# Mindanao State University
# General Santos City
# Submitted by: Carren C. Sibongga
# Math Department
# March 16, 2023
# Processing of continuous data
# Using random number generators
# 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) # count number of elements
## [1] 1000
data[1:20]
## [1] 1.0511219 1.6484431 1.7116414 3.4657927 2.9802089 1.6319889
## [7] -1.5782971 5.7705469 0.6292199 5.7934519 0.3224348 3.0019272
## [13] 2.4683443 3.2173389 3.7784123 1.5973321 1.3226749 3.9594400
## [19] 1.0122077 0.7379540
data[1:300]
## [1] 1.05112185 1.64844305 1.71164141 3.46579274 2.98020887 1.63198892
## [7] -1.57829706 5.77054695 0.62921992 5.79345187 0.32243479 3.00192724
## [13] 2.46834434 3.21733890 3.77841233 1.59733210 1.32267486 3.95944003
## [19] 1.01220772 0.73795399 3.71729088 2.31873913 0.30066782 0.82468362
## [25] 1.65318229 2.72341851 1.39053000 1.50880028 3.94878725 2.34498058
## [31] -0.58556836 0.51417491 2.15924687 1.54325822 1.18577153 2.81023558
## [37] 6.07384037 3.72509786 0.34286086 1.47101149 4.23216790 3.38664242
## [43] 4.00503789 2.83253996 3.49165449 -0.37840704 0.29797436 1.18918183
## [49] 0.86034139 2.79037844 3.71973362 -0.50496260 3.92988589 4.60882404
## [55] 0.10233427 2.27896629 1.46073011 1.85172229 -0.96700184 2.20165082
## [61] 3.71586656 2.28128123 1.41098765 1.74828215 2.56713284 2.29183503
## [67] 3.01495656 2.18147377 2.23293967 0.36734644 1.69172879 -0.08858575
## [73] 2.20472940 1.38630188 1.80968984 0.35862628 3.44068045 -0.28281146
## [79] 0.32434930 1.82266177 3.15839525 1.81398568 2.75511511 3.32271617
## [85] 3.18256500 3.72003487 2.81528970 3.39997135 3.69172794 0.68314335
## [91] 3.43658625 1.52395531 1.97587716 2.61430315 0.76898362 3.57168765
## [97] 2.45398045 2.07130103 2.92458641 2.77111447 2.82132334 -0.81440911
## [103] -3.64417405 2.87902042 3.02966275 2.53477993 2.69746841 1.33360658
## [109] 2.12988666 2.23205496 2.27851296 -0.56802029 1.08115314 3.10278421
## [115] 3.20270848 3.79380409 0.80867055 1.49066971 3.88924486 1.65273907
## [121] 2.29631088 1.40081186 2.20246848 2.93985862 4.38775139 -1.32683035
## [127] 3.96856461 -0.57497575 1.49559887 1.74217704 0.17956846 0.32312993
## [133] 1.10170633 -0.70491220 1.88856706 2.62552258 3.79146173 0.39329506
## [139] 1.09801638 1.66590387 2.75170772 2.26963110 -0.03568655 2.43419494
## [145] 2.22855497 1.27591453 5.35432185 2.56025239 1.25111100 1.67314549
## [151] 3.88664087 0.45162624 1.54369211 0.36747755 1.74532699 1.75957411
## [157] 4.09562046 -0.56701887 2.82290925 0.25570028 0.86266926 3.69277664
## [163] 1.19193088 2.38536160 1.46768153 2.70357140 0.89688395 3.38229272
## [169] 4.48159136 0.80555701 2.28662265 2.29218028 2.82411020 0.42307110
## [175] 2.18057695 -2.24346460 3.11013137 3.21988025 1.96597024 2.29261011
## [181] 3.56285384 0.68416610 0.37331072 1.31144102 -0.70897585 2.00959065
## [187] 0.31278955 2.92106240 2.67432421 1.47762900 2.34285497 4.75906880
## [193] 3.21616180 3.39105487 3.75662484 2.18324575 0.43131817 1.36015573
## [199] 1.63424303 1.80198607 0.90665487 3.08498024 2.03095751 3.06597151
## [205] 2.18661135 4.01212791 1.62227378 3.26054562 3.36071885 1.65881124
## [211] 1.75265770 1.06009680 0.30790691 3.43551867 1.89651055 1.73830777
## [217] 1.84117461 4.33301998 2.89331285 1.67367573 -0.12539445 2.82331668
## [223] 3.28167888 3.14011604 1.62333264 0.31342161 5.20671793 3.54588424
## [229] 2.66247575 5.45375041 2.07426665 1.23616565 2.91503428 1.55533512
## [235] 2.10380839 1.16884783 3.72013402 2.28056990 1.22849257 -0.03922284
## [241] 0.97976704 2.45465075 1.81852553 -0.67751594 0.47549962 2.46380837
## [247] 2.49293870 -0.78718851 1.03410435 0.31580669 1.47126441 2.17672288
## [253] 2.93512034 2.13992332 2.33824489 2.29843598 0.41760948 1.44283280
## [259] 2.65647119 1.46878616 2.50644206 5.50432777 2.66500571 1.47152302
## [265] -2.49728409 1.67893220 1.38047422 1.26971957 2.92212251 2.54734283
## [271] 2.33247781 1.17878882 2.99995896 4.80544833 2.04082502 4.54374470
## [277] 3.96023751 2.04485024 3.99797183 1.87916682 0.37793245 -0.92274194
## [283] 2.37041898 2.78587214 3.55942777 2.50127998 1.12926645 2.14503925
## [289] 4.27578529 3.38961912 3.24354504 2.91390317 1.37211887 2.73679585
## [295] -0.46494779 2.57707312 4.79753463 0.15021592 1.86345372 1.89636687
# 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)
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=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
# Question: What causes the subtitle to be in the second line?
# 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] -3.64417405 -3.54601229 -3.44785053 -3.34968877 -3.25152701 -3.15336524
## [7] -3.05520348 -2.95704172 -2.85887996 -2.76071820 -2.66255643 -2.56439467
## [13] -2.46623291 -2.36807115 -2.26990939 -2.17174763 -2.07358586 -1.97542410
## [19] -1.87726234 -1.77910058 -1.68093882 -1.58277705 -1.48461529 -1.38645353
## [25] -1.28829177 -1.19013001 -1.09196825 -0.99380648 -0.89564472 -0.79748296
## [31] -0.69932120 -0.60115944 -0.50299767 -0.40483591 -0.30667415 -0.20851239
## [37] -0.11035063 -0.01218886 0.08597290 0.18413466 0.28229642 0.38045818
## [43] 0.47861994 0.57678171 0.67494347 0.77310523 0.87126699 0.96942875
## [49] 1.06759052 1.16575228 1.26391404 1.36207580 1.46023756 1.55839932
## [55] 1.65656109 1.75472285 1.85288461 1.95104637 2.04920813 2.14736990
## [61] 2.24553166 2.34369342 2.44185518 2.54001694 2.63817870 2.73634047
## [67] 2.83450223 2.93266399 3.03082575 3.12898751 3.22714928 3.32531104
## [73] 3.42347280 3.52163456 3.61979632 3.71795808 3.81611985 3.91428161
## [79] 4.01244337 4.11060513 4.20876689 4.30692866 4.40509042 4.50325218
## [85] 4.60141394 4.69957570 4.79773747 4.89589923 4.99406099 5.09222275
## [91] 5.19038451 5.28854627 5.38670804 5.48486980 5.58303156 5.68119332
## [97] 5.77935508 5.87751685 5.97567861 6.07384037
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)
Quantiles
## 0% 25% 50% 75% 100%
## -3.644174 1.009255 2.001096 2.940750 6.073840
# 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] 1.051121853 1.648443052 1.711641405 3.465792744 2.980208871
## [6] 1.631988921 -1.578297058 5.770546949 0.629219922 5.793451871
## [11] 0.322434789 3.001927239 2.468344340 3.217338900 3.778412332
## [16] 1.597332096 1.322674865 3.959440026 1.012207722 0.737953989
## [21] 3.717290876 2.318739130 0.300667823 0.824683620 1.653182285
## [26] 2.723418515 1.390530001 1.508800282 3.948787254 2.344980576
## [31] -0.585568356 0.514174908 2.159246869 1.543258215 1.185771529
## [36] 2.810235576 6.073840369 3.725097856 0.342860864 1.471011495
## [41] 4.232167900 3.386642419 4.005037893 2.832539962 3.491654491
## [46] -0.378407038 0.297974356 1.189181834 0.860341395 2.790378438
## [51] 3.719733616 -0.504962603 3.929885889 4.608824044 0.102334270
## [56] 2.278966289 1.460730115 1.851722287 -0.967001843 2.201650817
## [61] 3.715866555 2.281281230 1.410987648 1.748282154 2.567132841
## [66] 2.291835026 3.014956565 2.181473769 2.232939671 0.367346435
## [71] 1.691728795 -0.088585755 2.204729402 1.386301878 1.809689840
## [76] 0.358626282 3.440680446 -0.282811461 0.324349298 1.822661773
## [81] 3.158395249 1.813985684 2.755115112 3.322716174 3.182564996
## [86] 3.720034868 2.815289699 3.399971350 3.691727945 0.683143350
## [91] 3.436586247 1.523955307 1.975877156 2.614303149 0.768983623
## [96] 3.571687649 2.453980452 2.071301027 2.924586413 2.771114466
## [101] 2.821323341 -0.814409112 -3.644174053 2.879020421 3.029662750
## [106] 2.534779929 2.697468414 1.333606578 2.129886664 2.232054961
## [111] 2.278512960 -0.568020290 1.081153143 3.102784209 3.202708479
## [116] 3.793804089 0.808670550 1.490669708 3.889244855 1.652739074
## [121] 2.296310877 1.400811863 2.202468477 2.939858624 4.387751393
## [126] -1.326830354 3.968564607 -0.574975755 1.495598874 1.742177036
## [131] 0.179568457 0.323129927 1.101706325 -0.704912196 1.888567062
## [136] 2.625522577 3.791461727 0.393295057 1.098016379 1.665903866
## [141] 2.751707723 2.269631103 -0.035686548 2.434194945 2.228554966
## [146] 1.275914528 5.354321851 2.560252387 1.251110995 1.673145487
## [151] 3.886640872 0.451626238 1.543692108 0.367477551 1.745326986
## [156] 1.759574112 4.095620457 -0.567018867 2.822909248 0.255700279
## [161] 0.862669257 3.692776643 1.191930876 2.385361600 1.467681528
## [166] 2.703571401 0.896883948 3.382292723 4.481591358 0.805557009
## [171] 2.286622645 2.292180280 2.824110204 0.423071101 2.180576946
## [176] -2.243464603 3.110131372 3.219880251 1.965970236 2.292610115
## [181] 3.562853837 0.684166096 0.373310718 1.311441021 -0.708975853
## [186] 2.009590648 0.312789548 2.921062399 2.674324215 1.477629000
## [191] 2.342854966 4.759068798 3.216161800 3.391054866 3.756624844
## [196] 2.183245749 0.431318167 1.360155728 1.634243027 1.801986072
## [201] 0.906654871 3.084980240 2.030957509 3.065971505 2.186611349
## [206] 4.012127913 1.622273783 3.260545618 3.360718854 1.658811245
## [211] 1.752657705 1.060096801 0.307906911 3.435518669 1.896510546
## [216] 1.738307774 1.841174605 4.333019985 2.893312851 1.673675734
## [221] -0.125394451 2.823316676 3.281678877 3.140116039 1.623332638
## [226] 0.313421606 5.206717932 3.545884237 2.662475749 5.453750405
## [231] 2.074266653 1.236165652 2.915034281 1.555335124 2.103808385
## [236] 1.168847826 3.720134020 2.280569904 1.228492572 -0.039222840
## [241] 0.979767043 2.454650746 1.818525532 -0.677515940 0.475499625
## [246] 2.463808373 2.492938700 -0.787188506 1.034104352 0.315806690
## [251] 1.471264410 2.176722881 2.935120336 2.139923317 2.338244891
## [256] 2.298435976 0.417609479 1.442832797 2.656471192 1.468786160
## [261] 2.506442061 5.504327769 2.665005713 1.471523016 -2.497284094
## [266] 1.678932200 1.380474221 1.269719573 2.922122514 2.547342831
## [271] 2.332477807 1.178788815 2.999958963 4.805448328 2.040825018
## [276] 4.543744697 3.960237509 2.044850236 3.997971835 1.879166823
## [281] 0.377932445 -0.922741941 2.370418979 2.785872144 3.559427768
## [286] 2.501279976 1.129266452 2.145039246 4.275785293 3.389619122
## [291] 3.243545037 2.913903171 1.372118867 2.736795853 -0.464947787
## [296] 2.577073122 4.797534632 0.150215920 1.863453717 1.896366874
## [301] 0.262275387 2.097121177 -0.716237359 1.520269708 3.366986228
## [306] 1.796807209 1.747512836 2.639835052 1.966863967 3.530474056
## [311] 0.607248831 3.325844410 0.839441505 0.118624306 2.331104965
## [316] 1.503945119 3.615312517 4.180444149 2.396946352 1.754392276
## [321] 1.544044798 1.507083151 2.126155794 0.616003104 0.964845230
## [326] 1.790833187 0.321721809 2.974714986 3.878000510 0.696731779
## [331] 2.971493961 2.150832043 3.218842699 1.390378769 1.052681824
## [336] 2.722300141 5.883971502 2.068378283 3.576695222 3.909652694
## [341] 4.604385200 2.576243149 4.610330338 1.045026772 2.230467641
## [346] 2.478456375 2.288624802 0.342938128 1.215755658 -0.964113840
## [351] 1.766093804 0.002558338 0.084690631 -0.951715682 2.930617128
## [356] 1.611806268 3.080736329 2.676006270 2.408157731 4.591462833
## [361] 2.423660782 1.092080029 1.557939976 1.625969154 2.500799632
## [366] 2.663700306 1.872351761 1.307090125 3.947778952 -0.805797019
## [371] -0.499442266 0.715970872 2.512298881 1.370866073 1.965210117
## [376] 1.659963299 2.194170274 1.069937201 1.498825061 3.279656198
## [381] 0.888520402 3.129872048 0.382329435 0.152496231 1.113890513
## [386] -1.584557672 -2.700052851 3.771320859 2.153663464 5.063265931
## [391] 4.216505700 0.601748780 1.974492783 0.237145210 0.892495223
## [396] 1.148657983 0.271497149 2.091587854 4.496270693 2.001430628
## [401] 2.479937055 -1.138849999 2.612775320 -0.594836310 3.723483441
## [406] 1.915220485 -1.557265139 1.904487051 2.230637652 1.906232630
## [411] -0.488856303 2.999047256 0.047195492 2.343905562 1.629119713
## [416] 3.740780940 3.725018124 1.736536556 -1.180751133 2.596387593
## [421] 3.676427287 1.407849884 2.548641335 1.614341149 1.715417763
## [426] 3.659445847 1.189357743 -0.237290324 2.512179183 1.137197379
## [431] 2.622266254 4.279646794 0.799109590 0.051792082 1.221367105
## [436] 1.991135155 4.147333355 1.030700899 2.255169564 4.508924503
## [441] 0.377695534 2.256876784 3.088040801 3.040679522 0.188743524
## [446] 1.572860172 1.533878052 3.948006729 5.102597199 2.834050614
## [451] 2.324164703 3.742294509 0.473511581 3.275422461 2.152251099
## [456] 3.934504940 4.081911484 1.214188211 1.541194420 3.572623038
## [461] 2.611763819 2.160894388 2.502191404 0.221534525 2.717756700
## [466] 0.587939241 0.434634981 1.198711786 0.996303982 2.431854134
## [471] 1.038164039 0.779025872 3.148144459 4.632257347 -0.469741552
## [476] 2.151595518 3.035542069 2.149431546 -1.086415182 1.751785615
## [481] 0.873806837 4.206539366 0.311421544 -0.443284981 3.397578605
## [486] 1.699207238 3.708662477 1.590331325 4.653996663 0.105246432
## [491] 4.096921370 -0.402891002 3.293017300 0.887255326 4.015897229
## [496] 2.283596573 0.386198271 1.985322932 2.078253878 4.789562286
## [501] 1.696393445 1.308601382 4.541495981 2.829188468 2.622740996
## [506] 0.861837223 3.480658300 4.118370527 2.880967564 1.957382074
## [511] 2.917191793 -0.385060950 2.003299240 2.032156021 0.578349515
## [516] 1.751895495 0.858553209 2.748124618 0.957842873 0.366838926
## [521] 0.770278049 0.282217793 2.000761059 1.744102208 0.976404712
## [526] 3.337081592 4.012964491 1.888059132 2.710758668 1.737881363
## [531] 3.726236750 -0.345817800 3.413697404 2.821000298 3.022061525
## [536] 0.216534334 2.747506980 1.168214364 0.749196246 3.090766567
## [541] 2.447689784 3.745782091 2.531062994 2.603288694 1.161093148
## [546] 1.092538607 3.731826482 2.112562257 0.132213893 3.062313590
## [551] 1.089302187 0.104979847 2.977466755 1.299347318 4.894462267
## [556] 2.453719388 0.476641974 0.577036999 1.005380084 3.448507777
## [561] -1.469934030 1.667626377 3.700609353 0.120744080 0.729753090
## [566] 1.241163958 2.401219662 2.629619590 1.930632558 2.097368421
## [571] 1.784515505 4.100243186 0.843537253 -0.685746795 3.418811887
## [576] 2.073683083 1.255615522 -0.554192079 2.110723554 0.577246608
## [581] 2.530246219 0.488668206 2.341455068 1.538373242 3.269644156
## [586] 2.232531968 3.642088499 1.825601402 -0.849526403 2.012711314
## [591] 4.566123303 -0.537175614 1.883690824 -0.594452442 1.873018875
## [596] 3.146151674 -0.229065704 3.598582804 0.797460896 1.388463495
## [601] 0.295132918 0.507171719 2.283370825 1.760024498 -0.195620422
## [606] -0.189775435 1.729101716 1.417459345 3.034184325 2.320720267
## [611] 2.712359748 3.119984612 2.517874254 3.735414675 2.679679786
## [616] 3.434127494 3.370971698 1.964390140 1.792909768 1.759199973
## [621] 1.651525677 2.273911462 2.532236720 -0.498897977 0.357959358
## [626] 4.825938474 0.440833830 2.206606278 3.867798961 1.517705449
## [631] -0.898272557 1.533725629 -0.361845170 -0.806956191 3.876676424
## [636] 2.672421916 1.096613659 1.950277023 0.114520063 0.864590694
## [641] 2.344774015 3.648609408 2.234939204 1.194933993 0.923888028
## [646] 2.581597993 0.944988330 2.531974216 1.725235618 1.092899198
## [651] 2.262264818 1.590518513 -0.188019535 2.123482135 1.532994935
## [656] 3.233182865 2.285408146 0.838144658 3.262833476 3.166983224
## [661] 2.978842563 2.824489206 0.483882296 4.198055741 1.730986647
## [666] 0.389576863 -0.200074429 2.231556290 3.699924910 -0.101612087
## [671] 1.149951355 1.325678753 1.001907039 2.969530329 2.943424237
## [676] 2.392887448 2.036734002 2.051642819 4.540813616 1.664787707
## [681] 1.518047687 2.066301908 2.409878687 1.885513128 0.902878854
## [686] 4.348388007 2.211644869 3.947894044 -0.199791239 1.236354358
## [691] 5.050526649 0.931146199 1.806283329 1.081315855 2.491257738
## [696] 3.608908314 1.141029993 1.809071310 4.570373744 3.157531626
## [701] 3.475199348 -0.309046991 1.944909223 1.006838405 3.688828945
## [706] 3.560516970 2.508604836 2.779810028 1.941674168 2.103482746
## [711] 2.471656164 -1.696146090 1.009822778 2.288158526 3.966085805
## [716] 1.185640029 1.445872721 2.274304677 2.711878943 1.194784985
## [721] 1.263597307 1.884994403 2.858693440 1.816101142 1.843533130
## [726] 1.321241388 -1.517836037 3.180858328 2.737125468 0.878549324
## [731] 1.115536136 3.101286760 2.524989862 1.974384325 -0.022838562
## [736] 1.891405580 4.951079019 1.230218645 0.840636631 3.173911265
## [741] 3.321044916 2.922502289 2.235900859 2.605909267 3.321676305
## [746] 3.075048519 0.950727822 2.520400819 3.263691737 0.302020315
## [751] 4.400328165 1.220797723 1.388266128 -0.331407271 3.570553631
## [756] 2.328860393 2.075686779 -0.379865516 0.918809829 2.452020713
## [761] 0.908271080 0.338054968 -0.522490621 0.007433005 0.983663604
## [766] -0.717553847 2.922281688 3.044202385 4.017476376 3.647595449
## [771] 2.786301418 -0.338486953 0.750365767 1.512225779 5.008780013
## [776] 1.572668938 3.297892016 2.064559629 2.465542954 1.818613691
## [781] 1.632019632 3.308416296 0.128904572 0.689879936 2.041593454
## [786] 3.011664246 2.358067543 2.318370970 1.832732512 0.427762589
## [791] 0.764148379 1.726621777 1.057760043 1.564668629 4.168887586
## [796] 2.477892398 2.771335811 1.686638479 2.379837911 0.896810311
## [801] 0.516438162 0.529919437 -0.091864012 1.007553519 2.868167402
## [806] 3.100957999 3.344020131 3.972053737 2.366029186 1.405078168
## [811] 3.879420699 -0.171119922 3.020482874 2.956007851 1.032782813
## [816] 4.380819188 3.801342771 1.996068101 0.009912741 1.256832222
## [821] 1.144259295 2.020826375 1.936964891 3.503661711 1.937231760
## [826] -0.296323808 1.989076547 0.440329780 2.562106191 0.626284366
## [831] 0.959577754 2.199217888 1.107623500 1.066121976 2.979939230
## [836] 0.570797661 0.618229117 2.905977733 2.167318883 1.952182534
## [841] 2.758424325 2.841894921 2.120801172 -0.506216701 -0.349469107
## [846] 2.143900752 4.234198849 2.768522971 1.556158619 3.918760714
## [851] 0.796945545 0.761830751 1.765264984 0.501576644 0.287324678
## [856] 1.737187453 -0.068833607 3.770925215 1.735352996 2.371293003
## [861] 0.566132685 4.237688289 3.338079116 -1.201295722 2.284915323
## [866] 0.837905154 3.964337843 4.393077347 1.933599979 2.348394982
## [871] 3.327704007 2.261867421 2.937008198 2.529585787 4.137173853
## [876] 0.122131429 0.988693950 3.905894539 1.460160009 1.912176733
## [881] 1.943225395 4.015631068 2.160746642 1.664310987 5.268946137
## [886] 1.119436567 1.850097851 0.499087143 2.264964786 0.349797626
## [891] 2.734081240 2.416116949 1.827521312 0.021434515 2.137701200
## [896] 2.986741454 1.006042065 0.651509254 -1.033893610 0.078296964
## [901] 3.686192887 1.624868324 0.956519440 2.278137105 2.908018923
## [906] 1.244862273 0.028659642 2.245814908 1.742297047 1.074906208
## [911] 0.855078167 -0.021972484 1.930213388 2.866979748 4.249849903
## [916] 3.890639354 2.930061488 3.636213947 3.385445696 3.748271731
## [921] 0.234415205 4.024322997 0.727447375 2.821240879 2.033054681
## [926] -0.547302807 1.275264477 0.554162379 2.998454054 1.665037851
## [931] 2.711056008 5.755659838 0.047774556 0.117643092 -1.653375814
## [936] 4.016767302 1.993875418 3.242992143 2.267971082 1.869935026
## [941] 2.343035864 -0.389041798 3.245389183 1.239873377 3.173228051
## [946] 3.019503037 1.225412900 2.697248011 4.120426815 0.774436455
## [951] 2.031010947 1.277916079 3.683334541 3.223166993 3.744027843
## [956] 0.267676174 0.378694416 1.374085374 4.194666875 0.916096910
## [961] 4.439149838 4.906376025 1.394244070 3.448883128 2.316628364
## [966] 2.550390267 5.169542912 1.923567699 4.874678836 3.741558145
## [971] 0.531849745 -1.287747122 2.406131453 3.425019316 1.682056870
## [976] -0.214728329 1.563584672 2.187441742 1.151593507 1.575595270
## [981] 0.401313636 2.728285723 2.085032653 0.357241722 2.686406697
## [986] 3.642403111 3.169983250 0.399562279 -0.108169502 -0.122936833
## [991] 3.101560748 -1.079664891 4.928022110 3.994746625 1.866041050
## [996] 2.931731243 2.804225704 2.890966511 1.963849634 1.187633062
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.644 1.009 2.001 1.972 2.941 6.074
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%
## -0.4706973
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%
## 4.234373
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%
## -0.4706973
# 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [61] FALSE FALSE FALSE FALSE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## [133] FALSE TRUE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE
## [409] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 FALSE TRUE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [577] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] TRUE FALSE FALSE TRUE FALSE TRUE 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 TRUE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE 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 TRUE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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
# count all true values using the sum command
sum(Low5Percent[TRUE]) # there are 50 of them
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -1.5782971 -0.5855684 -0.5049626 -0.9670018 -0.8144091 -3.6441741
## [7] -0.5680203 -1.3268304 -0.5749758 -0.7049122 -0.5670189 -2.2434646
## [13] -0.7089759 -0.6775159 -0.7871885 -2.4972841 -0.9227419 -0.7162374
## [19] -0.9641138 -0.9517157 -0.8057970 -0.4994423 -1.5845577 -2.7000529
## [25] -1.1388500 -0.5948363 -1.5572651 -0.4888563 -1.1807511 -1.0864152
## [31] -1.4699340 -0.6857468 -0.5541921 -0.8495264 -0.5371756 -0.5944524
## [37] -0.4988980 -0.8982726 -0.8069562 -1.6961461 -1.5178360 -0.5224906
## [43] -0.7175538 -0.5062167 -1.2012957 -1.0338936 -0.5473028 -1.6533758
## [49] -1.2877471 -1.0796649
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.234373
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [229] FALSE TRUE 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 TRUE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [505] FALSE FALSE FALSE 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 TRUE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE 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 TRUE
## [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 TRUE FALSE FALSE
## [865] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] TRUE TRUE FALSE FALSE FALSE FALSE TRUE FALSE 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 TRUE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.770547 5.793452 6.073840 4.608824 4.387751 5.354322 4.481591 4.759069
## [9] 4.333020 5.206718 5.453750 5.504328 4.805448 4.543745 4.275785 4.797535
## [17] 5.883972 4.604385 4.610330 4.591463 5.063266 4.496271 4.279647 4.508925
## [25] 5.102597 4.632257 4.653997 4.789562 4.541496 4.894462 4.566123 4.825938
## [33] 4.540814 4.348388 5.050527 4.570374 4.951079 4.400328 5.008780 4.380819
## [41] 4.237688 4.393077 5.268946 4.249850 5.755660 4.439150 4.906376 5.169543
## [49] 4.874679 4.928022