# Mindanao State University
# General Santos City
# Introduction to R base commands
# Prepared by: Prof. Carlito O. Daarol
# Faculty
# Math Department
# March 16, 2023
#Submitted by: Jovel Jade Casidsid
# 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] # display first 20 elements
## [1] 2.1677187 2.3869106 2.3832399 0.6474248 0.6936942 3.5092479
## [7] -0.0631861 2.2292847 0.2159811 -0.6124755 2.9760238 0.8910585
## [13] -1.1081320 2.8546589 2.6302404 3.3258438 3.8037318 1.5507332
## [19] 0.8673013 0.8133797
data[1:300] # display the first 300 elements
## [1] 2.16771868 2.38691057 2.38323991 0.64742476 0.69369417 3.50924791
## [7] -0.06318610 2.22928471 0.21598115 -0.61247550 2.97602383 0.89105854
## [13] -1.10813201 2.85465885 2.63024040 3.32584375 3.80373175 1.55073320
## [19] 0.86730133 0.81337972 1.14642481 0.11038864 1.42365515 2.76213761
## [25] 0.49600380 2.76725257 3.87733213 3.53056355 1.22189434 0.03834107
## [31] 2.99773680 3.56112644 2.99428605 1.57594624 2.67358113 1.55448125
## [37] 0.87270660 1.28091487 1.46157253 3.41666848 2.94716610 1.32706812
## [43] 1.82911985 0.73940459 1.22572875 -0.18707629 0.54938563 0.63817377
## [49] 1.44658542 3.06611041 3.29440513 2.75862542 4.48961241 1.76440698
## [55] 0.37819797 1.72093245 2.90199769 -0.44618441 0.94257976 -0.54774580
## [61] 2.52715319 2.18116404 -0.11212984 -0.89372508 -0.49707722 1.28646739
## [67] 2.01363067 1.43763007 0.83464956 2.02086015 1.70189828 3.45113571
## [73] 1.80479229 -0.29999611 3.47667735 3.27904189 2.63797809 3.31378691
## [79] 4.38457396 1.57568024 -1.51324614 1.40090184 2.76250957 0.63846166
## [85] 2.39550741 3.05414698 -1.56593468 2.36060481 4.84192607 3.06930346
## [91] 4.52699838 0.35439871 3.99412259 4.64583025 0.62658949 2.86132694
## [97] 2.77922623 1.72409457 3.41426591 -1.28383756 2.22276108 2.87756495
## [103] 1.29237666 1.15749551 2.10490424 2.92550201 3.57369158 2.77334418
## [109] 0.14160658 2.56843810 1.13728323 1.74775023 2.14514618 1.35814215
## [115] 3.44312324 0.13543795 1.15947623 0.06893855 0.11611272 1.63375061
## [121] 1.89307227 0.94606819 1.80570214 1.34001334 1.81938443 3.15552438
## [127] 2.07594479 3.03579306 -0.40791873 -0.16499957 2.20145394 1.42305486
## [133] 0.36087368 4.95646759 4.29617149 1.38479258 1.39056087 -0.78650731
## [139] 3.33769590 1.22423021 2.42048668 0.77206503 2.34793883 3.85510108
## [145] -0.05754593 2.03883682 3.12745975 1.10559550 2.55112119 -0.43449541
## [151] 2.58073561 0.88254127 3.96553569 -0.31734083 3.11077817 3.31405375
## [157] 0.28025715 3.71758100 1.24330537 1.01497307 1.64931371 2.53923188
## [163] -0.07400937 0.81574990 1.76464117 3.41670337 1.57239412 2.52205756
## [169] -0.25484215 4.33229016 0.40621424 3.08803642 0.72897756 1.50109670
## [175] 2.92983280 1.60900040 1.76211611 2.19973600 0.80097206 2.98026736
## [181] 3.31270996 -2.29008059 2.74129009 0.36348712 -0.10783457 3.67773881
## [187] 3.46640411 0.53767381 2.00747739 -2.68491969 4.99805414 1.50371536
## [193] 1.32862328 0.94065823 -0.85301569 3.33886288 0.34709119 3.38535988
## [199] 2.44477269 3.19218942 3.59157722 3.41647724 1.79466886 3.93437534
## [205] 1.79334601 2.20623339 1.26987529 0.51783931 0.54435153 6.40180093
## [211] 1.10974985 2.13840664 1.50323371 1.23550244 1.39218452 2.50262950
## [217] 2.32080601 2.32350114 -0.64186623 -0.27414630 0.19775871 -1.84978554
## [223] 3.49011409 0.24214506 2.13598723 2.16154609 2.95120892 2.13003073
## [229] 5.60451712 1.08586916 1.18427984 0.35551930 5.05908890 4.10193366
## [235] -0.73585899 0.87759106 -0.04053743 3.02290172 2.88587511 3.99896311
## [241] 1.80932767 2.44393339 2.42112238 0.63081151 3.64838104 1.09907073
## [247] 4.29256350 0.16056861 1.91365713 5.40783096 1.94207139 3.36273589
## [253] 2.58180278 0.85276259 3.95643003 0.70934800 3.04169197 4.43277400
## [259] 2.79143039 1.58738469 0.73218332 1.36790817 0.62875571 7.05930526
## [265] 0.91089076 1.73353415 2.69334397 0.43013203 0.10486883 2.09770382
## [271] 0.06243005 5.30272634 0.66482141 1.31738767 3.46643962 3.05940907
## [277] 1.34279717 0.91627646 0.02054827 1.54012144 2.58693529 1.32907573
## [283] 2.45297716 -0.24860889 0.49366631 3.35173767 2.11006598 1.68159353
## [289] 2.07883159 2.09107096 4.03792796 2.12885698 3.05376042 2.51386413
## [295] 2.89990056 3.61845104 2.82304525 -0.12271252 4.67717155 0.61265628
# 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] -3.065036762 -2.962770680 -2.860504599 -2.758238518 -2.655972437
## [6] -2.553706356 -2.451440275 -2.349174194 -2.246908113 -2.144642032
## [11] -2.042375951 -1.940109870 -1.837843789 -1.735577708 -1.633311627
## [16] -1.531045546 -1.428779464 -1.326513383 -1.224247302 -1.121981221
## [21] -1.019715140 -0.917449059 -0.815182978 -0.712916897 -0.610650816
## [26] -0.508384735 -0.406118654 -0.303852573 -0.201586492 -0.099320411
## [31] 0.002945671 0.105211752 0.207477833 0.309743914 0.412009995
## [36] 0.514276076 0.616542157 0.718808238 0.821074319 0.923340400
## [41] 1.025606481 1.127872562 1.230138643 1.332404724 1.434670806
## [46] 1.536936887 1.639202968 1.741469049 1.843735130 1.946001211
## [51] 2.048267292 2.150533373 2.252799454 2.355065535 2.457331616
## [56] 2.559597697 2.661863778 2.764129859 2.866395941 2.968662022
## [61] 3.070928103 3.173194184 3.275460265 3.377726346 3.479992427
## [66] 3.582258508 3.684524589 3.786790670 3.889056751 3.991322832
## [71] 4.093588913 4.195854994 4.298121076 4.400387157 4.502653238
## [76] 4.604919319 4.707185400 4.809451481 4.911717562 5.013983643
## [81] 5.116249724 5.218515805 5.320781886 5.423047967 5.525314048
## [86] 5.627580129 5.729846211 5.832112292 5.934378373 6.036644454
## [91] 6.138910535 6.241176616 6.343442697 6.445708778 6.547974859
## [96] 6.650240940 6.752507021 6.854773102 6.957039183 7.059305264
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%
## -3.0650368 0.9074813 1.9597486 3.0248912 7.0593053
# 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] 2.167718684 2.386910565 2.383239909 0.647424759 0.693694174
## [6] 3.509247913 -0.063186095 2.229284707 0.215981146 -0.612475501
## [11] 2.976023828 0.891058545 -1.108132014 2.854658855 2.630240402
## [16] 3.325843754 3.803731751 1.550733204 0.867301327 0.813379718
## [21] 1.146424810 0.110388640 1.423655151 2.762137608 0.496003796
## [26] 2.767252569 3.877332128 3.530563549 1.221894342 0.038341066
## [31] 2.997736802 3.561126443 2.994286049 1.575946245 2.673581128
## [36] 1.554481251 0.872706596 1.280914869 1.461572530 3.416668481
## [41] 2.947166102 1.327068119 1.829119846 0.739404588 1.225728752
## [46] -0.187076290 0.549385626 0.638173771 1.446585423 3.066110407
## [51] 3.294405129 2.758625419 4.489612413 1.764406975 0.378197970
## [56] 1.720932451 2.901997695 -0.446184410 0.942579764 -0.547745804
## [61] 2.527153191 2.181164041 -0.112129836 -0.893725084 -0.497077224
## [66] 1.286467394 2.013630670 1.437630072 0.834649558 2.020860154
## [71] 1.701898284 3.451135709 1.804792286 -0.299996110 3.476677346
## [76] 3.279041894 2.637978092 3.313786914 4.384573956 1.575680245
## [81] -1.513246145 1.400901842 2.762509567 0.638461663 2.395507409
## [86] 3.054146978 -1.565934684 2.360604813 4.841926065 3.069303456
## [91] 4.526998377 0.354398715 3.994122594 4.645830254 0.626589494
## [96] 2.861326937 2.779226226 1.724094566 3.414265907 -1.283837561
## [101] 2.222761084 2.877564948 1.292376659 1.157495510 2.104904235
## [106] 2.925502009 3.573691583 2.773344183 0.141606580 2.568438103
## [111] 1.137283232 1.747750228 2.145146177 1.358142148 3.443123236
## [116] 0.135437952 1.159476235 0.068938546 0.116112716 1.633750612
## [121] 1.893072274 0.946068194 1.805702139 1.340013339 1.819384431
## [126] 3.155524378 2.075944789 3.035793057 -0.407918733 -0.164999573
## [131] 2.201453940 1.423054856 0.360873679 4.956467588 4.296171485
## [136] 1.384792579 1.390560867 -0.786507306 3.337695904 1.224230205
## [141] 2.420486677 0.772065033 2.347938830 3.855101081 -0.057545927
## [146] 2.038836820 3.127459755 1.105595504 2.551121194 -0.434495415
## [151] 2.580735610 0.882541270 3.965535686 -0.317340825 3.110778168
## [156] 3.314053754 0.280257152 3.717581003 1.243305375 1.014973071
## [161] 1.649313708 2.539231877 -0.074009370 0.815749896 1.764641170
## [166] 3.416703374 1.572394120 2.522057556 -0.254842152 4.332290161
## [171] 0.406214236 3.088036416 0.728977558 1.501096701 2.929832795
## [176] 1.609000401 1.762116111 2.199736005 0.800972063 2.980267364
## [181] 3.312709955 -2.290080588 2.741290093 0.363487119 -0.107834566
## [186] 3.677738814 3.466404115 0.537673814 2.007477393 -2.684919693
## [191] 4.998054141 1.503715361 1.328623283 0.940658227 -0.853015693
## [196] 3.338862876 0.347091185 3.385359882 2.444772686 3.192189422
## [201] 3.591577224 3.416477238 1.794668855 3.934375343 1.793346009
## [206] 2.206233387 1.269875287 0.517839312 0.544351529 6.401800933
## [211] 1.109749855 2.138406636 1.503233708 1.235502443 1.392184522
## [216] 2.502629497 2.320806013 2.323501143 -0.641866232 -0.274146303
## [221] 0.197758708 -1.849785543 3.490114088 0.242145062 2.135987234
## [226] 2.161546088 2.951208922 2.130030734 5.604517115 1.085869162
## [231] 1.184279839 0.355519303 5.059088897 4.101933663 -0.735858993
## [236] 0.877591056 -0.040537427 3.022901716 2.885875108 3.998963115
## [241] 1.809327667 2.443933389 2.421122375 0.630811515 3.648381041
## [246] 1.099070730 4.292563497 0.160568611 1.913657129 5.407830961
## [251] 1.942071388 3.362735894 2.581802777 0.852762590 3.956430033
## [256] 0.709347999 3.041691970 4.432773999 2.791430389 1.587384685
## [261] 0.732183323 1.367908169 0.628755706 7.059305264 0.910890757
## [266] 1.733534149 2.693343973 0.430132029 0.104868831 2.097703823
## [271] 0.062430046 5.302726345 0.664821407 1.317387674 3.466439621
## [276] 3.059409073 1.342797171 0.916276461 0.020548268 1.540121436
## [281] 2.586935290 1.329075731 2.452977161 -0.248608888 0.493666307
## [286] 3.351737670 2.110065979 1.681593531 2.078831592 2.091070960
## [291] 4.037927957 2.128856981 3.053760415 2.513864131 2.899900564
## [296] 3.618451038 2.823045252 -0.122712521 4.677171548 0.612656282
## [301] 0.587440614 2.325776327 1.585885157 4.569200335 1.406383904
## [306] 0.075658195 2.498961782 3.483129920 3.803211352 1.615864442
## [311] 2.841190976 1.643706727 3.629971122 3.592617558 3.386786744
## [316] 2.369964182 0.862304107 2.397777819 2.439075893 -1.243509601
## [321] 1.422890365 0.002976181 2.623384341 1.239845443 1.253386787
## [326] 0.899777115 1.706151291 -0.083045138 0.602103256 0.877007001
## [331] 0.570112828 4.448033789 2.107552277 -1.069969849 -0.513554008
## [336] -0.247472733 1.583264678 1.176423420 1.622687819 -0.166762233
## [341] 2.187262215 1.553876373 2.005402114 1.385296279 2.754139579
## [346] 1.850829818 1.587914290 4.019383346 4.381213070 3.937634637
## [351] 0.589688536 1.674269169 2.512945434 0.605198208 1.859266990
## [356] 2.522843265 0.831856880 4.504813037 2.986760930 1.224380873
## [361] 1.823491495 4.327587590 2.740052529 -0.097842393 3.139911264
## [366] 3.096952870 1.427725478 0.138313508 4.707497686 3.286949515
## [371] 4.201059686 3.603569569 0.193506540 1.481107806 0.772866900
## [376] 1.624418795 2.211053207 0.195627041 4.374004244 -0.256630850
## [381] 0.913615364 1.147753574 2.109872113 5.289398233 0.643863002
## [386] 2.857680069 0.910049360 -0.531942416 2.335803430 0.926264807
## [391] 1.873074775 2.841319820 1.479079685 3.183425468 3.387750191
## [396] 3.012665312 1.964832722 1.426814101 1.978726768 0.892450208
## [401] -0.741858065 0.363559763 0.147653422 3.417931160 -0.367901096
## [406] 1.094563945 4.860674536 0.329284134 3.187793573 0.261426314
## [411] 0.545102997 3.355491743 2.473030260 -0.111417810 2.188409214
## [416] -0.658972286 0.478232035 2.430764708 1.446751402 1.076987700
## [421] 3.254149277 3.351451966 3.166574787 1.938780053 4.100160066
## [426] 4.006447234 1.419957568 1.243489734 2.064490939 -1.120704041
## [431] 2.097547658 3.413953047 4.711636220 0.536597506 3.249684938
## [436] 2.942263276 3.202388538 2.209963898 0.696439414 -2.047737774
## [441] 3.352410212 2.472456825 4.117437018 4.017283612 3.213429773
## [446] 2.554707509 -0.044794571 0.068656982 1.177542175 3.735384171
## [451] 0.228687305 3.160072766 -1.694368407 2.167044050 0.225924409
## [456] 1.245592656 3.547811868 1.883383039 1.655615391 1.727411770
## [461] 1.090991811 4.085573609 1.718798644 2.680137179 0.515241097
## [466] 3.821306586 3.701879773 1.980427976 1.967757022 0.364880312
## [471] 3.485241614 1.923509832 2.005032886 1.282357466 2.232488446
## [476] 1.418286956 2.086696634 1.633698888 3.394721420 3.428307722
## [481] 2.729284722 6.528111812 1.142865914 3.547114216 0.426805304
## [486] 3.304538603 0.969723887 4.047417775 0.755957546 3.698899485
## [491] 3.433100359 1.669988340 -0.374065441 4.214012503 3.482287700
## [496] 1.217525862 1.116188188 3.095470188 1.484267451 0.604461624
## [501] -0.665782538 3.003862580 2.247703527 -0.264059092 0.865178498
## [506] 0.315174372 1.959462759 4.179288225 2.509095339 3.282365348
## [511] 1.728614746 4.440951722 1.120907991 3.551602528 0.573773357
## [516] 2.441338113 2.850278333 3.226687048 2.672645315 3.040101855
## [521] 3.580715628 3.350322397 3.710666033 2.462346336 1.170166352
## [526] 2.076934566 1.165013722 2.040800136 3.321130968 1.513048145
## [531] 2.127693676 1.543713490 0.136104297 2.265093061 3.236135299
## [536] 2.301561523 -0.334975887 -0.111514819 2.357309232 2.633788053
## [541] 1.763897702 1.361800019 1.560969832 0.638315725 3.417825881
## [546] 3.149988073 0.718035289 4.776553208 1.914905329 2.670966702
## [551] 0.795642835 2.599349135 3.139141738 3.447747582 1.116023162
## [556] 4.023343244 1.829624065 2.599515375 2.374103220 0.604031765
## [561] 1.516976553 -2.312833355 4.473872405 2.024024632 3.299890877
## [566] -0.045910762 0.526376552 1.986800016 1.142316942 0.047708700
## [571] 0.915764977 1.585033868 0.343083279 1.590870169 -0.146783716
## [576] 1.287227794 4.450699707 1.197124984 1.204527388 -0.107787024
## [581] 1.763553304 1.732206525 0.452994453 2.182845554 1.238545028
## [586] 2.053572642 1.421950634 2.983228257 2.010244053 1.478076295
## [591] 1.176697542 1.447096034 3.260149215 0.779115629 -0.311842828
## [596] 3.578140888 2.040736671 3.142195492 -1.355214326 1.951746051
## [601] 0.361253681 5.085839536 0.737816326 5.366391562 1.812558803
## [606] 4.041895202 5.137356593 5.570569667 4.089861100 2.557908130
## [611] 5.263036426 1.143716633 2.733926871 2.484111175 1.065170128
## [616] 3.123570880 2.358683475 0.735367584 1.203917567 0.656454398
## [621] 0.794484757 1.290405082 1.771134003 1.534550757 2.307937075
## [626] 2.946007767 0.189198397 0.912120514 3.105533354 3.669943247
## [631] 1.779073817 1.586738951 1.308467599 1.796368597 3.342147993
## [636] 0.370416561 2.913836917 1.287696730 1.118472767 3.104244055
## [641] 0.850606531 3.186167537 3.107024814 2.541596776 2.409815398
## [646] 1.446853298 3.323725222 2.396731943 3.008485566 1.963368457
## [651] 2.298150669 5.174408250 2.416102820 1.340133140 2.276013020
## [656] 2.821045618 1.328219011 0.733337849 3.334277013 2.536721687
## [661] 2.523950952 4.371755835 5.056077930 2.853763671 0.604478113
## [666] 1.710419228 0.692786241 2.087494759 1.525376957 0.226204491
## [671] 3.188386267 2.656402865 3.585551258 3.129473227 3.451198590
## [676] 0.537860688 6.621070728 -0.940514134 4.683089990 3.362634617
## [681] 3.814415839 1.834100197 3.380767128 2.272632945 0.993262532
## [686] -0.194431254 2.063785692 0.701287628 1.687123026 3.861386939
## [691] 1.062266064 0.088659147 2.143874115 4.408717813 0.935566458
## [696] 2.733905766 1.783400462 0.830613388 2.331179677 2.876808570
## [701] 3.681348125 0.354712858 2.414907113 1.292027681 3.138228051
## [706] 3.234029577 3.035934936 2.508504021 4.863630859 -0.629734718
## [711] -3.065036762 3.124181314 3.691671995 0.522597514 2.557717182
## [716] 2.587849429 2.758795012 2.479289476 1.991089895 1.827842395
## [721] -0.498395494 4.357669073 2.669930609 0.993535589 3.096649377
## [726] 1.522674554 0.657283673 2.640177800 -0.481879825 2.565830613
## [731] -0.772483256 1.115792428 -1.349006949 2.743719198 2.663145783
## [736] 2.877117774 5.349097931 5.170014864 6.271594407 2.196648125
## [741] -0.219020713 4.879218399 0.195562548 3.207702208 3.840434419
## [746] 2.018924823 1.870088953 2.015559662 0.770103533 4.263318942
## [751] 6.216565987 0.531467609 1.436775186 2.226377653 2.550865082
## [756] 1.573973584 1.606877276 1.737490123 3.648525524 1.481378964
## [761] -1.099345573 0.287972905 3.767099422 1.415261733 2.979744865
## [766] 3.494132501 1.374917486 1.853515053 0.838966432 0.780454572
## [771] 4.293719960 0.769114720 3.984727069 0.036531167 2.178547153
## [776] 1.880539194 0.739856279 -1.058985784 -0.153987163 2.183932569
## [781] 3.463172778 1.936207433 -0.527729217 4.023351063 0.696178839
## [786] 0.635341125 3.030859586 -0.889450047 2.648772505 1.692322458
## [791] 2.573077075 -0.076090787 2.333889107 2.795327324 2.307497828
## [796] 1.771750598 0.971979948 1.463279030 4.569134322 2.712047432
## [801] 1.615765137 1.172401402 2.167272824 1.335247988 -0.145726301
## [806] 3.918660658 0.982910226 3.102311110 -0.029568518 1.765583841
## [811] 3.532265677 2.284008292 0.839983617 0.021716347 1.973692614
## [816] 0.600320558 1.851284493 2.753014947 2.491507821 1.855984378
## [821] 2.040245755 1.371894969 2.827321404 2.802466415 5.540952255
## [826] 2.744408879 3.033967743 2.300955023 2.714781279 1.867278027
## [831] 1.841221072 1.380308922 -0.213461301 2.862550523 2.280197133
## [836] 0.598517611 2.669153004 2.596293309 1.687778613 2.747914144
## [841] 1.761430579 0.459585663 0.736989401 4.438424112 3.032564460
## [846] 2.477104730 1.659644517 1.155807647 2.677117789 2.793964733
## [851] 0.204467016 0.993068562 2.051370558 1.960553483 1.978816086
## [856] -0.024343572 3.237775899 3.336757132 4.052886252 3.494548919
## [861] 2.718655618 0.170981542 0.721116863 0.528103310 -0.106047033
## [866] -0.076442881 0.639927982 1.820928201 2.053754351 0.862733782
## [871] 3.307420645 1.224132742 1.988961515 2.082810171 3.456490181
## [876] 2.187868933 -0.120080367 0.428861520 2.567335706 1.997395445
## [881] 3.258275764 1.967580986 1.844393196 3.068527476 3.306947172
## [886] 0.350497558 2.745167316 0.537841957 0.639117365 1.750191724
## [891] -1.237687234 0.672119276 2.353815586 3.501905029 3.894168600
## [896] 1.231376035 0.564378771 1.234723601 1.390641978 3.429411782
## [901] 1.436206617 -0.782970606 0.370505933 0.228351512 2.188881597
## [906] 4.373329318 2.014358626 2.129498635 0.776674874 4.568141099
## [911] 1.915072324 2.498105241 -0.367498660 4.545308009 1.797217363
## [916] 3.733142862 0.155606449 -0.514527760 0.589624302 -2.299625334
## [921] 2.597500261 3.676256712 2.006608677 2.208176946 1.834442879
## [926] -0.208260386 2.682504934 1.908207802 3.947724155 2.437532064
## [931] 3.741553218 0.507049859 3.342287726 2.766344185 1.368826794
## [936] 1.339697547 3.694724500 2.016418189 1.448939366 1.173375619
## [941] 1.960034430 3.510831720 1.216461115 4.303961286 3.430552630
## [946] 1.407656501 1.814374652 1.210629047 1.716399861 2.770925335
## [951] 0.867202298 2.109702759 1.093264082 3.839763729 3.169550045
## [956] 0.650127196 3.333800940 3.251263614 1.584724185 2.702443265
## [961] 2.198575552 2.312204411 0.691900095 2.200613140 2.923956026
## [966] 3.079081622 1.652726243 5.332094604 2.153138673 0.311275739
## [971] 2.434943996 1.623673220 1.776934244 1.387809600 3.124966598
## [976] 1.013371537 1.178693678 1.573209228 1.169887819 2.341171351
## [981] 2.797518468 4.386103268 3.414543577 0.205153194 1.174422485
## [986] 2.633946102 3.559173011 0.182415107 1.644006461 0.146263383
## [991] -0.467133783 3.084739840 0.223664115 1.339583207 2.701635860
## [996] 3.301906639 2.099505130 3.333086383 -0.135237524 1.427413135
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.0650 0.9075 1.9597 1.9575 3.0249 7.0593
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%
## -0.3182226
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%
## 4.381381
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%
## -0.3182226
# 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 FALSE FALSE TRUE FALSE FALSE
## [13] TRUE 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] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE
## [61] FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [85] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE
## [181] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [193] FALSE FALSE TRUE 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 TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
## [337] FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 FALSE TRUE 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 TRUE 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 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 TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
## [733] TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [781] FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 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 TRUE 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] -0.6124755 -1.1081320 -0.4461844 -0.5477458 -0.8937251 -0.4970772
## [7] -1.5132461 -1.5659347 -1.2838376 -0.4079187 -0.7865073 -0.4344954
## [13] -2.2900806 -2.6849197 -0.8530157 -0.6418662 -1.8497855 -0.7358590
## [19] -1.2435096 -1.0699698 -0.5135540 -0.5319424 -0.7418581 -0.3679011
## [25] -0.6589723 -1.1207040 -2.0477378 -1.6943684 -0.3740654 -0.6657825
## [31] -0.3349759 -2.3128334 -1.3552143 -0.9405141 -0.6297347 -3.0650368
## [37] -0.4983955 -0.4818798 -0.7724833 -1.3490069 -1.0993456 -1.0589858
## [43] -0.5277292 -0.8894500 -1.2376872 -0.7829706 -0.3674987 -0.5145278
## [49] -2.2996253 -0.4671338
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.381381
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE TRUE FALSE FALSE TRUE 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 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 FALSE 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 TRUE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [301] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE
## [433] TRUE 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 FALSE FALSE
## [481] FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] TRUE 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 TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE 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 FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE 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] TRUE 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 TRUE TRUE FALSE FALSE TRUE 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 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 TRUE 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 TRUE 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 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 FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [913] FALSE TRUE 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 FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 4.489612 4.384574 4.841926 4.526998 4.645830 4.956468 4.998054 6.401801
## [9] 5.604517 5.059089 5.407831 4.432774 7.059305 5.302726 4.677172 4.569200
## [17] 4.448034 4.504813 4.707498 5.289398 4.860675 4.711636 6.528112 4.440952
## [25] 4.776553 4.473872 4.450700 5.085840 5.366392 5.137357 5.570570 5.263036
## [33] 5.174408 5.056078 6.621071 4.683090 4.408718 4.863631 5.349098 5.170015
## [41] 6.271594 4.879218 6.216566 4.569134 5.540952 4.438424 4.568141 4.545308
## [49] 5.332095 4.386103