# Exer1: generate data with mean 2 and standard deviation 1.5 using rnorm() command
data <- rnorm(1000,2,1.5)
# 1 thousand values
length(data)
## [1] 1000
# count number of elements
data[1:20]
## [1] 3.2009123 3.0237494 4.3572042 3.3387089 3.1155914 1.7061506
## [7] 2.6476068 -1.1340420 2.4510877 4.2088753 2.9262838 2.1308570
## [13] 3.0479925 0.5835284 4.2065059 1.4385558 5.2861530 4.3048954
## [19] 3.0799716 2.5141564
data[1:300]
## [1] 3.200912340 3.023749437 4.357204190 3.338708852 3.115591373
## [6] 1.706150558 2.647606834 -1.134041983 2.451087703 4.208875315
## [11] 2.926283841 2.130856999 3.047992510 0.583528363 4.206505857
## [16] 1.438555842 5.286152954 4.304895354 3.079971566 2.514156408
## [21] 1.956792637 2.451811728 0.921247833 -0.041689227 2.652164424
## [26] -0.319349710 -1.348668751 2.462035694 2.875986463 -0.003035858
## [31] 5.350219975 2.298825830 2.416344211 2.725687425 2.819707146
## [36] 0.157476289 3.680611832 2.192310500 2.628071344 1.616865904
## [41] 4.296041237 2.021387393 2.504442233 2.588449355 0.820124538
## [46] 1.680649894 -1.332351023 1.249603318 0.162366654 3.049400678
## [51] 2.502014733 1.737405886 1.494253537 2.777584892 1.770172353
## [56] 1.971742203 3.605225684 3.344697806 1.348794425 2.967654619
## [61] 4.930631981 2.734265361 2.753443681 5.767394240 1.428817936
## [66] 0.567573576 1.492280672 0.913866204 2.758310326 1.569527462
## [71] 4.020333971 2.879690454 0.017946866 2.638575118 2.399652526
## [76] 2.859495845 0.906938634 3.062216590 -0.398040252 0.885807787
## [81] 1.695942559 0.639639663 1.753941982 1.550897336 0.523040410
## [86] 1.905560779 1.319466038 1.805610053 -0.032781357 1.687896421
## [91] 0.822513583 0.347464402 1.951926756 0.453492209 1.895828695
## [96] 1.966192090 1.254620246 -0.524699666 1.074278636 3.284242779
## [101] 4.106652068 1.496521766 3.352739824 1.642645292 3.780822570
## [106] 1.914201502 2.170834664 0.720719371 1.881731125 -1.534671038
## [111] 1.930724611 0.861359677 1.097133365 0.350493307 1.981715063
## [116] 2.709411814 0.011170040 3.927884711 4.515368469 0.041524719
## [121] 1.838554041 2.512457742 4.554551246 0.927907449 3.723610182
## [126] 1.573634827 1.702721840 3.520186286 2.430032674 1.071294542
## [131] 1.736239567 2.739036080 1.011705106 3.223911463 2.734131973
## [136] 1.159233033 2.310926852 0.031821095 -1.401981414 1.962910888
## [141] 2.046145493 0.980449233 1.396985861 2.580970947 3.081924169
## [146] 5.491114410 -0.244578687 1.305629744 1.842288708 2.168814020
## [151] 2.165353095 2.034979902 3.666440910 1.391542262 0.871042599
## [156] 3.872756417 2.172619776 -1.036336830 0.918146427 1.134246108
## [161] -0.029583231 1.872629933 3.642381995 3.442954678 2.975226030
## [166] 2.380379399 1.688684005 2.873751683 1.038484112 4.577721602
## [171] 2.046911925 1.692878091 4.198268593 6.090775348 0.073699494
## [176] 2.951062770 2.806822855 0.523208458 3.684836895 2.935265872
## [181] 2.969338827 1.409608427 2.719926905 2.386517004 1.579074589
## [186] 1.944528941 4.615199070 2.117004716 2.968865773 2.161570119
## [191] 0.415658639 0.513956163 2.595355001 3.581718230 1.960681541
## [196] 3.222590879 1.092737459 2.541743384 3.682000771 1.663142408
## [201] 0.974859061 5.242690257 5.812134943 4.049182075 2.284427034
## [206] 2.959889959 2.437594006 1.040405817 1.974692430 1.080906558
## [211] 1.627214047 2.990977471 1.597968431 1.385803897 1.615126119
## [216] 1.349142313 3.575306251 1.983484551 0.929564644 0.147183515
## [221] 2.574887050 0.035407393 0.545427166 1.578485488 3.726441583
## [226] 4.244131966 1.099300411 -0.202668617 2.063195189 1.723968408
## [231] 1.894243941 -0.052676052 2.693664957 3.015941102 2.749815415
## [236] 0.938916290 3.084851977 2.381312001 0.746764348 1.322618106
## [241] 2.501322050 0.693079123 0.015875095 -0.480081255 4.521827448
## [246] 2.499076274 3.893033523 1.852846799 2.467751874 1.912695632
## [251] 2.733639470 -0.430692748 -0.264676822 2.428597864 1.155047503
## [256] 1.688226760 3.877298191 1.797552386 1.955188374 3.025035141
## [261] 2.746515735 0.220081043 2.643664391 0.820547263 0.355681409
## [266] 0.750658578 3.087308746 0.373654952 2.115043353 2.875145358
## [271] 2.350885259 0.947069383 -0.177433537 2.840498441 1.327457727
## [276] 3.926156967 1.490733756 0.577680916 0.032915558 3.911707048
## [281] 2.152899983 0.218129097 3.995818690 4.521731145 4.335798258
## [286] 2.758709449 4.791665657 1.103875136 2.063913441 1.038278928
## [291] 0.502098725 2.891736159 2.432925159 0.146172384 1.360591409
## [296] 3.782523649 2.692437300 0.629280280 1.106927273 1.067133246
# Exer2: Draw histogram with one main title and different thickness
maintitle <- "Histogram and Density Plot"
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
3
## [1] 3
hist(data, breaks=100,col="gray",main = maintitle)
hist(data, breaks=300,col="gray",main = maintitle)
# Exer3: Draw histogram with one main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
# Exer4: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# # Add density curve. We define the range of the density curve
x = seq(from=min(data), to=max(data), length.out=100)
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/ 20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
# Exer5: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# Add density curve and the location of the mean value
(x = seq(from=min(data), to=max(data), length.out=100))
## [1] -2.18700228 -2.09513133 -2.00326039 -1.91138944 -1.81951850 -1.72764756
## [7] -1.63577661 -1.54390567 -1.45203472 -1.36016378 -1.26829283 -1.17642189
## [13] -1.08455094 -0.99268000 -0.90080905 -0.80893811 -0.71706716 -0.62519622
## [19] -0.53332527 -0.44145433 -0.34958338 -0.25771244 -0.16584149 -0.07397055
## [25] 0.01790039 0.10977134 0.20164228 0.29351323 0.38538417 0.47725512
## [31] 0.56912606 0.66099701 0.75286795 0.84473890 0.93660984 1.02848079
## [37] 1.12035173 1.21222268 1.30409362 1.39596457 1.48783551 1.57970646
## [43] 1.67157740 1.76344835 1.85531929 1.94719023 2.03906118 2.13093212
## [49] 2.22280307 2.31467401 2.40654496 2.49841590 2.59028685 2.68215779
## [55] 2.77402874 2.86589968 2.95777063 3.04964157 3.14151252 3.23338346
## [61] 3.32525441 3.41712535 3.50899630 3.60086724 3.69273818 3.78460913
## [67] 3.87648007 3.96835102 4.06022196 4.15209291 4.24396385 4.33583480
## [73] 4.42770574 4.51957669 4.61144763 4.70331858 4.79518952 4.88706047
## [79] 4.97893141 5.07080236 5.16267330 5.25454425 5.34641519 5.43828614
## [85] 5.53015708 5.62202802 5.71389897 5.80576991 5.89764086 5.98951180
## [91] 6.08138275 6.17325369 6.26512464 6.35699558 6.44886653 6.54073747
## [97] 6.63260842 6.72447936 6.81635031 6.90822125
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/ 20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
abline(v = mean(data), col="black", lwd=3, lty=2)
# Add legend to top right position
legend("topright",
legend = c("Histogram", "density curve", "Average"),
col = c("lightblue", "violet", "black"),
lty = 1)
# Compute Quartile values Q1,Q2 and Q3
# These quantities divide the data into 4 equal parts
hist(data, breaks=20,col="lightblue",main = maintitle)
Quantiles = quantile(data)
# locate the quartiles Q1, Q2, Q3
abline(v = Quantiles[2], col="black", lwd=3, lty=3)
abline(v = Quantiles[3], col="red", lwd=3, lty=3)
abline(v = Quantiles[4], col="blue", lwd=3, lty=3)
# Exer6: Locate the lowest 5% and the highest 5% of the distribution
data
## [1] 3.200912340 3.023749437 4.357204190 3.338708852 3.115591373
## [6] 1.706150558 2.647606834 -1.134041983 2.451087703 4.208875315
## [11] 2.926283841 2.130856999 3.047992510 0.583528363 4.206505857
## [16] 1.438555842 5.286152954 4.304895354 3.079971566 2.514156408
## [21] 1.956792637 2.451811728 0.921247833 -0.041689227 2.652164424
## [26] -0.319349710 -1.348668751 2.462035694 2.875986463 -0.003035858
## [31] 5.350219975 2.298825830 2.416344211 2.725687425 2.819707146
## [36] 0.157476289 3.680611832 2.192310500 2.628071344 1.616865904
## [41] 4.296041237 2.021387393 2.504442233 2.588449355 0.820124538
## [46] 1.680649894 -1.332351023 1.249603318 0.162366654 3.049400678
## [51] 2.502014733 1.737405886 1.494253537 2.777584892 1.770172353
## [56] 1.971742203 3.605225684 3.344697806 1.348794425 2.967654619
## [61] 4.930631981 2.734265361 2.753443681 5.767394240 1.428817936
## [66] 0.567573576 1.492280672 0.913866204 2.758310326 1.569527462
## [71] 4.020333971 2.879690454 0.017946866 2.638575118 2.399652526
## [76] 2.859495845 0.906938634 3.062216590 -0.398040252 0.885807787
## [81] 1.695942559 0.639639663 1.753941982 1.550897336 0.523040410
## [86] 1.905560779 1.319466038 1.805610053 -0.032781357 1.687896421
## [91] 0.822513583 0.347464402 1.951926756 0.453492209 1.895828695
## [96] 1.966192090 1.254620246 -0.524699666 1.074278636 3.284242779
## [101] 4.106652068 1.496521766 3.352739824 1.642645292 3.780822570
## [106] 1.914201502 2.170834664 0.720719371 1.881731125 -1.534671038
## [111] 1.930724611 0.861359677 1.097133365 0.350493307 1.981715063
## [116] 2.709411814 0.011170040 3.927884711 4.515368469 0.041524719
## [121] 1.838554041 2.512457742 4.554551246 0.927907449 3.723610182
## [126] 1.573634827 1.702721840 3.520186286 2.430032674 1.071294542
## [131] 1.736239567 2.739036080 1.011705106 3.223911463 2.734131973
## [136] 1.159233033 2.310926852 0.031821095 -1.401981414 1.962910888
## [141] 2.046145493 0.980449233 1.396985861 2.580970947 3.081924169
## [146] 5.491114410 -0.244578687 1.305629744 1.842288708 2.168814020
## [151] 2.165353095 2.034979902 3.666440910 1.391542262 0.871042599
## [156] 3.872756417 2.172619776 -1.036336830 0.918146427 1.134246108
## [161] -0.029583231 1.872629933 3.642381995 3.442954678 2.975226030
## [166] 2.380379399 1.688684005 2.873751683 1.038484112 4.577721602
## [171] 2.046911925 1.692878091 4.198268593 6.090775348 0.073699494
## [176] 2.951062770 2.806822855 0.523208458 3.684836895 2.935265872
## [181] 2.969338827 1.409608427 2.719926905 2.386517004 1.579074589
## [186] 1.944528941 4.615199070 2.117004716 2.968865773 2.161570119
## [191] 0.415658639 0.513956163 2.595355001 3.581718230 1.960681541
## [196] 3.222590879 1.092737459 2.541743384 3.682000771 1.663142408
## [201] 0.974859061 5.242690257 5.812134943 4.049182075 2.284427034
## [206] 2.959889959 2.437594006 1.040405817 1.974692430 1.080906558
## [211] 1.627214047 2.990977471 1.597968431 1.385803897 1.615126119
## [216] 1.349142313 3.575306251 1.983484551 0.929564644 0.147183515
## [221] 2.574887050 0.035407393 0.545427166 1.578485488 3.726441583
## [226] 4.244131966 1.099300411 -0.202668617 2.063195189 1.723968408
## [231] 1.894243941 -0.052676052 2.693664957 3.015941102 2.749815415
## [236] 0.938916290 3.084851977 2.381312001 0.746764348 1.322618106
## [241] 2.501322050 0.693079123 0.015875095 -0.480081255 4.521827448
## [246] 2.499076274 3.893033523 1.852846799 2.467751874 1.912695632
## [251] 2.733639470 -0.430692748 -0.264676822 2.428597864 1.155047503
## [256] 1.688226760 3.877298191 1.797552386 1.955188374 3.025035141
## [261] 2.746515735 0.220081043 2.643664391 0.820547263 0.355681409
## [266] 0.750658578 3.087308746 0.373654952 2.115043353 2.875145358
## [271] 2.350885259 0.947069383 -0.177433537 2.840498441 1.327457727
## [276] 3.926156967 1.490733756 0.577680916 0.032915558 3.911707048
## [281] 2.152899983 0.218129097 3.995818690 4.521731145 4.335798258
## [286] 2.758709449 4.791665657 1.103875136 2.063913441 1.038278928
## [291] 0.502098725 2.891736159 2.432925159 0.146172384 1.360591409
## [296] 3.782523649 2.692437300 0.629280280 1.106927273 1.067133246
## [301] 2.641644344 2.853224630 4.352759256 0.323468439 2.681051595
## [306] 2.960980068 4.373533035 0.070445439 1.927387821 2.314042654
## [311] -0.075931100 0.630691635 1.869493798 2.273592544 2.890064050
## [316] 1.604270839 4.644778434 -0.189917103 3.398182188 2.108971326
## [321] 1.534045964 2.660875443 -1.236065997 3.870657005 3.482147873
## [326] 5.382311149 2.636381559 0.647472322 -0.994193546 1.752425806
## [331] 1.900193559 1.473542518 0.695587160 1.609912537 3.003330338
## [336] 1.142186559 0.676641801 1.332135239 0.721887035 2.617677658
## [341] 2.057994583 4.646399733 4.870112247 -0.609280050 2.375022214
## [346] 1.649943526 1.124449231 -0.644152150 -0.378981304 3.649792200
## [351] 3.829956043 1.300262425 1.795258877 -0.074437264 1.327036169
## [356] 3.178710454 0.457764321 2.544168474 1.046652139 2.398368754
## [361] 0.287773051 2.618894334 2.680937109 -0.273903903 1.671715733
## [366] 3.451166898 1.979783288 1.663815132 2.823003420 4.078833275
## [371] 2.008997844 0.500335475 1.097184553 1.648139162 1.175568394
## [376] -0.426896601 1.322810909 1.816280420 0.775065771 1.821889034
## [381] 1.839579227 2.017385471 2.012268192 1.869466413 1.384828874
## [386] 1.934964872 0.051301544 3.989461648 -0.071058235 2.416466958
## [391] 4.825566096 4.977927242 4.565638545 4.812681035 4.373539045
## [396] 4.259831576 3.842115162 1.107789452 1.807983845 0.757227300
## [401] 2.321748322 3.403905136 1.980415102 3.156630880 1.753938126
## [406] 4.324788454 0.522671341 2.208632573 1.373493284 1.361519833
## [411] 2.517546354 3.054451808 3.238609274 3.110970288 3.124163008
## [416] 2.690095038 3.437818410 1.408533715 5.198994567 0.559918101
## [421] 5.073259148 5.282813244 3.461688003 2.771618097 -0.573265536
## [426] 0.797975700 3.794204794 4.444557954 3.155069327 4.585469008
## [431] 1.506952715 1.920897990 2.315602166 1.913813969 2.681793579
## [436] 1.388190072 3.540999233 2.526404545 -0.494644471 1.451956665
## [441] 0.462645266 1.816747648 2.334479324 0.449643055 0.611442371
## [446] 0.069571412 0.210607263 0.517470838 2.315158217 2.460505256
## [451] 2.008441294 1.057520580 5.284920228 1.773731215 0.846733967
## [456] -0.646545141 0.509858816 1.066737946 1.072442874 0.242285736
## [461] 0.374421878 2.487430800 3.262450755 1.025718053 1.664562993
## [466] -0.522611712 2.146493801 5.513303246 2.168425287 4.907023863
## [471] 2.376428842 0.370689274 -0.321977299 0.693619949 2.225729596
## [476] 2.978683083 -0.059179200 -0.240011811 1.993385275 1.936475929
## [481] -0.239278836 -0.880517369 -1.231222462 3.450211860 0.673583465
## [486] 3.190975303 0.748029233 0.662321819 0.081332842 2.463459218
## [491] 1.388183936 0.711859022 3.752963412 1.310903475 1.417008450
## [496] 3.358669170 3.096279015 0.273423647 3.175193100 2.007982048
## [501] 2.266417967 3.267328829 1.917903212 2.548453091 3.854328640
## [506] 0.357430881 -1.064043341 0.403107579 0.904661718 3.535201296
## [511] 2.665350952 1.275396638 1.862213983 4.788839311 2.937926131
## [516] 0.753176880 0.959981335 3.173580718 1.136040515 4.016060219
## [521] 1.621361683 1.522763110 -0.252542596 3.049765966 2.928921649
## [526] 2.331573740 -0.021509172 0.259338333 4.795957505 1.100441610
## [531] 0.994957541 2.025307415 2.303506667 2.557075156 2.190607802
## [536] -0.104773081 2.023365558 0.409219027 4.638086437 -0.259698003
## [541] 1.493925779 1.355471175 2.645569882 2.108960494 5.574303138
## [546] 3.091061211 3.431298106 2.034419311 3.948643613 2.230349908
## [551] 0.063010188 0.365269015 2.608876546 1.041897674 1.024752814
## [556] 0.548530432 5.784065444 2.066868933 0.807988017 -1.078357198
## [561] 1.945244064 1.897203124 2.406646535 1.140722645 3.253783374
## [566] 2.490558496 0.523257096 1.327162224 4.110986608 0.717198688
## [571] 1.811713036 1.975322764 3.012691737 3.751289079 2.750191295
## [576] 1.855484612 4.148415703 3.120743781 2.769075291 2.591938857
## [581] 2.956073069 4.767313030 -0.277574026 5.564133226 3.266651761
## [586] 3.352243185 2.472868338 2.599177163 3.988730043 2.353800833
## [591] 4.030417772 5.245247778 4.592020618 1.829903301 2.338137000
## [596] 2.455122598 2.377273943 0.794579565 3.262085702 2.835449920
## [601] 2.137970154 1.202435303 4.144414230 2.474886388 1.328973424
## [606] 1.677279975 3.082884256 1.275164217 1.658686201 0.431371544
## [611] 3.513997023 3.521764724 2.173831902 2.438272523 1.306589264
## [616] 3.579436831 1.837324672 2.929404582 0.773388144 1.938217263
## [621] 1.215867442 2.280180065 2.223572615 -0.286598514 1.955648573
## [626] 0.598674534 3.589012347 -0.142823229 5.512350418 0.654827295
## [631] 1.210750810 3.031380217 2.463767337 4.170258124 2.074709182
## [636] -0.401647153 2.506536888 5.118338462 0.192237912 2.527307893
## [641] 2.681953243 3.673425774 2.909335956 5.013210820 1.012110466
## [646] 0.331644423 -0.711393545 -0.244600993 0.097317478 3.798835652
## [651] 2.513050207 3.645820194 1.541628373 1.526689226 0.693801986
## [656] 1.570371308 2.011985034 1.165057117 0.646684519 0.904034806
## [661] 3.071575355 1.471949281 2.073541217 1.922748248 3.415952198
## [666] 4.955167708 0.459889093 -1.983933644 1.702758577 1.327815476
## [671] 0.897590519 -0.677853685 0.974167662 2.933641997 2.816837003
## [676] 2.671691619 2.244453057 2.509185363 2.638437833 0.274975575
## [681] 2.923485538 2.651025462 2.176716504 4.106265962 4.038327534
## [686] 5.566338666 4.437898700 2.301869459 1.866217095 0.536764285
## [691] 5.258347249 3.253913463 2.355550972 3.489517562 -1.561490604
## [696] 2.807333714 3.910305035 -1.059028745 2.428659709 1.837440423
## [701] 2.249456724 2.180587022 0.727053094 1.902274360 -2.187002279
## [706] -0.502549549 1.002707589 -1.187386944 4.157368018 3.083945657
## [711] 2.542018158 5.111198843 0.183441159 -0.902214154 4.125250104
## [716] 0.771602884 -0.517153152 1.747044401 2.295708663 2.528364763
## [721] 1.959344117 2.449303190 3.188578760 2.733876382 0.680621281
## [726] 3.233496734 2.807871672 -0.205501341 0.192583032 2.490827703
## [731] 0.671913682 0.897099329 -0.003050026 5.362519319 3.898733761
## [736] 1.928622390 2.739287804 5.255178212 2.424485478 2.786139891
## [741] 4.987743334 2.468202377 1.504765835 2.111973189 0.396039899
## [746] 4.868261862 0.399464333 2.065380951 0.792635729 1.097731603
## [751] 1.962710522 1.651911581 1.977478060 1.539039854 1.505307794
## [756] 3.890717519 4.572518748 1.095120008 0.548654178 1.530155904
## [761] 2.607810808 3.080416612 2.105896598 0.872933777 1.176457816
## [766] 1.681777538 0.290476491 1.466084887 -0.323828589 -0.069320546
## [771] 2.097882989 2.544942068 0.753494046 1.651928482 1.952913516
## [776] 1.207327347 0.767479681 1.150329255 3.652920608 0.047664578
## [781] 3.677556993 5.929974742 1.928839260 1.498946625 3.451607746
## [786] 1.512357892 0.707843422 0.725612968 1.430722965 1.615089696
## [791] 1.894869740 2.826704860 3.218885059 3.961490602 3.646580027
## [796] 1.990947260 0.360887644 -1.273899247 0.121181417 2.382519687
## [801] 3.571705273 2.388979218 3.836971272 0.222161756 1.261903433
## [806] 3.504942590 3.316275867 4.124061187 -0.123254223 0.753201926
## [811] 0.766834521 2.976967311 3.000425002 3.108369404 2.478402652
## [816] 1.810003300 -1.382891039 3.280718791 -1.210752148 1.725419420
## [821] 1.486566432 2.704860542 3.244806727 2.517388389 -0.397444876
## [826] 1.536202962 3.551367576 1.296933616 1.343340679 2.523568591
## [831] 0.536871597 1.024462483 3.846165023 1.807713759 3.083726137
## [836] 0.748567130 1.200491310 -0.101266489 3.940775066 3.531013873
## [841] 1.411549937 1.882377520 3.542423875 0.570985142 0.030541025
## [846] 0.543480959 0.756888472 2.199263463 2.701405649 -0.318318675
## [851] 1.579722030 2.311513114 -1.249772697 1.367788020 1.899511557
## [856] 2.435477355 2.297706572 4.056858264 0.816868341 4.411071986
## [861] -0.383695340 -1.283112645 3.573664351 3.641535538 3.023842514
## [866] 2.402642133 3.347306568 2.145223469 1.705972623 2.445240682
## [871] 4.458712625 3.882348962 1.219016704 0.273780699 3.400143585
## [876] 1.617856875 2.543115020 3.096757004 0.698324811 1.890118645
## [881] 2.740764351 1.934802081 -0.903138062 1.407626004 3.137770148
## [886] 3.326551579 0.675445267 0.622057918 0.558996212 0.555861153
## [891] 1.685658675 3.728164816 4.378440406 3.119368211 0.050773306
## [896] 2.582544662 1.834591137 6.666608531 2.519242667 0.741279780
## [901] 1.095251062 2.753873931 2.134399341 -0.163503004 1.623965589
## [906] 1.684158895 3.054872711 -0.505169782 3.790175219 1.768423670
## [911] 1.467616642 0.900418017 2.270457999 3.450896189 3.501867825
## [916] -0.193195433 2.769695687 2.824955522 0.790361680 1.948552978
## [921] 2.965141618 0.129939567 3.420382125 1.062012529 1.569331994
## [926] 2.109073852 0.150336628 1.780496710 -1.869723541 3.162944137
## [931] -1.172170089 1.109011051 3.806379155 3.308853089 2.293321522
## [936] 1.584413996 1.095754025 -0.325424610 6.403524757 6.908221251
## [941] 0.775717280 2.767021161 2.426943768 1.742089535 1.884646779
## [946] 2.554213886 2.101808093 -0.539798545 1.832794293 1.362217419
## [951] 0.975060837 1.349304952 2.124645271 2.229501114 0.577022517
## [956] 1.947253955 5.856284285 3.710218665 0.524588717 -1.795161656
## [961] 2.483274814 2.422781096 1.756190605 1.538808773 0.736956529
## [966] 1.689096140 2.339355054 -1.081854972 -0.722758194 2.551687964
## [971] 0.037852622 1.778281210 1.587932064 1.253715014 0.202768077
## [976] 2.211488221 2.803680959 1.595050754 3.136303706 2.697091360
## [981] 3.130894248 1.183800216 2.050985500 2.653369684 2.191857384
## [986] 2.344701052 2.315189440 2.101241617 2.406530548 0.423603345
## [991] 0.118105084 4.599540893 2.023418436 2.648271619 4.047995329
## [996] 0.198412795 0.514825755 3.339118308 0.883497046 1.755385607
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.1870 0.9706 1.9690 2.0025 2.9412 6.9082
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# Add density curve (define the range of the density curve)
x = seq(from=min(data), to=max(data), length.out=100)
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/ 20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
abline(v = mean(data), col="black", lwd=3, lty=2)
# Add legend
legend("topright",
# Add legend to plot
legend = c("Histogram", "density curve", "Average"),
col = c("lightblue", "violet", "black"),
lty = 1)
# Locate lowest 5% and highest 5% of the data
quantile(data,prob = 0.05)
## 5%
## -0.3281024
abline(v = quantile(data,prob = 0.05), col="red", lwd=3, lty=3)
# Area to the left of the red line is lowest 5% of the data
abline(v = quantile(data,prob = 0.05), col="red", lwd=3, lty=3)
# Area to the left of the red line is lowest 5% of the data
quantile(data,prob = 0.95)
## 95%
## 4.578109
abline(v = quantile(data,prob = 0.95), col="blue", lwd=3, lty=3)
# Area to the right of the blue line is top 5% of the data
# Area in between the red line and the blue line is 90%
# of the data
# How to get the values (lowest 5%)
(Cutoff <- quantile(data,prob = 0.05))
## 5%
## -0.3281024
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [325] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## [349] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [697] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE
## [709] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
# count all true values using the sum command
sum(Low5Percent[TRUE])
## [1] 50
# there are 50 of them
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -1.1340420 -1.3486688 -1.3323510 -0.3980403 -0.5246997 -1.5346710
## [7] -1.4019814 -1.0363368 -0.4800813 -0.4306927 -1.2360660 -0.9941935
## [13] -0.6092800 -0.6441521 -0.3789813 -0.4268966 -0.5732655 -0.4946445
## [19] -0.6465451 -0.5226117 -0.8805174 -1.2312225 -1.0640433 -1.0783572
## [25] -0.4016472 -0.7113935 -1.9839336 -0.6778537 -1.5614906 -1.0590287
## [31] -2.1870023 -0.5025495 -1.1873869 -0.9022142 -0.5171532 -1.2738992
## [37] -1.3828910 -1.2107521 -0.3974449 -1.2497727 -0.3836953 -1.2831126
## [43] -0.9031381 -0.5051698 -1.8697235 -1.1721701 -0.5397985 -1.7951617
## [49] -1.0818550 -0.7227582
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.578109
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [421] TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [469] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [541] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE
## [745] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE])
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.286153 5.350220 4.930632 5.767394 5.491114 6.090775 4.615199 5.242690
## [9] 5.812135 4.791666 4.644778 5.382311 4.646400 4.870112 4.825566 4.977927
## [17] 4.812681 5.198995 5.073259 5.282813 4.585469 5.284920 5.513303 4.907024
## [25] 4.788839 4.795958 4.638086 5.574303 5.784065 4.767313 5.564133 5.245248
## [33] 4.592021 5.512350 5.118338 5.013211 4.955168 5.566339 5.258347 5.111199
## [41] 5.362519 5.255178 4.987743 4.868262 5.929975 6.666609 6.403525 6.908221
## [49] 5.856284 4.599541