# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Joshua Marie H. Casador
# Prepared by: Prof. Carlito O. Daarol
# Faculty
# 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] # display first 20 elements
## [1] 2.43308007 3.12963999 1.13899759 0.65646197 1.65978206 2.67877146
## [7] 0.14565055 2.19802183 4.20414066 1.67547383 5.30805798 1.27674653
## [13] 3.80774994 2.33390286 2.95437620 -0.34040613 1.73922674 1.02126591
## [19] -0.09702569 2.21903793
data[1:300] # display the first 300 elements
## [1] 2.433080071 3.129639990 1.138997594 0.656461970 1.659782061
## [6] 2.678771460 0.145650547 2.198021828 4.204140663 1.675473826
## [11] 5.308057979 1.276746532 3.807749937 2.333902863 2.954376201
## [16] -0.340406127 1.739226735 1.021265912 -0.097025688 2.219037927
## [21] 1.254189260 2.432665134 2.172951344 3.751926240 0.559327796
## [26] -0.374681469 3.262040250 2.457528823 0.363175978 1.339511973
## [31] 2.278521881 2.436012463 2.513786703 4.594760621 1.311384562
## [36] 4.659656172 1.165418470 1.609757366 2.252371736 1.465213053
## [41] -0.004305806 0.076024233 1.190634530 1.630303902 0.532495513
## [46] 2.976908228 1.516196761 0.258650618 1.805318379 2.731332183
## [51] 3.365033788 0.043301557 3.538367316 2.209811389 1.373826093
## [56] 1.719111002 3.717126523 3.684543828 4.930653795 4.592762464
## [61] 1.650991011 3.971570854 2.104349196 -0.384747512 3.981380001
## [66] 2.087149707 3.859642836 4.232854805 3.490824352 4.893909192
## [71] 0.781942214 3.878596439 -0.047282521 0.460368019 5.735467996
## [76] 3.861210143 0.954377209 4.970172693 4.808926387 2.035725031
## [81] 4.286131563 1.503665220 2.485443063 2.649201847 4.687322873
## [86] 1.608011302 0.696537129 4.323999404 1.431564431 0.311889296
## [91] 3.449540640 1.043770545 0.594808207 2.794622674 1.711234958
## [96] 1.593003621 3.973581940 2.579946737 1.650889476 0.196516159
## [101] 2.928423398 2.677928487 2.861708975 4.229968887 2.514273845
## [106] 2.885838901 -0.019608548 1.362974100 3.105470035 1.914125976
## [111] 3.008128453 3.061744643 2.987088933 2.535489038 0.940233432
## [116] -1.739762450 0.612567451 1.138371413 1.222096640 5.168424519
## [121] 3.137037582 0.648799553 0.965939157 3.257638289 0.185830624
## [126] 2.930148807 1.992686733 0.031986771 3.918094913 2.692817619
## [131] 3.772055472 1.122228598 3.160033350 2.081555490 -1.158380951
## [136] -0.217465651 2.784137453 2.906703038 1.891893818 0.250538144
## [141] 1.621415146 3.595793255 -0.185022747 0.003619876 3.381027249
## [146] 2.881518757 3.241928259 0.602873301 0.766061637 2.035785386
## [151] 2.708387996 3.012945672 -0.560209048 2.045272212 0.356482499
## [156] 1.322607907 2.197958128 -0.955041568 0.609784364 2.812588019
## [161] 1.611272725 2.302607395 2.578436192 1.917571657 1.878000268
## [166] 0.571805627 0.558392797 1.516861579 7.813983920 1.590137679
## [171] -1.049497247 3.993742392 1.221229681 1.717354795 3.655664418
## [176] 1.623233902 1.842110633 1.416536254 3.440895309 4.916283139
## [181] 2.201714062 -0.232226534 2.572160105 5.017516914 3.443434367
## [186] 0.208864968 -0.174187392 3.160054988 2.882470339 4.694753214
## [191] 0.511386835 5.843437396 0.253979952 2.971517956 0.130474916
## [196] 0.987511326 2.341552394 3.033788153 2.993996255 2.527692160
## [201] -1.628721945 2.137885261 4.309330466 -0.117504633 4.537833545
## [206] 3.839616754 3.163738576 1.558343653 4.427459828 1.618525499
## [211] 2.090232575 3.643736617 2.750810167 2.084642418 2.778819542
## [216] 2.894110865 1.176088669 4.732222895 1.917058419 3.447138594
## [221] 1.524485544 0.684490811 1.272745024 2.836224145 1.288237224
## [226] 3.571976933 2.381390248 2.315750406 0.413555264 3.319014159
## [231] 1.920099854 3.953559179 5.052340482 2.144185947 3.675413096
## [236] 3.050608596 1.623191690 3.620425249 2.308279046 1.815237940
## [241] 0.597204816 2.547390821 3.051604567 0.475310078 1.698028368
## [246] 0.380559592 -0.235966727 3.681942697 3.276741007 4.346845860
## [251] 2.893755965 2.295682660 1.379942713 2.045246756 2.675754988
## [256] 2.531384363 1.832797757 2.530026693 2.228657487 -0.640624422
## [261] 4.623479878 3.665258648 1.105703466 1.080802094 1.896406393
## [266] -0.581054988 3.017923364 1.917309277 2.737256788 3.596477936
## [271] 1.158535048 3.157619394 1.330266897 2.309377347 1.188049107
## [276] 3.699220302 1.713071949 2.219486560 4.666715509 -0.024319447
## [281] 2.746767514 3.930232643 5.122757382 3.316907320 2.327874612
## [286] 0.469509780 3.841641499 1.213513261 0.220426261 2.685608610
## [291] 1.352301844 -1.985825373 1.412233483 1.614941750 1.355569096
## [296] 1.703134961 0.869378191 2.472148490 3.220233161 -2.550426239
# 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] -3.10951645 -2.99917806 -2.88883968 -2.77850129 -2.66816290 -2.55782451
## [7] -2.44748613 -2.33714774 -2.22680935 -2.11647096 -2.00613258 -1.89579419
## [13] -1.78545580 -1.67511741 -1.56477903 -1.45444064 -1.34410225 -1.23376386
## [19] -1.12342547 -1.01308709 -0.90274870 -0.79241031 -0.68207192 -0.57173354
## [25] -0.46139515 -0.35105676 -0.24071837 -0.13037999 -0.02004160 0.09029679
## [31] 0.20063518 0.31097356 0.42131195 0.53165034 0.64198873 0.75232711
## [37] 0.86266550 0.97300389 1.08334228 1.19368066 1.30401905 1.41435744
## [43] 1.52469583 1.63503421 1.74537260 1.85571099 1.96604938 2.07638777
## [49] 2.18672615 2.29706454 2.40740293 2.51774132 2.62807970 2.73841809
## [55] 2.84875648 2.95909487 3.06943325 3.17977164 3.29011003 3.40044842
## [61] 3.51078680 3.62112519 3.73146358 3.84180197 3.95214035 4.06247874
## [67] 4.17281713 4.28315552 4.39349390 4.50383229 4.61417068 4.72450907
## [73] 4.83484745 4.94518584 5.05552423 5.16586262 5.27620101 5.38653939
## [79] 5.49687778 5.60721617 5.71755456 5.82789294 5.93823133 6.04856972
## [85] 6.15890811 6.26924649 6.37958488 6.48992327 6.60026166 6.71060004
## [91] 6.82093843 6.93127682 7.04161521 7.15195359 7.26229198 7.37263037
## [97] 7.48296876 7.59330714 7.70364553 7.81398392
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%
## -3.109516 1.097231 2.068978 3.066278 7.813984
# 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] 2.433080071 3.129639990 1.138997594 0.656461970 1.659782061
## [6] 2.678771460 0.145650547 2.198021828 4.204140663 1.675473826
## [11] 5.308057979 1.276746532 3.807749937 2.333902863 2.954376201
## [16] -0.340406127 1.739226735 1.021265912 -0.097025688 2.219037927
## [21] 1.254189260 2.432665134 2.172951344 3.751926240 0.559327796
## [26] -0.374681469 3.262040250 2.457528823 0.363175978 1.339511973
## [31] 2.278521881 2.436012463 2.513786703 4.594760621 1.311384562
## [36] 4.659656172 1.165418470 1.609757366 2.252371736 1.465213053
## [41] -0.004305806 0.076024233 1.190634530 1.630303902 0.532495513
## [46] 2.976908228 1.516196761 0.258650618 1.805318379 2.731332183
## [51] 3.365033788 0.043301557 3.538367316 2.209811389 1.373826093
## [56] 1.719111002 3.717126523 3.684543828 4.930653795 4.592762464
## [61] 1.650991011 3.971570854 2.104349196 -0.384747512 3.981380001
## [66] 2.087149707 3.859642836 4.232854805 3.490824352 4.893909192
## [71] 0.781942214 3.878596439 -0.047282521 0.460368019 5.735467996
## [76] 3.861210143 0.954377209 4.970172693 4.808926387 2.035725031
## [81] 4.286131563 1.503665220 2.485443063 2.649201847 4.687322873
## [86] 1.608011302 0.696537129 4.323999404 1.431564431 0.311889296
## [91] 3.449540640 1.043770545 0.594808207 2.794622674 1.711234958
## [96] 1.593003621 3.973581940 2.579946737 1.650889476 0.196516159
## [101] 2.928423398 2.677928487 2.861708975 4.229968887 2.514273845
## [106] 2.885838901 -0.019608548 1.362974100 3.105470035 1.914125976
## [111] 3.008128453 3.061744643 2.987088933 2.535489038 0.940233432
## [116] -1.739762450 0.612567451 1.138371413 1.222096640 5.168424519
## [121] 3.137037582 0.648799553 0.965939157 3.257638289 0.185830624
## [126] 2.930148807 1.992686733 0.031986771 3.918094913 2.692817619
## [131] 3.772055472 1.122228598 3.160033350 2.081555490 -1.158380951
## [136] -0.217465651 2.784137453 2.906703038 1.891893818 0.250538144
## [141] 1.621415146 3.595793255 -0.185022747 0.003619876 3.381027249
## [146] 2.881518757 3.241928259 0.602873301 0.766061637 2.035785386
## [151] 2.708387996 3.012945672 -0.560209048 2.045272212 0.356482499
## [156] 1.322607907 2.197958128 -0.955041568 0.609784364 2.812588019
## [161] 1.611272725 2.302607395 2.578436192 1.917571657 1.878000268
## [166] 0.571805627 0.558392797 1.516861579 7.813983920 1.590137679
## [171] -1.049497247 3.993742392 1.221229681 1.717354795 3.655664418
## [176] 1.623233902 1.842110633 1.416536254 3.440895309 4.916283139
## [181] 2.201714062 -0.232226534 2.572160105 5.017516914 3.443434367
## [186] 0.208864968 -0.174187392 3.160054988 2.882470339 4.694753214
## [191] 0.511386835 5.843437396 0.253979952 2.971517956 0.130474916
## [196] 0.987511326 2.341552394 3.033788153 2.993996255 2.527692160
## [201] -1.628721945 2.137885261 4.309330466 -0.117504633 4.537833545
## [206] 3.839616754 3.163738576 1.558343653 4.427459828 1.618525499
## [211] 2.090232575 3.643736617 2.750810167 2.084642418 2.778819542
## [216] 2.894110865 1.176088669 4.732222895 1.917058419 3.447138594
## [221] 1.524485544 0.684490811 1.272745024 2.836224145 1.288237224
## [226] 3.571976933 2.381390248 2.315750406 0.413555264 3.319014159
## [231] 1.920099854 3.953559179 5.052340482 2.144185947 3.675413096
## [236] 3.050608596 1.623191690 3.620425249 2.308279046 1.815237940
## [241] 0.597204816 2.547390821 3.051604567 0.475310078 1.698028368
## [246] 0.380559592 -0.235966727 3.681942697 3.276741007 4.346845860
## [251] 2.893755965 2.295682660 1.379942713 2.045246756 2.675754988
## [256] 2.531384363 1.832797757 2.530026693 2.228657487 -0.640624422
## [261] 4.623479878 3.665258648 1.105703466 1.080802094 1.896406393
## [266] -0.581054988 3.017923364 1.917309277 2.737256788 3.596477936
## [271] 1.158535048 3.157619394 1.330266897 2.309377347 1.188049107
## [276] 3.699220302 1.713071949 2.219486560 4.666715509 -0.024319447
## [281] 2.746767514 3.930232643 5.122757382 3.316907320 2.327874612
## [286] 0.469509780 3.841641499 1.213513261 0.220426261 2.685608610
## [291] 1.352301844 -1.985825373 1.412233483 1.614941750 1.355569096
## [296] 1.703134961 0.869378191 2.472148490 3.220233161 -2.550426239
## [301] 2.472583123 2.527248475 1.966188183 1.943684524 0.950828336
## [306] 1.913276991 -0.019489198 1.953818092 1.260416313 3.354205006
## [311] 2.360622112 2.052141023 0.729118476 1.828997956 2.288430234
## [316] 1.815902126 2.319745806 2.728282781 1.724578264 5.128576470
## [321] -0.281307305 2.430273939 -0.514195140 2.303042886 3.947846425
## [326] 1.401498064 2.913599202 1.362505963 4.187122785 1.452665334
## [331] -0.068153120 2.296372572 0.447235901 1.599158976 0.469846248
## [336] 2.664118006 2.275182477 0.365310599 2.370027848 0.489081883
## [341] 3.289374113 0.289868908 5.883119423 0.322883782 2.233637583
## [346] 3.434102749 2.213906913 0.593540397 2.883640047 1.149921583
## [351] 0.452612352 -0.853950204 -0.680474765 2.348623046 2.789424245
## [356] 0.450245363 2.679382743 5.291314695 2.565935919 0.529827668
## [361] 3.249263978 1.848862326 -0.104783639 4.946087914 1.963504481
## [366] 1.230638649 2.121242063 1.976753463 2.603902817 -0.266790826
## [371] -2.423282830 2.302152284 1.995970337 0.127922003 2.300466917
## [376] 2.673829964 3.427931574 1.172149665 2.838813766 2.560185721
## [381] 2.912838651 1.100866394 2.295003946 4.078225073 3.961370640
## [386] 3.358762412 0.207319131 1.543031348 3.349052962 -0.507692876
## [391] 2.246390828 4.529452742 5.426371942 3.564742265 0.706179410
## [396] -1.069631016 0.572106094 4.471121913 2.437790735 2.606741936
## [401] 4.620891949 5.008496352 1.764634247 1.856069938 2.872437988
## [406] 1.298811524 3.581544988 0.999826969 -0.513515440 1.867281769
## [411] 3.646207518 -0.748063581 0.046882642 3.819802488 2.720458611
## [416] 0.959486721 5.310002624 2.798418474 3.835421301 -1.357936106
## [421] 3.822401405 4.121072620 1.277829963 0.439226432 -0.280301804
## [426] 1.854218250 2.800731362 1.071317391 -1.408645467 4.257078642
## [431] 2.703367819 0.818071019 3.202199822 3.407045697 3.309087453
## [436] 2.231266698 1.575154549 -0.356781025 4.510992604 1.511928882
## [441] 1.427735421 0.906352846 2.755604052 1.131282256 0.194364466
## [446] 4.029076141 -0.977001087 2.394697471 3.092408273 5.301544723
## [451] 0.881535757 0.038712906 3.247071362 -0.824360955 2.968235156
## [456] 1.970097649 2.585886603 2.878929280 0.423300732 0.157750707
## [461] 1.364298271 1.728577699 2.006487077 2.340374088 -0.778393198
## [466] 0.860246551 1.061474214 2.844117193 3.026028312 -0.070155764
## [471] 1.541217882 3.069291950 5.369355538 2.094120981 2.739413814
## [476] 0.331981269 3.108361528 4.068470634 3.528247215 4.390885042
## [481] 3.791152462 2.841878439 1.574404993 4.933401114 3.342068431
## [486] 1.562185737 3.646128989 4.804453623 0.545198330 4.926849243
## [491] 2.806856513 1.781717272 1.963368468 1.978828114 1.436753627
## [496] 2.535432474 0.024230905 3.273935949 -0.126446017 0.041428246
## [501] 0.249356597 2.592315257 2.506760254 -1.485096805 0.882351343
## [506] 2.062080189 4.613934844 -0.095239482 1.645763615 1.827074295
## [511] 0.687735631 -0.073254497 3.124339676 2.550098465 3.286803566
## [516] 2.515282251 -0.574345140 2.565253476 4.147832930 4.372672921
## [521] 0.098494142 2.303568187 2.294416106 -0.413310281 1.929426325
## [526] 1.517607174 1.352436938 1.966613680 3.839605195 5.818673343
## [531] 0.985901705 3.004612845 2.849540179 2.550799281 -0.650442271
## [536] 2.890445317 3.697507930 5.042925507 1.353345043 1.925203714
## [541] 0.722211787 1.032917504 2.934254401 0.159899290 1.684020379
## [546] 2.041878143 -1.474770886 1.165213645 1.695559298 0.515142444
## [551] 5.602951154 2.823854779 1.919071252 1.090288517 2.423910717
## [556] 0.255116678 2.926814152 2.004161353 3.343601247 4.165169403
## [561] -1.021323642 1.233920085 2.031101123 2.085872225 0.755850191
## [566] 1.908282936 2.590388987 3.520055467 1.365636805 2.543103734
## [571] 1.471289660 3.690320997 0.906926613 1.538689680 3.350093169
## [576] 2.267146754 1.565031669 1.482348799 2.354622329 1.819368916
## [581] 2.983569137 -0.233180840 0.220936169 -0.230493180 3.883074980
## [586] 2.258551297 2.526897119 0.199233591 4.353248297 3.844239516
## [591] 2.891870212 4.017239301 0.554834441 1.501477397 3.960562937
## [596] 0.336607512 2.256038034 1.469719547 1.559832194 -0.371548614
## [601] 0.703544143 3.429140930 1.871908279 3.323703973 3.159584627
## [606] -0.305044361 2.086794289 1.361374599 0.914868448 3.123353491
## [611] 3.725260511 1.959943805 0.879836685 3.501076201 2.664116969
## [616] 5.055475010 -0.850018354 -1.631527485 1.341450859 3.618651606
## [621] 4.778686400 3.584392144 2.149021460 0.882961008 3.503882828
## [626] 1.097478483 -0.126797424 -0.037687569 2.408637082 1.256070257
## [631] 0.125085134 0.787538760 1.114384538 2.830576835 -0.039716433
## [636] 3.444133064 3.089150480 3.389865026 2.070352036 2.080724428
## [641] 1.469984982 0.223514480 1.684954421 0.506591272 -0.035216140
## [646] 3.561772849 4.270393051 3.086241113 3.785160291 2.308908176
## [651] 1.726072924 1.098763248 3.511468180 3.173370573 2.230429333
## [656] 3.243079542 2.807341170 1.871774444 1.893964127 2.742082186
## [661] 1.754974447 3.389344770 1.643823954 -3.109516451 2.779796943
## [666] 2.875587678 3.620552373 3.020174574 2.139197206 0.886912244
## [671] 3.062294945 3.733970055 1.850645061 2.027635731 2.290350300
## [676] 1.530476379 0.151142727 1.795758889 3.761151698 1.461273929
## [681] 2.055472241 0.083537801 0.761299243 3.163791219 1.648197042
## [686] 3.196937661 -0.081783239 3.281682952 -1.267743362 2.084897088
## [691] 2.894635279 5.287775559 4.383542969 5.597405699 0.039133377
## [696] 2.309327774 2.454313541 3.375347685 2.522814839 0.228239139
## [701] 5.165514737 4.518080668 3.794311065 1.869971749 3.858736801
## [706] -0.257635688 1.708707087 2.527185031 1.803424844 4.172961616
## [711] 1.854948349 -0.271231918 2.468084532 2.787339501 -0.105274622
## [716] 1.209712524 1.441140431 -1.257508822 3.520779548 3.618121143
## [721] 2.244279256 -0.090615005 3.050447304 0.142537275 -1.115840662
## [726] 2.323509086 2.605214106 4.156930078 1.410795804 3.468415286
## [731] 3.127607524 3.038707937 0.931101472 2.238670182 2.674908590
## [736] -0.639627608 2.557385120 3.224392670 2.360163340 2.822211310
## [741] 0.086785359 2.321977888 1.787499981 -1.715843152 2.636897098
## [746] 1.810426591 0.901475243 2.389109535 1.799150544 1.213362341
## [751] -0.420653858 1.309369828 2.278192455 1.048113512 -1.657273324
## [756] 0.352343439 1.072946930 0.666494610 1.931835123 2.995707181
## [761] 3.995012186 2.839277835 4.602245425 1.787087214 1.208831329
## [766] 2.402953585 1.820739390 1.026884172 -1.685831551 3.961591784
## [771] 0.607555158 3.876821876 1.613337701 3.065273357 -2.116555088
## [776] 1.622543303 1.208025174 1.740884670 0.455388690 3.077258363
## [781] 0.252933603 2.244913594 2.344017806 -0.744399241 2.000326009
## [786] 1.220758266 3.516432072 1.392623071 3.290188564 6.045382265
## [791] -0.255402271 4.135577414 2.285040518 1.300218710 1.503630955
## [796] 1.137453777 -0.353976465 4.181648766 4.084487115 1.114641547
## [801] 4.548274466 5.394534866 4.822706797 1.993659595 1.551784314
## [806] 1.259540092 2.238505616 3.149850620 3.088677471 1.910545473
## [811] 4.708705700 2.277233298 1.080363896 1.853858700 0.514409196
## [816] 0.981904615 2.655008071 1.280008001 1.176097947 3.678249136
## [821] 2.058051255 2.496479449 1.384847057 4.446289475 -1.516298928
## [826] 2.785868408 3.412448844 4.914957569 1.588456042 0.416539653
## [831] 3.721240271 3.434940421 3.737907676 3.364504297 1.595441061
## [836] 2.390055196 0.439096037 1.086519697 2.112809290 0.151513244
## [841] 1.187593966 3.155626400 0.689812105 1.096488787 1.602913885
## [846] 3.931531041 3.887345468 0.663882383 0.242919879 2.991802626
## [851] 1.571998727 1.974421575 2.867806916 3.500581699 1.496389007
## [856] 3.746111168 3.252535041 1.712210102 -0.475701875 2.242874265
## [861] 2.728740178 2.587629812 2.067603717 1.373573376 4.201376675
## [866] 1.634810040 3.901495966 1.665936897 1.255082716 1.847920384
## [871] -0.306287219 1.172027561 4.810621959 3.382691099 -0.267752056
## [876] 1.778972480 3.126240458 2.791480725 1.605824779 1.999161268
## [881] -0.373133095 1.693128044 1.241083348 0.748010981 2.458369310
## [886] 1.509313864 2.610486519 -0.160309101 4.635207917 1.261257975
## [891] 0.737085582 1.278409276 2.946181544 1.236477049 3.603558670
## [896] 1.982788992 1.046667212 1.303327947 4.109625635 2.896597525
## [901] 1.940691663 2.280189252 5.049616263 3.249416610 3.827859802
## [906] -0.135737824 0.663539464 4.283124653 1.125835383 1.187152367
## [911] 3.475435119 1.573659405 2.483104109 2.811310179 0.877048844
## [916] 2.272074847 2.334740708 2.992237817 4.934811553 1.410859922
## [921] 1.710835967 2.243631480 1.045345975 1.673914910 1.741944267
## [926] 2.086006921 6.095332397 2.267680510 1.844552801 0.393511342
## [931] 0.783997939 2.953068938 1.096354662 -0.328579774 3.754884755
## [936] 0.304556494 2.969769043 0.381656103 1.802684771 0.925079049
## [941] 1.143979524 0.132240991 2.671793135 1.540474598 2.950464181
## [946] -0.485670617 1.862829016 3.527912071 2.196344892 4.681617724
## [951] 3.616212585 1.114764750 1.185391832 4.746618711 0.057409965
## [956] 1.681401614 1.946427884 2.968239617 0.025932140 1.521939438
## [961] 3.112345809 -0.708046457 2.827832453 2.246853657 0.111560002
## [966] 2.976385406 0.838636559 1.981525821 0.942881698 -0.432804328
## [971] 2.445127160 2.396197696 2.845356334 2.942815009 1.090744725
## [976] 1.077748455 -0.143021076 2.554651583 1.948276252 2.408683267
## [981] 2.132477138 2.197139972 2.238388042 2.022454326 -0.897027993
## [986] 3.988689632 2.303446713 3.572765283 2.775416042 2.624631453
## [991] 3.269945904 2.016668440 5.120508500 3.169847530 2.169761682
## [996] 2.304347181 -0.106548295 -1.261291047 4.031227405 1.586506762
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.110 1.097 2.069 2.059 3.066 7.814
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%
## -0.3751848
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%
## 4.63643
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%
## -0.3751848
# 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 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [157] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [265] FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE TRUE TRUE 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 TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] 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 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 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 TRUE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE TRUE 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] -0.3847475 -1.7397624 -1.1583810 -0.5602090 -0.9550416 -1.0494972
## [7] -1.6287219 -0.6406244 -0.5810550 -1.9858254 -2.5504262 -0.5141951
## [13] -0.8539502 -0.6804748 -2.4232828 -0.5076929 -1.0696310 -0.5135154
## [19] -0.7480636 -1.3579361 -1.4086455 -0.9770011 -0.8243610 -0.7783932
## [25] -1.4850968 -0.5743451 -0.4133103 -0.6504423 -1.4747709 -1.0213236
## [31] -0.8500184 -1.6315275 -3.1095165 -1.2677434 -1.2575088 -1.1158407
## [37] -0.6396276 -1.7158432 -0.4206539 -1.6572733 -1.6858316 -2.1165551
## [43] -0.7443992 -1.5162989 -0.4757019 -0.4856706 -0.7080465 -0.4328043
## [49] -0.8970280 -1.2612910
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.63643
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [73] FALSE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [85] TRUE 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 TRUE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [181] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE
## [229] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE TRUE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [361] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [553] FALSE FALSE FALSE 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 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 TRUE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE TRUE FALSE FALSE FALSE TRUE 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 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] 5.308058 4.659656 4.930654 4.893909 5.735468 4.970173 4.808926 4.687323
## [9] 5.168425 7.813984 4.916283 5.017517 4.694753 5.843437 4.732223 5.052340
## [17] 4.666716 5.122757 5.128576 5.883119 5.291315 4.946088 5.426372 5.008496
## [25] 5.310003 5.301545 5.369356 4.933401 4.804454 4.926849 5.818673 5.042926
## [33] 5.602951 5.055475 4.778686 5.287776 5.597406 5.165515 6.045382 5.394535
## [41] 4.822707 4.708706 4.914958 4.810622 5.049616 4.934812 6.095332 4.681618
## [49] 4.746619 5.120509