77.2 77.3 77.4 77.5
## [771] 77.6 77.7 77.8 77.9 78.0 78.1 78.2 78.3 78.4 78.5 78.6
## [782] 78.7 78.8 78.9 79.0 79.1 79.2 79.3 79.4 79.5 79.6 79.7
## [793] 79.8 79.9 80.0 80.1 80.2 80.3 80.4 80.5 80.6 80.7 80.8
## [804] 80.9 81.0 81.1 81.2 81.3 81.4 81.5 81.6 81.7 81.8 81.9
## [815] 82.0 82.1 82.2 82.3 82.4 82.5 82.6 82.7 82.8 82.9 83.0
## [826] 83.1 83.2 83.3 83.4 83.5 83.6 83.7 83.8 83.9 84.0 84.1
## [837] 84.2 84.3 84.4 84.5 84.6 84.7 84.8 84.9 85.0 85.1 85.2
## [848] 85.3 85.4 85.5 85.6 85.7 85.8 85.9 86.0 86.1 86.2 86.3
## [859] 86.4 86.5 86.6 86.7 86.8 86.9 87.0 87.1 87.2 87.3 87.4
## [870] 87.5 87.6 87.7 87.8 87.9 88.0 88.1 88.2 88.3 88.4 88.5
## [881] 88.6 88.7 88.8 88.9 89.0 89.1 89.2 89.3 89.4 89.5 89.6
## [892] 89.7 89.8 89.9 90.0 90.1 90.2 90.3 90.4 90.5 90.6 90.7
## [903] 90.8 90.9 91.0 91.1 91.2 91.3 91.4 91.5 91.6 91.7 91.8
## [914] 91.9 92.0 92.1 92.2 92.3 92.4 92.5 92.6 92.7 92.8 92.9
## [925] 93.0 93.1 93.2 93.3 93.4 93.5 93.6 93.7 93.8 93.9 94.0
## [936] 94.1 94.2 94.3 94.4 94.5 94.6 94.7 94.8 94.9 95.0 95.1
## [947] 95.2 95.3 95.4 95.5 95.6 95.7 95.8 95.9 96.0 96.1 96.2
## [958] 96.3 96.4 96.5 96.6 96.7 96.8 96.9 97.0 97.1 97.2 97.3
## [969] 97.4 97.5 97.6 97.7 97.8 97.9 98.0 98.1 98.2 98.3 98.4
## [980] 98.5 98.6 98.7 98.8 98.9 99.0 99.1 99.2 99.3 99.4 99.5
## [991] 99.6 99.7 99.8 99.9 100.0 100.1 100.2 100.3 100.4 100.5 100.6
## [1002] 100.7 100.8 100.9 101.0 101.1 101.2 101.3 101.4 101.5 101.6 101.7
## [1013] 101.8 101.9 102.0 102.1 102.2 102.3 102.4 102.5 102.6 102.7 102.8
## [1024] 102.9 103.0 103.1 103.2 103.3 103.4 103.5 103.6 103.7 103.8 103.9
## [1035] 104.0 104.1 104.2 104.3 104.4 104.5 104.6 104.7 104.8 104.9 105.0
## [1046] 105.1 105.2 105.3 105.4 105.5 105.6 105.7 105.8 105.9 106.0 106.1
## [1057] 106.2 106.3 106.4 106.5 106.6 106.7 106.8 106.9 107.0 107.1 107.2
## [1068] 107.3 107.4 107.5 107.6 107.7 107.8 107.9 108.0 108.1 108.2 108.3
## [1079] 108.4 108.5 108.6 108.7 108.8 108.9 109.0 109.1 109.2 109.3 109.4
## [1090] 109.5 109.6 109.7 109.8 109.9 110.0 110.1 110.2 110.3 110.4 110.5
## [1101] 110.6 110.7 110.8 110.9 111.0 111.1 111.2 111.3 111.4 111.5 111.6
## [1112] 111.7 111.8 111.9 112.0 112.1 112.2 112.3 112.4 112.5 112.6 112.7
## [1123] 112.8 112.9 113.0 113.1 113.2 113.3 113.4 113.5 113.6 113.7 113.8
## [1134] 113.9 114.0 114.1 114.2 114.3 114.4 114.5 114.6 114.7 114.8 114.9
## [1145] 115.0 115.1 115.2 115.3 115.4 115.5 115.6 115.7 115.8 115.9 116.0
## [1156] 116.1 116.2 116.3 116.4 116.5 116.6 116.7 116.8 116.9 117.0 117.1
## [1167] 117.2 117.3 117.4 117.5 117.6 117.7 117.8 117.9 118.0 118.1 118.2
## [1178] 118.3 118.4 118.5 118.6 118.7 118.8 118.9 119.0 119.1 119.2 119.3
## [1189] 119.4 119.5 119.6 119.7 119.8 119.9 120.0 120.1 120.2 120.3 120.4
## [1200] 120.5 120.6 120.7 120.8 120.9 121.0 121.1 121.2 121.3 121.4 121.5
## [1211] 121.6 121.7 121.8 121.9 122.0 122.1 122.2 122.3 122.4 122.5 122.6
## [1222] 122.7 122.8 122.9 123.0 123.1 123.2 123.3 123.4 123.5 123.6 123.7
## [1233] 123.8 123.9 124.0 124.1 124.2 124.3 124.4 124.5 124.6 124.7 124.8
## [1244] 124.9 125.0 125.1 125.2 125.3 125.4 125.5 125.6 125.7 125.8 125.9
## [1255] 126.0 126.1 126.2 126.3 126.4 126.5 126.6 126.7 126.8 126.9 127.0
## [1266] 127.1 127.2 127.3 127.4 127.5 127.6 127.7 127.8 127.9 128.0 128.1
## [1277] 128.2 128.3 128.4 128.5 128.6 128.7 128.8 128.9 129.0 129.1 129.2
## [1288] 129.3 129.4 129.5 129.6 129.7 129.8 129.9 130.0 130.1 130.2 130.3
## [1299] 130.4 130.5 130.6 130.7 130.8 130.9 131.0 131.1 131.2 131.3 131.4
## [1310] 131.5 131.6 131.7 131.8 131.9 132.0 132.1 132.2 132.3 132.4 132.5
## [1321] 132.6 132.7 132.8 132.9 133.0 133.1 133.2 133.3 133.4 133.5 133.6
## [1332] 133.7 133.8 133.9 134.0 134.1 134.2 134.3 134.4 134.5 134.6 134.7
## [1343] 134.8 134.9 135.0 135.1 135.2 135.3 135.4 135.5 135.6 135.7 135.8
## [1354] 135.9 136.0 136.1 136.2 136.3 136.4 136.5 136.6 136.7 136.8 136.9
## [1365] 137.0 137.1 137.2 137.3 137.4 137.5 137.6 137.7 137.8 137.9 138.0
## [1376] 138.1 138.2 138.3 138.4 138.5 138.6 138.7 138.8 138.9 139.0 139.1
## [1387] 139.2 139.3 139.4 139.5 139.6 139.7 139.8 139.9 140.0 140.1 140.2
## [1398] 140.3 140.4 140.5 140.6 140.7 140.8 140.9 141.0 141.1 141.2 141.3
## [1409] 141.4 141.5 141.6 141.7 141.8 141.9 142.0 142.1 142.2 142.3 142.4
## [1420] 142.5 142.6 142.7 142.8 142.9 143.0 143.1 143.2 143.3 143.4 143.5
## [1431] 143.6 143.7 143.8 143.9 144.0 144.1 144.2 144.3 144.4 144.5 144.6
## [1442] 144.7 144.8 144.9 145.0 145.1 145.2 145.3 145.4 145.5 145.6 145.7
## [1453] 145.8 145.9 146.0 146.1 146.2 146.3 146.4 146.5 146.6 146.7 146.8
## [1464] 146.9 147.0 147.1 147.2 147.3 147.4 147.5 147.6 147.7 147.8 147.9
## [1475] 148.0 148.1 148.2 148.3 148.4 148.5 148.6 148.7 148.8 148.9 149.0
## [1486] 149.1 149.2 149.3 149.4 149.5 149.6 149.7 149.8 149.9 150.0 150.1
## [1497] 150.2 150.3 150.4 150.5 150.6 150.7 150.8 150.9 151.0 151.1 151.2
## [1508] 151.3 151.4 151.5 151.6 151.7 151.8 151.9 152.0 152.1 152.2 152.3
## [1519] 152.4 152.5 152.6 152.7 152.8 152.9 153.0 153.1 153.2 153.3 153.4
## [1530] 153.5 153.6 153.7 153.8 153.9 154.0 154.1 154.2 154.3 154.4 154.5
## [1541] 154.6 154.7 154.8 154.9 155.0 155.1 155.2 155.3 155.4 155.5 155.6
## [1552] 155.7 155.8 155.9 156.0 156.1 156.2 156.3 156.4 156.5 156.6 156.7
## [1563] 156.8 156.9 157.0 157.1 157.2 157.3 157.4 157.5 157.6 157.7 157.8
## [1574] 157.9 158.0 158.1 158.2 158.3 158.4 158.5 158.6 158.7 158.8 158.9
## [1585] 159.0 159.1 159.2 159.3 159.4 159.5 159.6 159.7 159.8 159.9 160.0
## [1596] 160.1 160.2 160.3 160.4 160.5 160.6 160.7 160.8 160.9 161.0 161.1
## [1607] 161.2 161.3 161.4 161.5 161.6 161.7 161.8 161.9 162.0 162.1 162.2
## [1618] 162.3 162.4 162.5 162.6 162.7 162.8 162.9 163.0 163.1 163.2 163.3
## [1629] 163.4 163.5 163.6 163.7 163.8 163.9 164.0 164.1 164.2 164.3 164.4
## [1640] 164.5 164.6 164.7 164.8 164.9 165.0 165.1 165.2 165.3 165.4 165.5
## [1651] 165.6 165.7 165.8 165.9 166.0 166.1 166.2 166.3 166.4 166.5 166.6
## [1662] 166.7 166.8 166.9 167.0 167.1 167.2 167.3 167.4 167.5 167.6 167.7
## [1673] 167.8 167.9 168.0 168.1 168.2 168.3 168.4 168.5 168.6 168.7 168.8
## [1684] 168.9 169.0
##
## $counts
## [1] 1902 4667 1024 298 184 50 27 25 21 17 10 11 7
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## [1246] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1251] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1256] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1261] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1266] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1271] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1276] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1281] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1286] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1291] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1296] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1301] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1306] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1311] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1316] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1321] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1326] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1331] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1336] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1341] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1346] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1351] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1356] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1361] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1366] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1371] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1376] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1381] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1386] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1391] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1396] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1401] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1406] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1411] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1416] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1421] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1426] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1431] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1436] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1441] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1446] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1451] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1456] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1461] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1466] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1471] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1476] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1481] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1486] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1491] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1496] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1501] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1506] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1511] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1516] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1521] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1526] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1531] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1536] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1541] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1546] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1551] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1556] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1561] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1566] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1571] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1576] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1581] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1586] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1591] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1596] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1601] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1606] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1611] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1616] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1621] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1626] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1631] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1636] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1641] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1646] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1651] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1656] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1661] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1666] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1671] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1676] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [1681] 0.000000000 0.000000000 0.000000000 0.001193033
##
## $mids
## [1] 0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35 1.45
## [10] 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25 2.35
## [19] 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25
## [28] 3.35 3.45 3.55 3.65 3.75 3.85 3.95 4.05 4.15
## [37] 4.25 4.35 4.45 4.55 4.65 4.75 4.85 4.95 5.05
## [46] 5.15 5.25 5.35 5.45 5.55 5.65 5.75 5.85 5.95
## [55] 6.05 6.15 6.25 6.35 6.45 6.55 6.65 6.75 6.85
## [64] 6.95 7.05 7.15 7.25 7.35 7.45 7.55 7.65 7.75
## [73] 7.85 7.95 8.05 8.15 8.25 8.35 8.45 8.55 8.65
## [82] 8.75 8.85 8.95 9.05 9.15 9.25 9.35 9.45 9.55
## [91] 9.65 9.75 9.85 9.95 10.05 10.15 10.25 10.35 10.45
## [100] 10.55 10.65 10.75 10.85 10.95 11.05 11.15 11.25 11.35
## [109] 11.45 11.55 11.65 11.75 11.85 11.95 12.05 12.15 12.25
## [118] 12.35 12.45 12.55 12.65 12.75 12.85 12.95 13.05 13.15
## [127] 13.25 13.35 13.45 13.55 13.65 13.75 13.85 13.95 14.05
## [136] 14.15 14.25 14.35 14.45 14.55 14.65 14.75 14.85 14.95
## [145] 15.05 15.15 15.25 15.35 15.45 15.55 15.65 15.75 15.85
## [154] 15.95 16.05 16.15 16.25 16.35 16.45 16.55 16.65 16.75
## [163] 16.85 16.95 17.05 17.15 17.25 17.35 17.45 17.55 17.65
## [172] 17.75 17.85 17.95 18.05 18.15 18.25 18.35 18.45 18.55
## [181] 18.65 18.75 18.85 18.95 19.05 19.15 19.25 19.35 19.45
## [190] 19.55 19.65 19.75 19.85 19.95 20.05 20.15 20.25 20.35
## [199] 20.45 20.55 20.65 20.75 20.85 20.95 21.05 21.15 21.25
## [208] 21.35 21.45 21.55 21.65 21.75 21.85 21.95 22.05 22.15
## [217] 22.25 22.35 22.45 22.55 22.65 22.75 22.85 22.95 23.05
## [226] 23.15 23.25 23.35 23.45 23.55 23.65 23.75 23.85 23.95
## [235] 24.05 24.15 24.25 24.35 24.45 24.55 24.65 24.75 24.85
## [244] 24.95 25.05 25.15 25.25 25.35 25.45 25.55 25.65 25.75
## [253] 25.85 25.95 26.05 26.15 26.25 26.35 26.45 26.55 26.65
## [262] 26.75 26.85 26.95 27.05 27.15 27.25 27.35 27.45 27.55
## [271] 27.65 27.75 27.85 27.95 28.05 28.15 28.25 28.35 28.45
## [280] 28.55 28.65 28.75 28.85 28.95 29.05 29.15 29.25 29.35
## [289] 29.45 29.55 29.65 29.75 29.85 29.95 30.05 30.15 30.25
## [298] 30.35 30.45 30.55 30.65 30.75 30.85 30.95 31.05 31.15
## [307] 31.25 31.35 31.45 31.55 31.65 31.75 31.85 31.95 32.05
## [316] 32.15 32.25 32.35 32.45 32.55 32.65 32.75 32.85 32.95
## [325] 33.05 33.15 33.25 33.35 33.45 33.55 33.65 33.75 33.85
## [334] 33.95 34.05 34.15 34.25 34.35 34.45 34.55 34.65 34.75
## [343] 34.85 34.95 35.05 35.15 35.25 35.35 35.45 35.55 35.65
## [352] 35.75 35.85 35.95 36.05 36.15 36.25 36.35 36.45 36.55
## [361] 36.65 36.75 36.85 36.95 37.05 37.15 37.25 37.35 37.45
## [370] 37.55 37.65 37.75 37.85 37.95 38.05 38.15 38.25 38.35
## [379] 38.45 38.55 38.65 38.75 38.85 38.95 39.05 39.15 39.25
## [388] 39.35 39.45 39.55 39.65 39.75 39.85 39.95 40.05 40.15
## [397] 40.25 40.35 40.45 40.55 40.65 40.75 40.85 40.95 41.05
## [406] 41.15 41.25 41.35 41.45 41.55 41.65 41.75 41.85 41.95
## [415] 42.05 42.15 42.25 42.35 42.45 42.55 42.65 42.75 42.85
## [424] 42.95 43.05 43.15 43.25 43.35 43.45 43.55 43.65 43.75
## [433] 43.85 43.95 44.05 44.15 44.25 44.35 44.45 44.55 44.65
## [442] 44.75 44.85 44.95 45.05 45.15 45.25 45.35 45.45 45.55
## [451] 45.65 45.75 45.85 45.95 46.05 46.15 46.25 46.35 46.45
## [460] 46.55 46.65 46.75 46.85 46.95 47.05 47.15 47.25 47.35
## [469] 47.45 47.55 47.65 47.75 47.85 47.95 48.05 48.15 48.25
## [478] 48.35 48.45 48.55 48.65 48.75 48.85 48.95 49.05 49.15
## [487] 49.25 49.35 49.45 49.55 49.65 49.75 49.85 49.95 50.05
## [496] 50.15 50.25 50.35 50.45 50.55 50.65 50.75 50.85 50.95
## [505] 51.05 51.15 51.25 51.35 51.45 51.55 51.65 51.75 51.85
## [514] 51.95 52.05 52.15 52.25 52.35 52.45 52.55 52.65 52.75
## [523] 52.85 52.95 53.05 53.15 53.25 53.35 53.45 53.55 53.65
## [532] 53.75 53.85 53.95 54.05 54.15 54.25 54.35 54.45 54.55
## [541] 54.65 54.75 54.85 54.95 55.05 55.15 55.25 55.35 55.45
## [550] 55.55 55.65 55.75 55.85 55.95 56.05 56.15 56.25 56.35
## [559] 56.45 56.55 56.65 56.75 56.85 56.95 57.05 57.15 57.25
## [568] 57.35 57.45 57.55 57.65 57.75 57.85 57.95 58.05 58.15
## [577] 58.25 58.35 58.45 58.55 58.65 58.75 58.85 58.95 59.05
## [586] 59.15 59.25 59.35 59.45 59.55 59.65 59.75 59.85 59.95
## [595] 60.05 60.15 60.25 60.35 60.45 60.55 60.65 60.75 60.85
## [604] 60.95 61.05 61.15 61.25 61.35 61.45 61.55 61.65 61.75
## [613] 61.85 61.95 62.05 62.15 62.25 62.35 62.45 62.55 62.65
## [622] 62.75 62.85 62.95 63.05 63.15 63.25 63.35 63.45 63.55
## [631] 63.65 63.75 63.85 63.95 64.05 64.15 64.25 64.35 64.45
## [640] 64.55 64.65 64.75 64.85 64.95 65.05 65.15 65.25 65.35
## [649] 65.45 65.55 65.65 65.75 65.85 65.95 66.05 66.15 66.25
## [658] 66.35 66.45 66.55 66.65 66.75 66.85 66.95 67.05 67.15
## [667] 67.25 67.35 67.45 67.55 67.65 67.75 67.85 67.95 68.05
## [676] 68.15 68.25 68.35 68.45 68.55 68.65 68.75 68.85 68.95
## [685] 69.05 69.15 69.25 69.35 69.45 69.55 69.65 69.75 69.85
## [694] 69.95 70.05 70.15 70.25 70.35 70.45 70.55 70.65 70.75
## [703] 70.85 70.95 71.05 71.15 71.25 71.35 71.45 71.55 71.65
## [712] 71.75 71.85 71.95 72.05 72.15 72.25 72.35 72.45 72.55
## [721] 72.65 72.75 72.85 72.95 73.05 73.15 73.25 73.35 73.45
## [730] 73.55 73.65 73.75 73.85 73.95 74.05 74.15 74.25 74.35
## [739] 74.45 74.55 74.65 74.75 74.85 74.95 75.05 75.15 75.25
## [748] 75.35 75.45 75.55 75.65 75.75 75.85 75.95 76.05 76.15
## [757] 76.25 76.35 76.45 76.55 76.65 76.75 76.85 76.95 77.05
## [766] 77.15 77.25 77.35 77.45 77.55 77.65 77.75 77.85 77.95
## [775] 78.05 78.15 78.25 78.35 78.45 78.55 78.65 78.75 78.85
## [784] 78.95 79.05 79.15 79.25 79.35 79.45 79.55 79.65 79.75
## [793] 79.85 79.95 80.05 80.15 80.25 80.35 80.45 80.55 80.65
## [802] 80.75 80.85 80.95 81.05 81.15 81.25 81.35 81.45 81.55
## [811] 81.65 81.75 81.85 81.95 82.05 82.15 82.25 82.35 82.45
## [820] 82.55 82.65 82.75 82.85 82.95 83.05 83.15 83.25 83.35
## [829] 83.45 83.55 83.65 83.75 83.85 83.95 84.05 84.15 84.25
## [838] 84.35 84.45 84.55 84.65 84.75 84.85 84.95 85.05 85.15
## [847] 85.25 85.35 85.45 85.55 85.65 85.75 85.85 85.95 86.05
## [856] 86.15 86.25 86.35 86.45 86.55 86.65 86.75 86.85 86.95
## [865] 87.05 87.15 87.25 87.35 87.45 87.55 87.65 87.75 87.85
## [874] 87.95 88.05 88.15 88.25 88.35 88.45 88.55 88.65 88.75
## [883] 88.85 88.95 89.05 89.15 89.25 89.35 89.45 89.55 89.65
## [892] 89.75 89.85 89.95 90.05 90.15 90.25 90.35 90.45 90.55
## [901] 90.65 90.75 90.85 90.95 91.05 91.15 91.25 91.35 91.45
## [910] 91.55 91.65 91.75 91.85 91.95 92.05 92.15 92.25 92.35
## [919] 92.45 92.55 92.65 92.75 92.85 92.95 93.05 93.15 93.25
## [928] 93.35 93.45 93.55 93.65 93.75 93.85 93.95 94.05 94.15
## [937] 94.25 94.35 94.45 94.55 94.65 94.75 94.85 94.95 95.05
## [946] 95.15 95.25 95.35 95.45 95.55 95.65 95.75 95.85 95.95
## [955] 96.05 96.15 96.25 96.35 96.45 96.55 96.65 96.75 96.85
## [964] 96.95 97.05 97.15 97.25 97.35 97.45 97.55 97.65 97.75
## [973] 97.85 97.95 98.05 98.15 98.25 98.35 98.45 98.55 98.65
## [982] 98.75 98.85 98.95 99.05 99.15 99.25 99.35 99.45 99.55
## [991] 99.65 99.75 99.85 99.95 100.05 100.15 100.25 100.35 100.45
## [1000] 100.55 100.65 100.75 100.85 100.95 101.05 101.15 101.25 101.35
## [1009] 101.45 101.55 101.65 101.75 101.85 101.95 102.05 102.15 102.25
## [1018] 102.35 102.45 102.55 102.65 102.75 102.85 102.95 103.05 103.15
## [1027] 103.25 103.35 103.45 103.55 103.65 103.75 103.85 103.95 104.05
## [1036] 104.15 104.25 104.35 104.45 104.55 104.65 104.75 104.85 104.95
## [1045] 105.05 105.15 105.25 105.35 105.45 105.55 105.65 105.75 105.85
## [1054] 105.95 106.05 106.15 106.25 106.35 106.45 106.55 106.65 106.75
## [1063] 106.85 106.95 107.05 107.15 107.25 107.35 107.45 107.55 107.65
## [1072] 107.75 107.85 107.95 108.05 108.15 108.25 108.35 108.45 108.55
## [1081] 108.65 108.75 108.85 108.95 109.05 109.15 109.25 109.35 109.45
## [1090] 109.55 109.65 109.75 109.85 109.95 110.05 110.15 110.25 110.35
## [1099] 110.45 110.55 110.65 110.75 110.85 110.95 111.05 111.15 111.25
## [1108] 111.35 111.45 111.55 111.65 111.75 111.85 111.95 112.05 112.15
## [1117] 112.25 112.35 112.45 112.55 112.65 112.75 112.85 112.95 113.05
## [1126] 113.15 113.25 113.35 113.45 113.55 113.65 113.75 113.85 113.95
## [1135] 114.05 114.15 114.25 114.35 114.45 114.55 114.65 114.75 114.85
## [1144] 114.95 115.05 115.15 115.25 115.35 115.45 115.55 115.65 115.75
## [1153] 115.85 115.95 116.05 116.15 116.25 116.35 116.45 116.55 116.65
## [1162] 116.75 116.85 116.95 117.05 117.15 117.25 117.35 117.45 117.55
## [1171] 117.65 117.75 117.85 117.95 118.05 118.15 118.25 118.35 118.45
## [1180] 118.55 118.65 118.75 118.85 118.95 119.05 119.15 119.25 119.35
## [1189] 119.45 119.55 119.65 119.75 119.85 119.95 120.05 120.15 120.25
## [1198] 120.35 120.45 120.55 120.65 120.75 120.85 120.95 121.05 121.15
## [1207] 121.25 121.35 121.45 121.55 121.65 121.75 121.85 121.95 122.05
## [1216] 122.15 122.25 122.35 122.45 122.55 122.65 122.75 122.85 122.95
## [1225] 123.05 123.15 123.25 123.35 123.45 123.55 123.65 123.75 123.85
## [1234] 123.95 124.05 124.15 124.25 124.35 124.45 124.55 124.65 124.75
## [1243] 124.85 124.95 125.05 125.15 125.25 125.35 125.45 125.55 125.65
## [1252] 125.75 125.85 125.95 126.05 126.15 126.25 126.35 126.45 126.55
## [1261] 126.65 126.75 126.85 126.95 127.05 127.15 127.25 127.35 127.45
## [1270] 127.55 127.65 127.75 127.85 127.95 128.05 128.15 128.25 128.35
## [1279] 128.45 128.55 128.65 128.75 128.85 128.95 129.05 129.15 129.25
## [1288] 129.35 129.45 129.55 129.65 129.75 129.85 129.95 130.05 130.15
## [1297] 130.25 130.35 130.45 130.55 130.65 130.75 130.85 130.95 131.05
## [1306] 131.15 131.25 131.35 131.45 131.55 131.65 131.75 131.85 131.95
## [1315] 132.05 132.15 132.25 132.35 132.45 132.55 132.65 132.75 132.85
## [1324] 132.95 133.05 133.15 133.25 133.35 133.45 133.55 133.65 133.75
## [1333] 133.85 133.95 134.05 134.15 134.25 134.35 134.45 134.55 134.65
## [1342] 134.75 134.85 134.95 135.05 135.15 135.25 135.35 135.45 135.55
## [1351] 135.65 135.75 135.85 135.95 136.05 136.15 136.25 136.35 136.45
## [1360] 136.55 136.65 136.75 136.85 136.95 137.05 137.15 137.25 137.35
## [1369] 137.45 137.55 137.65 137.75 137.85 137.95 138.05 138.15 138.25
## [1378] 138.35 138.45 138.55 138.65 138.75 138.85 138.95 139.05 139.15
## [1387] 139.25 139.35 139.45 139.55 139.65 139.75 139.85 139.95 140.05
## [1396] 140.15 140.25 140.35 140.45 140.55 140.65 140.75 140.85 140.95
## [1405] 141.05 141.15 141.25 141.35 141.45 141.55 141.65 141.75 141.85
## [1414] 141.95 142.05 142.15 142.25 142.35 142.45 142.55 142.65 142.75
## [1423] 142.85 142.95 143.05 143.15 143.25 143.35 143.45 143.55 143.65
## [1432] 143.75 143.85 143.95 144.05 144.15 144.25 144.35 144.45 144.55
## [1441] 144.65 144.75 144.85 144.95 145.05 145.15 145.25 145.35 145.45
## [1450] 145.55 145.65 145.75 145.85 145.95 146.05 146.15 146.25 146.35
## [1459] 146.45 146.55 146.65 146.75 146.85 146.95 147.05 147.15 147.25
## [1468] 147.35 147.45 147.55 147.65 147.75 147.85 147.95 148.05 148.15
## [1477] 148.25 148.35 148.45 148.55 148.65 148.75 148.85 148.95 149.05
## [1486] 149.15 149.25 149.35 149.45 149.55 149.65 149.75 149.85 149.95
## [1495] 150.05 150.15 150.25 150.35 150.45 150.55 150.65 150.75 150.85
## [1504] 150.95 151.05 151.15 151.25 151.35 151.45 151.55 151.65 151.75
## [1513] 151.85 151.95 152.05 152.15 152.25 152.35 152.45 152.55 152.65
## [1522] 152.75 152.85 152.95 153.05 153.15 153.25 153.35 153.45 153.55
## [1531] 153.65 153.75 153.85 153.95 154.05 154.15 154.25 154.35 154.45
## [1540] 154.55 154.65 154.75 154.85 154.95 155.05 155.15 155.25 155.35
## [1549] 155.45 155.55 155.65 155.75 155.85 155.95 156.05 156.15 156.25
## [1558] 156.35 156.45 156.55 156.65 156.75 156.85 156.95 157.05 157.15
## [1567] 157.25 157.35 157.45 157.55 157.65 157.75 157.85 157.95 158.05
## [1576] 158.15 158.25 158.35 158.45 158.55 158.65 158.75 158.85 158.95
## [1585] 159.05 159.15 159.25 159.35 159.45 159.55 159.65 159.75 159.85
## [1594] 159.95 160.05 160.15 160.25 160.35 160.45 160.55 160.65 160.75
## [1603] 160.85 160.95 161.05 161.15 161.25 161.35 161.45 161.55 161.65
## [1612] 161.75 161.85 161.95 162.05 162.15 162.25 162.35 162.45 162.55
## [1621] 162.65 162.75 162.85 162.95 163.05 163.15 163.25 163.35 163.45
## [1630] 163.55 163.65 163.75 163.85 163.95 164.05 164.15 164.25 164.35
## [1639] 164.45 164.55 164.65 164.75 164.85 164.95 165.05 165.15 165.25
## [1648] 165.35 165.45 165.55 165.65 165.75 165.85 165.95 166.05 166.15
## [1657] 166.25 166.35 166.45 166.55 166.65 166.75 166.85 166.95 167.05
## [1666] 167.15 167.25 167.35 167.45 167.55 167.65 167.75 167.85 167.95
## [1675] 168.05 168.15 168.25 168.35 168.45 168.55 168.65 168.75 168.85
## [1684] 168.95
##
## $xname
## [1] "data"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"