# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Rowie Grace N. Peralta
# Student
# Math Department
# March 19, 2023
# Processing of continuous data
# Using random number generators
# Exercise 1: 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] # display first 20 elements
## [1] -0.3123544 0.4930629 -0.7623690 3.4500248 1.9098662 2.7164918
## [7] 0.4348409 0.4968167 4.1992548 1.4525360 0.5650917 1.6645873
## [13] 4.6903418 -0.4937189 3.9618147 0.6627362 3.3292193 0.4897911
## [19] -1.3951732 4.0251840
data[1:300] # display the first 300 elements
## [1] -0.31235436 0.49306294 -0.76236900 3.45002482 1.90986620 2.71649176
## [7] 0.43484089 0.49681671 4.19925484 1.45253601 0.56509171 1.66458726
## [13] 4.69034175 -0.49371892 3.96181473 0.66273622 3.32921927 0.48979109
## [19] -1.39517317 4.02518402 2.10851902 0.43508622 0.58451272 2.81221402
## [25] 1.74073098 0.90285397 0.99877128 5.47342809 3.06005265 2.91914948
## [31] 2.51033651 4.23270551 0.79195601 1.56169147 3.06504841 4.90586448
## [37] 0.55401557 5.56768011 0.36388336 1.70880632 2.68494011 1.46143426
## [43] 2.23793950 2.69578121 5.51831745 2.62932551 5.93488292 2.02686234
## [49] 0.78284817 4.15754741 2.35582269 1.76503175 1.00797529 1.55432677
## [55] 5.65361514 0.94685764 2.53461845 2.09554806 3.39533338 0.40356312
## [61] 0.19617720 2.75163457 5.11969441 3.08750310 0.35683202 0.73208431
## [67] 3.59137642 4.52562621 3.81593049 7.73893799 2.56110629 2.58036508
## [73] 1.21973390 0.17464891 1.80602845 1.43108301 1.09693068 3.84380328
## [79] 1.92346016 2.93284458 4.32110862 0.49978062 2.25148965 1.88455587
## [85] 3.20607620 2.96457541 2.58679389 0.53557635 3.10906815 2.85981731
## [91] 1.68499425 2.23331609 2.24515169 1.88266977 2.43079560 3.32018709
## [97] 2.84796142 4.10239226 1.92476942 3.27106769 2.63243254 -0.39152982
## [103] 5.24571323 1.01820946 1.37329342 1.70964884 1.41281249 0.29868010
## [109] 1.84759607 1.76018873 1.89627267 0.47842078 -1.91312499 4.48381075
## [115] 1.83164127 2.40870445 2.40850937 1.91056548 0.93878597 0.59790137
## [121] 3.34111373 1.28208921 5.42428563 4.12026100 2.07154027 2.51322863
## [127] 2.09683950 -0.82522766 3.63933731 2.69584970 4.10229818 1.23787849
## [133] 0.71868212 1.82274218 2.65208972 0.89937791 3.51325870 1.24885672
## [139] -1.99677976 1.79799694 2.57575475 2.86404968 3.54585035 0.40989904
## [145] 1.84649678 1.56402265 2.78180995 1.06839690 3.55859795 1.30669223
## [151] 2.09893424 0.37892726 2.43306240 0.27784480 4.14039409 1.66352705
## [157] 1.77511876 2.15760184 1.46612692 0.43942230 3.40330455 2.91032097
## [163] 3.71234625 3.55497561 -0.27397970 -2.19292633 3.14077125 2.59288208
## [169] 2.16724400 -0.88842142 2.55783301 1.97962005 4.39106491 2.73188632
## [175] -1.87043369 0.68410641 3.25205339 4.29273670 4.50481051 2.95094902
## [181] 1.93072584 0.24101226 4.18292753 0.86761232 3.02315219 4.03925219
## [187] 2.42824139 2.99196769 3.92564271 2.22118134 3.89960890 1.42919610
## [193] 1.51863921 0.20946220 0.02611920 2.86534740 1.15156826 1.66193514
## [199] 2.08878086 3.54288145 1.21512119 1.23426374 1.04044798 0.48357481
## [205] 3.38739523 -1.04402836 2.34863333 0.38335247 2.91979639 0.10453731
## [211] -0.66193732 1.78656593 -0.57263588 0.01871248 3.75410186 0.58493267
## [217] -0.84582999 1.36210270 4.40378940 -0.99327927 1.51305133 1.34511668
## [223] 2.86978023 5.58633337 3.20858997 0.22709993 3.61092625 2.24620131
## [229] 1.44208334 4.33339034 2.22256174 2.63004255 3.72757190 3.13721796
## [235] 1.97135317 2.44573620 3.32702633 1.81626633 0.62937532 2.45879310
## [241] 0.12029438 1.90029227 2.49664849 1.49786024 2.44801672 0.70121562
## [247] 2.71281471 1.36053980 0.68445263 2.34158725 3.27229010 1.72608190
## [253] 4.32576098 -0.09934341 0.59778497 1.12395128 2.34193674 0.88667939
## [259] -0.38805469 2.97522184 6.04880530 2.86042238 1.59557883 -1.69169207
## [265] 3.21132398 2.79400369 0.96366146 2.52591704 0.80713195 2.26873387
## [271] -1.47137640 -0.38488044 3.16148585 1.27986008 0.12919649 3.06493207
## [277] 0.48938898 4.05310370 1.90480342 1.73346367 1.63047027 1.61490796
## [283] 0.12351050 0.16103759 1.05313129 2.93230237 1.37368138 1.53863032
## [289] 1.18351225 0.33458667 3.31710116 1.46629440 4.65037630 2.64592698
## [295] 1.96626053 1.52712231 2.71835287 2.37512517 2.35729767 3.44317647
# 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] -2.19292633 -2.09260447 -1.99228261 -1.89196075 -1.79163889 -1.69131702
## [7] -1.59099516 -1.49067330 -1.39035144 -1.29002958 -1.18970772 -1.08938585
## [13] -0.98906399 -0.88874213 -0.78842027 -0.68809841 -0.58777655 -0.48745468
## [19] -0.38713282 -0.28681096 -0.18648910 -0.08616724 0.01415463 0.11447649
## [25] 0.21479835 0.31512021 0.41544207 0.51576393 0.61608580 0.71640766
## [31] 0.81672952 0.91705138 1.01737324 1.11769511 1.21801697 1.31833883
## [37] 1.41866069 1.51898255 1.61930441 1.71962628 1.81994814 1.92027000
## [43] 2.02059186 2.12091372 2.22123559 2.32155745 2.42187931 2.52220117
## [49] 2.62252303 2.72284489 2.82316676 2.92348862 3.02381048 3.12413234
## [55] 3.22445420 3.32477607 3.42509793 3.52541979 3.62574165 3.72606351
## [61] 3.82638537 3.92670724 4.02702910 4.12735096 4.22767282 4.32799468
## [67] 4.42831655 4.52863841 4.62896027 4.72928213 4.82960399 4.92992585
## [73] 5.03024772 5.13056958 5.23089144 5.33121330 5.43153516 5.53185703
## [79] 5.63217889 5.73250075 5.83282261 5.93314447 6.03346633 6.13378820
## [85] 6.23411006 6.33443192 6.43475378 6.53507564 6.63539751 6.73571937
## [91] 6.83604123 6.93636309 7.03668495 7.13700681 7.23732868 7.33765054
## [97] 7.43797240 7.53829426 7.63861612 7.73893799
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%
## -2.1929263 0.9587842 2.0390303 3.0422586 7.7389380
# 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] -0.312354361 0.493062940 -0.762369004 3.450024825 1.909866196
## [6] 2.716491761 0.434840889 0.496816713 4.199254835 1.452536014
## [11] 0.565091711 1.664587260 4.690341754 -0.493718925 3.961814731
## [16] 0.662736225 3.329219270 0.489791092 -1.395173174 4.025184023
## [21] 2.108519016 0.435086218 0.584512725 2.812214018 1.740730977
## [26] 0.902853969 0.998771279 5.473428093 3.060052649 2.919149483
## [31] 2.510336505 4.232705511 0.791956010 1.561691469 3.065048408
## [36] 4.905864482 0.554015572 5.567680107 0.363883362 1.708806322
## [41] 2.684940109 1.461434255 2.237939498 2.695781208 5.518317451
## [46] 2.629325514 5.934882920 2.026862342 0.782848169 4.157547410
## [51] 2.355822690 1.765031754 1.007975290 1.554326769 5.653615143
## [56] 0.946857644 2.534618448 2.095548055 3.395333379 0.403563125
## [61] 0.196177197 2.751634568 5.119694413 3.087503100 0.356832016
## [66] 0.732084310 3.591376424 4.525626214 3.815930495 7.738937985
## [71] 2.561106285 2.580365085 1.219733898 0.174648910 1.806028446
## [76] 1.431083013 1.096930680 3.843803280 1.923460158 2.932844578
## [81] 4.321108625 0.499780619 2.251489654 1.884555873 3.206076203
## [86] 2.964575405 2.586793894 0.535576352 3.109068151 2.859817315
## [91] 1.684994255 2.233316087 2.245151695 1.882669772 2.430795604
## [96] 3.320187094 2.847961418 4.102392263 1.924769421 3.271067685
## [101] 2.632432540 -0.391529824 5.245713227 1.018209461 1.373293425
## [106] 1.709648840 1.412812495 0.298680100 1.847596068 1.760188728
## [111] 1.896272670 0.478420778 -1.913124985 4.483810752 1.831641274
## [116] 2.408704455 2.408509367 1.910565480 0.938785974 0.597901365
## [121] 3.341113725 1.282089213 5.424285634 4.120261005 2.071540272
## [126] 2.513228630 2.096839499 -0.825227657 3.639337309 2.695849701
## [131] 4.102298176 1.237878490 0.718682124 1.822742177 2.652089716
## [136] 0.899377914 3.513258697 1.248856724 -1.996779757 1.797996936
## [141] 2.575754748 2.864049678 3.545850348 0.409899035 1.846496779
## [146] 1.564022652 2.781809949 1.068396896 3.558597947 1.306692225
## [151] 2.098934243 0.378927258 2.433062395 0.277844798 4.140394091
## [156] 1.663527052 1.775118759 2.157601837 1.466126917 0.439422303
## [161] 3.403304550 2.910320969 3.712346246 3.554975614 -0.273979703
## [166] -2.192926334 3.140771252 2.592882078 2.167244005 -0.888421418
## [171] 2.557833009 1.979620055 4.391064909 2.731886322 -1.870433688
## [176] 0.684106408 3.252053395 4.292736703 4.504810506 2.950949016
## [181] 1.930725844 0.241012262 4.182927530 0.867612319 3.023152186
## [186] 4.039252187 2.428241389 2.991967694 3.925642715 2.221181342
## [191] 3.899608900 1.429196097 1.518639206 0.209462200 0.026119199
## [196] 2.865347398 1.151568257 1.661935141 2.088780857 3.542881452
## [201] 1.215121192 1.234263737 1.040447976 0.483574813 3.387395234
## [206] -1.044028357 2.348633327 0.383352475 2.919796393 0.104537307
## [211] -0.661937315 1.786565928 -0.572635884 0.018712484 3.754101860
## [216] 0.584932671 -0.845829990 1.362102699 4.403789401 -0.993279268
## [221] 1.513051325 1.345116677 2.869780227 5.586333374 3.208589970
## [226] 0.227099933 3.610926251 2.246201310 1.442083340 4.333390338
## [231] 2.222561743 2.630042548 3.727571903 3.137217965 1.971353168
## [236] 2.445736200 3.327026335 1.816266334 0.629375320 2.458793097
## [241] 0.120294380 1.900292271 2.496648492 1.497860241 2.448016720
## [246] 0.701215617 2.712814713 1.360539800 0.684452631 2.341587246
## [251] 3.272290095 1.726081902 4.325760978 -0.099343414 0.597784966
## [256] 1.123951281 2.341936739 0.886679395 -0.388054687 2.975221845
## [261] 6.048805304 2.860422377 1.595578834 -1.691692072 3.211323982
## [266] 2.794003687 0.963661461 2.525917043 0.807131952 2.268733869
## [271] -1.471376399 -0.384880435 3.161485850 1.279860077 0.129196486
## [276] 3.064932067 0.489388985 4.053103699 1.904803422 1.733463668
## [281] 1.630470272 1.614907958 0.123510496 0.161037587 1.053131286
## [286] 2.932302373 1.373681383 1.538630317 1.183512250 0.334586673
## [291] 3.317101158 1.466294400 4.650376302 2.645926978 1.966260531
## [296] 1.527122310 2.718352872 2.375125169 2.357297671 3.443176466
## [301] 1.385091973 3.728782644 0.697034381 1.893892039 3.588817167
## [306] 3.131206208 2.426282883 -0.828777621 0.496818770 0.206770496
## [311] 2.054844073 4.097534563 1.196266178 3.555081410 1.200173139
## [316] 2.020828008 3.834562216 -1.621360572 2.217791992 2.293169058
## [321] -0.244502961 1.314412185 1.745146557 2.521914899 1.181168868
## [326] 0.291539281 1.574504190 1.367658393 2.189743570 2.040463686
## [331] 0.925699101 2.084686930 -0.888003079 2.995228310 1.349707352
## [336] -0.116500248 1.232379682 0.520263668 3.688829001 -1.137789867
## [341] 4.756902513 3.420658532 -0.287851129 2.802537149 1.103928307
## [346] 3.592766741 3.219725148 1.162348654 0.025562977 3.452325130
## [351] 2.814485647 4.004029448 2.708224983 3.505650146 3.588291965
## [356] 1.053509326 0.805815340 0.742834748 3.421841078 1.240830401
## [361] 3.581662699 2.163796915 0.462306569 2.658849063 3.037116323
## [366] 2.893243744 2.937957381 3.317257665 -0.087675091 1.209335872
## [371] 3.654101640 0.942781337 2.222902723 1.071727864 0.870887044
## [376] 0.342828726 -1.087133833 4.522450008 4.039470198 -1.607981536
## [381] -0.267250349 3.636975203 2.167715627 2.076368355 1.829522349
## [386] 5.964324907 0.941203926 1.117076984 2.358395355 3.517297818
## [391] 3.690545645 4.325766874 2.372300200 1.397793067 1.800983811
## [396] 2.857565895 2.131236844 4.549664687 0.992151665 1.618825540
## [401] 0.730095150 2.152864463 2.613521447 1.054067176 3.119855674
## [406] -1.480618403 -0.086041630 0.973269879 2.418407978 -0.313117780
## [411] 2.811550285 4.193958306 2.993278976 1.014551018 3.865751092
## [416] -0.112132532 2.294770611 4.194098599 3.240028729 -1.603550963
## [421] 5.030126752 2.554864571 2.883070006 0.151645732 -0.267316171
## [426] 3.067903790 -0.095475182 0.640803389 4.437373630 4.763520549
## [431] 4.068726007 0.026024401 2.311341259 1.921957726 1.949982103
## [436] 1.876217695 2.892081836 3.060698611 1.903543902 2.582679669
## [441] 3.902053381 0.077091970 2.818496813 -0.786516249 3.762980258
## [446] 0.820529882 3.549968579 1.582082343 3.613006506 3.048407642
## [451] 2.428725074 2.938256554 6.401679423 4.411950144 2.239735521
## [456] 4.791427261 2.133076960 2.936148354 1.283950713 1.662815581
## [461] 5.559222864 4.926927495 0.689375790 1.395649205 1.240946037
## [466] 1.379682269 2.282736049 1.634883176 0.993923264 2.202886142
## [471] 2.956171236 1.462037273 2.938722748 0.599453207 1.692720344
## [476] -0.563664426 1.370523845 2.488234701 2.295625880 2.490112175
## [481] 0.594404684 3.859061474 -0.004010949 3.531480778 2.849753795
## [486] 2.084443735 4.077778694 1.157068627 2.068182670 3.360189083
## [491] 2.680097038 1.865351837 2.116829851 2.415325164 0.953271813
## [496] -0.262459951 2.183629931 3.913267826 0.491008848 1.970320746
## [501] 0.311381792 1.259730421 4.747051209 3.166620026 0.473477908
## [506] 2.658191723 0.484112306 2.131298907 3.157931849 2.975162945
## [511] -0.041434102 -0.992974317 1.053484921 3.222256539 2.037596898
## [516] 3.214121104 2.320420813 3.037948393 5.881979461 1.705823047
## [521] 0.985885874 1.865179333 4.304455215 2.908678395 2.050268652
## [526] 0.683408787 2.019464118 3.185325491 0.552318474 3.511093874
## [531] 0.521302296 1.427559890 0.115854684 1.970968319 2.676023920
## [536] 3.746831049 2.937966656 0.818388411 1.128232513 2.398798468
## [541] 0.995894958 1.716132857 3.095973581 1.787496419 3.023567475
## [546] 2.392222121 5.389647104 2.410987738 3.245538177 2.126616709
## [551] 1.547667262 1.942160855 -0.124205000 4.837683075 0.942210000
## [556] 0.439163762 1.306686125 0.328761595 1.611256004 -0.194163729
## [561] -0.745437940 -0.263660079 1.829419888 4.285118620 0.837450963
## [566] 2.042660825 2.956645846 3.966150395 2.429144168 2.477471471
## [571] 0.400155938 1.561664599 4.737096355 1.351667010 1.491614078
## [576] 1.042819563 0.525216705 0.096528740 2.430628618 4.168506165
## [581] 2.404913511 2.587863786 1.840510199 2.489583303 2.253193927
## [586] 4.470140690 3.141187754 1.861474041 1.492795374 3.270740473
## [591] -0.082150356 1.305117763 2.318586556 1.101474536 3.185761897
## [596] 0.262083843 2.155816225 2.913088019 3.308173210 2.718026448
## [601] 2.417339378 3.482976294 1.212809619 1.561616369 3.270881255
## [606] -0.965498502 1.707052899 0.844432210 1.530877103 2.851786774
## [611] 2.140497602 -1.793486700 -0.638020113 1.918719520 2.164564362
## [616] 1.569963106 0.512965630 0.997941346 1.411953487 2.821942587
## [621] 1.145544375 3.028055735 1.139625376 4.044871884 3.316239460
## [626] 0.449538550 4.996823856 1.404427692 1.465641077 1.451083027
## [631] 1.818079983 3.679039740 1.189837423 3.874752647 2.723266305
## [636] 1.874750314 2.683926613 4.790379126 -0.274525729 3.599659202
## [641] 1.383678915 3.355711439 1.768458011 1.339615549 0.417118402
## [646] 1.315764803 -0.230161026 0.545377088 -0.306341431 1.329254881
## [651] 4.229801569 1.895406397 2.703017903 2.582639258 1.791132692
## [656] 0.246280357 -0.575615567 0.156291221 2.649891254 1.136706232
## [661] 0.021684780 4.469810807 3.176109490 2.350114437 1.664235849
## [666] 3.034625730 1.453848358 3.059595570 3.325954570 2.415684225
## [671] 4.052789188 2.340250422 3.222962118 -0.018395209 1.552643862
## [676] 1.921912643 -0.763943806 3.200976136 3.027271730 0.318943322
## [681] 1.544569026 1.851082869 4.774719920 1.853884597 3.158750187
## [686] 1.832288177 1.944723820 3.041485172 -1.099663754 2.530439526
## [691] 0.584934998 2.271071293 -0.061089772 4.574206442 4.289959926
## [696] 2.832622074 1.472405034 2.396466129 3.323869361 1.150020568
## [701] 4.031368394 -1.201082753 3.553457215 1.420257980 1.986229686
## [706] 2.584837074 2.848298261 1.503547316 -0.247062718 2.063152431
## [711] 0.783642707 -0.225913301 1.596851720 2.469306957 2.813376613
## [716] 1.345156610 2.902852886 2.914952843 -0.211286809 2.748430283
## [721] 3.137845532 0.214184205 2.897771973 3.055085176 -1.908621146
## [726] -0.070356233 0.782608762 2.330831868 2.237053974 2.432853597
## [731] 2.225639527 1.948680749 2.972230343 0.130051973 3.488023131
## [736] 0.618971293 3.792600850 3.956008837 4.183053064 0.725007280
## [741] 3.630142632 2.516515290 3.439326627 3.721879704 0.400144320
## [746] 1.422407287 2.871593716 3.421528194 0.374534843 3.050150427
## [751] 1.180992575 2.414451680 1.609897739 3.141024973 2.346117803
## [756] -0.615994301 0.689223795 0.575722885 5.039141418 2.214162581
## [761] -1.782523880 -0.532952135 -0.653265079 1.510054026 0.698376349
## [766] 0.880536006 4.226984338 2.587167321 0.808382580 3.438176121
## [771] -0.730953572 4.477876789 1.927163156 4.698672603 -1.658494781
## [776] 3.126105507 3.210915012 4.154637840 1.128048302 0.960621635
## [781] 2.241420208 -1.270820386 1.703202748 2.841543446 3.714840844
## [786] 1.319358270 3.154260395 1.572519701 0.760032185 2.558834729
## [791] 3.035995448 0.610928850 -0.326629075 1.701504651 1.429788449
## [796] 0.040632257 2.549855390 0.517285543 -0.888967289 0.401230596
## [801] 0.596196356 2.679786971 1.969988934 3.052349513 2.032878058
## [806] 1.146026024 0.452408944 2.311498499 4.108792310 0.442932500
## [811] 2.295371684 3.153861444 0.950395474 2.121425234 0.491693074
## [816] 3.902779403 0.538049095 -1.077517420 0.576182624 1.974140367
## [821] 0.773827704 1.839898228 -0.644584269 2.298193651 3.105896651
## [826] 4.864918247 -0.760313017 -1.010113865 0.973295714 4.334624684
## [831] 3.026215735 2.715440781 3.276645425 1.212571534 2.551420197
## [836] 1.813402158 2.790513749 1.558882928 1.944461883 1.260442347
## [841] 2.745693552 1.939020873 2.844275328 0.730180191 1.348775075
## [846] 5.745663623 2.245144692 2.558777198 4.627124486 -0.015532560
## [851] 2.795359073 2.120955112 3.632548698 4.986960462 1.430611133
## [856] 0.617241417 1.920251491 1.204644999 -1.119567248 1.950647375
## [861] 0.435356635 0.537989450 3.428468714 1.206364598 -0.120103654
## [866] 0.746598484 2.638652763 0.566668578 2.739015432 2.706841285
## [871] 2.909142568 2.325566995 3.096184595 3.380659923 2.858667226
## [876] 1.406072180 2.513030788 -0.730864343 5.113945127 1.639854302
## [881] 2.064330276 2.707361839 3.992845574 2.316743073 1.199518013
## [886] 2.647110490 1.662043396 2.080780213 3.861489963 1.558014071
## [891] 1.653599366 3.093834100 4.158061832 2.207937148 3.126624892
## [896] 2.102888759 3.449188843 0.780526789 3.620554141 1.451132105
## [901] 4.977591492 3.395067242 4.442192612 3.465940029 3.660049742
## [906] 2.078440254 4.742554996 2.617856771 0.128045880 1.351135567
## [911] 2.297903817 2.162753900 2.718035270 2.903102651 3.962116869
## [916] 1.007594760 2.274632112 0.277618977 1.722865372 1.185410858
## [921] 3.637478292 2.524373566 2.454045863 0.003862589 0.576855617
## [926] 0.479413426 -0.898026600 0.539342343 -0.355262120 -0.873319585
## [931] 0.241678746 -0.463976087 1.390259139 3.354449714 -0.464657898
## [936] 3.130330507 -0.562732988 -0.252867125 1.451837355 1.970761839
## [941] 1.633495117 0.579132956 2.578242904 3.127837621 1.206261639
## [946] -1.396465218 -0.511905064 1.794132836 -0.390015354 0.988449317
## [951] 1.545017078 1.515964666 3.493210485 0.848367126 3.884144651
## [956] 1.323584253 1.213422566 5.364221507 0.843370664 4.052321024
## [961] 2.747094163 2.370852552 1.251385136 1.483512543 -0.595780959
## [966] 2.128586712 3.045357708 2.280043653 1.200665258 5.184922423
## [971] 1.296083335 2.748430511 3.044578787 2.580095337 3.269809991
## [976] 0.845507263 2.041316020 3.946010730 3.333484438 3.286939955
## [981] 4.589703791 2.817000186 0.831769982 2.309237228 3.227305518
## [986] 1.169118298 1.171725276 0.967436932 4.845090025 2.457047768
## [991] -0.139512388 3.863769628 4.676719038 1.746353423 4.610266297
## [996] 0.905496931 0.145634838 4.125951723 3.719210765 -0.185033201
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.1929 0.9588 2.0390 2.0004 3.0423 7.7389
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%
## -0.5727849
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%
## 4.484861
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%
## -0.5727849
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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] 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [169] FALSE TRUE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [217] TRUE FALSE FALSE TRUE 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 TRUE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE TRUE FALSE FALSE FALSE 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 TRUE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE
## [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 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 TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [613] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE 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 TRUE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [757] FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE TRUE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE TRUE
## [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 TRUE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE TRUE FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE TRUE 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 FALSE 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] -0.7623690 -1.3951732 -1.9131250 -0.8252277 -1.9967798 -2.1929263
## [7] -0.8884214 -1.8704337 -1.0440284 -0.6619373 -0.8458300 -0.9932793
## [13] -1.6916921 -1.4713764 -0.8287776 -1.6213606 -0.8880031 -1.1377899
## [19] -1.0871338 -1.6079815 -1.4806184 -1.6035510 -0.7865162 -0.9929743
## [25] -0.7454379 -0.9654985 -1.7934867 -0.6380201 -0.5756156 -0.7639438
## [31] -1.0996638 -1.2010828 -1.9086211 -0.6159943 -1.7825239 -0.6532651
## [37] -0.7309536 -1.6584948 -1.2708204 -0.8889673 -1.0775174 -0.6445843
## [43] -0.7603130 -1.0101139 -1.1195672 -0.7308643 -0.8980266 -0.8733196
## [49] -1.3964652 -0.5957810
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.484861
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [37] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE 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 TRUE 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 FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE TRUE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] TRUE FALSE 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 TRUE
## [457] FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE 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 TRUE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE TRUE 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 TRUE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [697] FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE
## [853] FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] TRUE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 4.690342 5.473428 4.905864 5.567680 5.518317 5.934883 5.653615 5.119694
## [9] 4.525626 7.738938 5.245713 5.424286 4.504811 5.586333 6.048805 4.650376
## [17] 4.756903 4.522450 5.964325 4.549665 5.030127 4.763521 6.401679 4.791427
## [25] 5.559223 4.926927 4.747051 5.881979 5.389647 4.837683 4.737096 4.996824
## [33] 4.790379 4.774720 4.574206 5.039141 4.698673 4.864918 5.745664 4.627124
## [41] 4.986960 5.113945 4.977591 4.742555 5.364222 5.184922 4.589704 4.845090
## [49] 4.676719 4.610266