# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Alwyn E. Felisilda, 1-BSMATH
# Mat108
# 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
## [1] 1000
data[1:20] # display first 20 elements
## [1] 0.6781120 2.5138930 3.9604991 1.6103351 4.3909095 0.2930962
## [7] 0.4642984 2.1723121 1.2946821 3.2213339 0.7091569 2.9656701
## [13] 0.5775825 1.7277426 -0.9565346 3.3649135 1.7063234 0.7798355
## [19] 0.9238820 1.1740129
data[1:300] # display the first 300 elements
## [1] 0.678112012 2.513892982 3.960499108 1.610335071 4.390909463
## [6] 0.293096244 0.464298373 2.172312060 1.294682105 3.221333935
## [11] 0.709156895 2.965670146 0.577582507 1.727742578 -0.956534567
## [16] 3.364913451 1.706323385 0.779835499 0.923881972 1.174012921
## [21] 1.212050118 0.293148121 0.843460784 3.599159830 2.902508179
## [26] -0.128992302 1.707960870 -0.431523112 1.253609682 1.217058947
## [31] 2.398917149 -0.747207144 1.778752236 2.176957575 -0.677309447
## [36] 2.558235146 2.735652496 2.693249430 1.444297301 4.092404208
## [41] -0.921759254 3.318024612 5.775454581 2.282798696 -0.183733656
## [46] 0.296229941 1.044486497 0.814371571 2.456859155 0.471381120
## [51] 0.490645220 -0.174984008 1.012785220 4.703106848 0.640425849
## [56] 0.183377234 3.187759752 3.692744890 2.709077888 0.602257934
## [61] 3.674851398 -1.250143446 0.222546135 0.745851600 1.227460030
## [66] 2.053737247 2.156114110 -0.934778127 1.705964759 3.660209030
## [71] 1.419931653 2.223792372 1.930426861 0.707512754 3.019685345
## [76] -0.183853504 2.729955343 1.573681014 1.439188807 0.687766552
## [81] 4.288092215 1.725378131 3.198149928 1.977345486 2.118981058
## [86] 1.239986875 0.599361740 -0.314066976 3.643784644 4.874097111
## [91] 0.581868155 0.528016258 -0.688929763 -0.683418972 0.663143013
## [96] 1.778558906 2.801814750 -0.473530767 2.571177663 2.292423817
## [101] -1.129026247 4.873076047 1.316825062 0.974327330 0.132635073
## [106] -0.135644855 3.345574556 1.213089168 2.460360203 4.007624787
## [111] 2.969091344 1.796573589 1.973765885 3.261384168 1.985033685
## [116] 1.067933356 3.630477619 3.537218823 1.385902390 2.396754586
## [121] 1.410863737 4.139070636 -0.994761847 2.159102594 2.756272115
## [126] 0.078539113 0.007287832 2.525159602 3.249116777 1.300845549
## [131] -0.189282446 1.709633710 2.709446118 4.119722215 1.597077424
## [136] 2.068992011 0.623805748 0.982377309 -0.538436035 1.903869461
## [141] 0.303430568 -2.214305895 0.429030984 2.888102495 5.913998062
## [146] 2.086209197 1.551743594 1.180913029 1.859621549 1.012724203
## [151] 3.326030920 3.915083121 3.588057478 1.682804079 1.318517753
## [156] 2.577142089 3.815010335 2.702072292 2.166086553 1.381318554
## [161] 2.167939848 3.724747310 -0.420213984 1.904430434 1.657606657
## [166] 3.891024168 0.608589055 1.701965496 1.734765836 1.142649101
## [171] -1.122111156 0.920545728 -0.721168615 0.793628689 -1.243063704
## [176] 1.763375854 4.632389969 2.285234429 2.130805349 0.590052369
## [181] 5.224712879 2.806827946 1.625613130 5.362811477 0.043497903
## [186] 2.659406656 1.650993493 1.638600777 0.230084418 -0.905621391
## [191] 1.991226775 1.160052556 3.159493610 3.801725755 0.796304232
## [196] 1.546337522 3.017258684 3.453886494 0.272861451 2.258112614
## [201] 2.050745143 1.605391670 4.516423221 4.141073343 -0.215419013
## [206] 3.772035368 1.065550209 -0.746229083 2.529759688 2.959824933
## [211] 2.586163933 1.623648989 3.182693342 3.861104148 0.024512881
## [216] 0.446574029 1.364733882 1.675997227 1.053577753 0.379518664
## [221] 0.776792878 2.796683646 1.959464959 2.584734364 0.490614857
## [226] 3.817339745 2.296605188 3.393059640 2.458983016 1.501344473
## [231] 4.274613681 0.039403500 0.889577812 4.151910347 2.280595875
## [236] 0.736496236 4.341509402 2.016303581 3.576373495 2.040942736
## [241] 1.291197804 1.403631040 3.915874695 1.833667393 0.466885878
## [246] -0.532164093 2.472029607 0.185838653 0.462593354 1.137419343
## [251] 2.404006450 2.185896117 0.718687213 1.027696951 3.592135736
## [256] 1.716434354 -1.228304309 2.473656121 0.947649333 2.730487310
## [261] -0.165587784 2.342885374 1.990693365 0.912772282 0.659959915
## [266] 2.612800760 2.259394860 4.862412944 1.888758744 4.187416227
## [271] 4.277371961 0.274118310 4.400960896 2.264518515 1.197034102
## [276] 3.030518022 5.257592425 2.491161357 3.132409630 2.033682147
## [281] 3.966961962 3.888976711 4.371625672 1.703782103 4.780883441
## [286] 3.531219378 0.973936386 0.794462152 1.680628180 -0.624479998
## [291] 2.915807993 2.341219405 1.678609286 1.445302696 3.093960267
## [296] 2.766251178 2.346480452 0.558687667 2.946159622 3.617761353
# 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 <- "Alwyn Graph"
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] -2.214305895 -2.122091418 -2.029876940 -1.937662463 -1.845447986
## [6] -1.753233509 -1.661019032 -1.568804554 -1.476590077 -1.384375600
## [11] -1.292161123 -1.199946646 -1.107732168 -1.015517691 -0.923303214
## [16] -0.831088737 -0.738874260 -0.646659782 -0.554445305 -0.462230828
## [21] -0.370016351 -0.277801874 -0.185587396 -0.093372919 -0.001158442
## [26] 0.091056035 0.183270512 0.275484990 0.367699467 0.459913944
## [31] 0.552128421 0.644342898 0.736557376 0.828771853 0.920986330
## [36] 1.013200807 1.105415284 1.197629762 1.289844239 1.382058716
## [41] 1.474273193 1.566487670 1.658702148 1.750916625 1.843131102
## [46] 1.935345579 2.027560056 2.119774534 2.211989011 2.304203488
## [51] 2.396417965 2.488632442 2.580846919 2.673061397 2.765275874
## [56] 2.857490351 2.949704828 3.041919305 3.134133783 3.226348260
## [61] 3.318562737 3.410777214 3.502991691 3.595206169 3.687420646
## [66] 3.779635123 3.871849600 3.964064077 4.056278555 4.148493032
## [71] 4.240707509 4.332921986 4.425136463 4.517350941 4.609565418
## [76] 4.701779895 4.793994372 4.886208849 4.978423327 5.070637804
## [81] 5.162852281 5.255066758 5.347281235 5.439495713 5.531710190
## [86] 5.623924667 5.716139144 5.808353621 5.900568099 5.992782576
## [91] 6.084997053 6.177211530 6.269426007 6.361640485 6.453854962
## [96] 6.546069439 6.638283916 6.730498393 6.822712871 6.914927348
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
7
## [1] 7
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%
## -2.214306 0.953355 1.986445 2.947643 6.914927
## 0% 25% 50% 75% 100%
## -2.883844 1.132859 2.123404 3.033119 7.493839
# 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] 0.678112012 2.513892982 3.960499108 1.610335071 4.390909463
## [6] 0.293096244 0.464298373 2.172312060 1.294682105 3.221333935
## [11] 0.709156895 2.965670146 0.577582507 1.727742578 -0.956534567
## [16] 3.364913451 1.706323385 0.779835499 0.923881972 1.174012921
## [21] 1.212050118 0.293148121 0.843460784 3.599159830 2.902508179
## [26] -0.128992302 1.707960870 -0.431523112 1.253609682 1.217058947
## [31] 2.398917149 -0.747207144 1.778752236 2.176957575 -0.677309447
## [36] 2.558235146 2.735652496 2.693249430 1.444297301 4.092404208
## [41] -0.921759254 3.318024612 5.775454581 2.282798696 -0.183733656
## [46] 0.296229941 1.044486497 0.814371571 2.456859155 0.471381120
## [51] 0.490645220 -0.174984008 1.012785220 4.703106848 0.640425849
## [56] 0.183377234 3.187759752 3.692744890 2.709077888 0.602257934
## [61] 3.674851398 -1.250143446 0.222546135 0.745851600 1.227460030
## [66] 2.053737247 2.156114110 -0.934778127 1.705964759 3.660209030
## [71] 1.419931653 2.223792372 1.930426861 0.707512754 3.019685345
## [76] -0.183853504 2.729955343 1.573681014 1.439188807 0.687766552
## [81] 4.288092215 1.725378131 3.198149928 1.977345486 2.118981058
## [86] 1.239986875 0.599361740 -0.314066976 3.643784644 4.874097111
## [91] 0.581868155 0.528016258 -0.688929763 -0.683418972 0.663143013
## [96] 1.778558906 2.801814750 -0.473530767 2.571177663 2.292423817
## [101] -1.129026247 4.873076047 1.316825062 0.974327330 0.132635073
## [106] -0.135644855 3.345574556 1.213089168 2.460360203 4.007624787
## [111] 2.969091344 1.796573589 1.973765885 3.261384168 1.985033685
## [116] 1.067933356 3.630477619 3.537218823 1.385902390 2.396754586
## [121] 1.410863737 4.139070636 -0.994761847 2.159102594 2.756272115
## [126] 0.078539113 0.007287832 2.525159602 3.249116777 1.300845549
## [131] -0.189282446 1.709633710 2.709446118 4.119722215 1.597077424
## [136] 2.068992011 0.623805748 0.982377309 -0.538436035 1.903869461
## [141] 0.303430568 -2.214305895 0.429030984 2.888102495 5.913998062
## [146] 2.086209197 1.551743594 1.180913029 1.859621549 1.012724203
## [151] 3.326030920 3.915083121 3.588057478 1.682804079 1.318517753
## [156] 2.577142089 3.815010335 2.702072292 2.166086553 1.381318554
## [161] 2.167939848 3.724747310 -0.420213984 1.904430434 1.657606657
## [166] 3.891024168 0.608589055 1.701965496 1.734765836 1.142649101
## [171] -1.122111156 0.920545728 -0.721168615 0.793628689 -1.243063704
## [176] 1.763375854 4.632389969 2.285234429 2.130805349 0.590052369
## [181] 5.224712879 2.806827946 1.625613130 5.362811477 0.043497903
## [186] 2.659406656 1.650993493 1.638600777 0.230084418 -0.905621391
## [191] 1.991226775 1.160052556 3.159493610 3.801725755 0.796304232
## [196] 1.546337522 3.017258684 3.453886494 0.272861451 2.258112614
## [201] 2.050745143 1.605391670 4.516423221 4.141073343 -0.215419013
## [206] 3.772035368 1.065550209 -0.746229083 2.529759688 2.959824933
## [211] 2.586163933 1.623648989 3.182693342 3.861104148 0.024512881
## [216] 0.446574029 1.364733882 1.675997227 1.053577753 0.379518664
## [221] 0.776792878 2.796683646 1.959464959 2.584734364 0.490614857
## [226] 3.817339745 2.296605188 3.393059640 2.458983016 1.501344473
## [231] 4.274613681 0.039403500 0.889577812 4.151910347 2.280595875
## [236] 0.736496236 4.341509402 2.016303581 3.576373495 2.040942736
## [241] 1.291197804 1.403631040 3.915874695 1.833667393 0.466885878
## [246] -0.532164093 2.472029607 0.185838653 0.462593354 1.137419343
## [251] 2.404006450 2.185896117 0.718687213 1.027696951 3.592135736
## [256] 1.716434354 -1.228304309 2.473656121 0.947649333 2.730487310
## [261] -0.165587784 2.342885374 1.990693365 0.912772282 0.659959915
## [266] 2.612800760 2.259394860 4.862412944 1.888758744 4.187416227
## [271] 4.277371961 0.274118310 4.400960896 2.264518515 1.197034102
## [276] 3.030518022 5.257592425 2.491161357 3.132409630 2.033682147
## [281] 3.966961962 3.888976711 4.371625672 1.703782103 4.780883441
## [286] 3.531219378 0.973936386 0.794462152 1.680628180 -0.624479998
## [291] 2.915807993 2.341219405 1.678609286 1.445302696 3.093960267
## [296] 2.766251178 2.346480452 0.558687667 2.946159622 3.617761353
## [301] 2.331636288 1.934581579 2.314265115 2.842066564 1.132814772
## [306] 2.243141532 3.093940335 0.190637130 0.510084368 1.413515843
## [311] 3.122769898 2.009242907 2.629062062 0.494219391 2.423120532
## [316] 3.030663250 2.392733209 4.234651354 1.487096767 1.700770139
## [321] 2.078532268 0.490907038 4.164228165 2.520885864 3.741646637
## [326] 3.312265068 2.109432358 1.548725562 0.680261956 2.968846966
## [331] 0.784371850 3.124568793 -0.589864578 1.297581903 1.532301803
## [336] 2.573571028 1.412689214 0.527691272 3.017300142 1.756637812
## [341] 3.900123600 1.930631642 1.183013755 2.763602942 1.823498493
## [346] 2.729253288 1.990939461 1.206983618 3.821089433 -1.641242339
## [351] 0.426314229 3.105343084 -0.889619043 2.368591238 2.649005277
## [356] 2.793546943 3.863495863 1.980647712 1.378486066 2.545616688
## [361] 2.079885450 -0.237893672 2.089921624 1.765249832 0.524912626
## [366] 3.468214481 2.635567467 3.170136111 1.801373628 3.945157150
## [371] -0.930804756 2.168340586 0.964992961 2.588314064 0.597054689
## [376] 3.871302184 2.006013711 0.172616721 2.134211999 1.649889204
## [381] 2.165271054 4.030679936 4.325775604 1.847760666 1.569564866
## [386] 1.146076003 2.393027911 2.477924493 4.244820627 2.279230482
## [391] 0.921849748 2.204284221 0.940176118 3.867479777 0.001404214
## [396] -1.489681408 1.514534495 3.117941394 2.012746490 -0.568640510
## [401] 0.580703637 1.923315047 -0.005520192 0.304981817 0.302586390
## [406] 2.637314789 1.180684704 4.491284675 0.874550074 1.330511506
## [411] 2.772997114 2.549098825 0.220766810 -0.110277234 0.135817466
## [416] 1.149771266 -0.589623927 1.253569000 3.484255306 0.196090391
## [421] 1.229497863 -1.752507215 2.228252135 -1.503381797 0.405156431
## [426] -0.171509583 2.572333662 1.867286033 1.222944282 1.459720456
## [431] 0.793312872 -0.742963884 3.110007505 0.793244816 0.713393201
## [436] 0.642221773 4.205628115 3.864646454 0.566638053 -0.638633402
## [441] -0.443724600 2.323324570 -0.232419578 4.538931831 1.780302726
## [446] 1.191983765 0.991779872 2.654558475 2.200604561 2.470670990
## [451] 2.612511136 1.720333353 0.791463016 1.237724762 0.190326692
## [456] 0.209829514 1.511757642 4.045572920 4.473046452 1.383854549
## [461] 1.458451013 -0.348579177 0.229619436 1.751711593 0.916898004
## [466] 3.661648493 0.727298370 4.495929918 4.720734439 3.022901869
## [471] 4.888150990 3.138498221 0.175807360 2.641643927 4.115829202
## [476] 3.263672583 2.058798547 3.674646296 3.851432954 -0.258123316
## [481] 0.881712897 3.140566341 2.378096513 1.651664567 2.072181690
## [486] 0.904041652 2.881726760 2.080073269 1.074860877 3.525817126
## [491] 4.226313096 0.891029713 -0.591481420 1.138914239 2.613512837
## [496] 2.336606772 2.006756237 3.621605225 4.188193786 4.768563189
## [501] 4.205694394 2.753536158 0.785021229 0.700945490 0.861054617
## [506] 2.899259517 4.178083969 0.378771630 -0.004462942 2.174971011
## [511] 2.126002958 0.817331282 3.345133760 2.553665854 4.807445205
## [516] 2.746810927 2.548290492 2.207537901 2.987867111 1.141591201
## [521] 2.812335634 4.477782028 1.128531216 2.924650900 2.370244158
## [526] 0.955256848 2.351045824 1.091123066 1.019740983 0.747249615
## [531] 3.382611708 2.913158025 1.001300518 2.492736152 -1.090856175
## [536] 1.038426262 1.600093480 3.453493058 3.613169152 0.898732241
## [541] 2.566641938 2.629286404 0.372136175 1.656405365 2.386775213
## [546] 1.698688188 3.776169622 1.412986145 3.846662442 2.518012595
## [551] 5.509954769 1.596533046 1.561223531 -0.869800361 3.065730366
## [556] 1.139928554 3.243532572 2.225286861 1.090504814 0.288994205
## [561] 1.552277456 3.375639358 1.788122649 0.310361233 1.041906933
## [566] 2.658463670 -1.303343607 2.044205376 2.315663504 1.444944734
## [571] 0.803488387 4.827542456 2.243897490 2.376547051 -1.081093439
## [576] 2.268777107 -0.220547382 3.109299168 -0.337575891 1.692034327
## [581] 2.589181351 1.987856879 3.769074429 2.694435220 3.375231177
## [586] -0.388812023 1.594549164 5.361822328 3.041602419 0.351706097
## [591] -0.308771780 -0.653109349 0.798571793 1.857656301 0.937929124
## [596] 1.344388939 2.308968423 1.295739277 2.311890309 -0.443451978
## [601] 1.587444189 4.003490555 2.420362489 4.593865477 3.418258796
## [606] 1.640814466 4.989796820 0.603775784 3.568405485 0.932442886
## [611] 0.584997401 0.819134078 1.309494410 0.427119512 0.455019591
## [616] 5.795096941 1.779739763 -0.262716429 1.616298126 1.232595787
## [621] 2.519215993 0.966893312 2.989810789 1.125507494 1.094713525
## [626] 0.798133664 2.713300258 2.800210296 0.517529142 3.166350568
## [631] 1.089327687 3.302205142 3.024274534 2.797322051 3.160030842
## [636] 1.617363676 2.496605654 1.125084557 2.688127857 4.608673285
## [641] 3.256258142 1.930142577 5.530771574 0.453795728 4.607057993
## [646] 0.351576166 1.207339049 1.581901527 3.559596371 3.343891981
## [651] 5.066809186 3.731501378 1.186731681 2.179567172 -1.450389459
## [656] -0.839513442 2.220767091 3.104264375 2.815714910 3.664690583
## [661] 2.925837455 3.077832033 2.200671592 2.340671321 3.031224935
## [666] 1.823837700 1.252618935 1.979185829 3.064213843 2.888452970
## [671] -0.042311070 2.054821112 5.058112300 0.900123499 2.379461762
## [676] 4.415133661 1.390829313 1.649914210 2.167348362 2.647790882
## [681] 0.924786482 1.968632967 1.832992306 0.520220378 1.066928935
## [686] 2.604951516 3.171264604 0.486304885 2.898115775 1.477289937
## [691] 2.143796303 2.248853478 4.846976490 1.833784370 2.201613961
## [696] 3.279313587 1.760064140 1.429418605 0.035000295 -0.321071068
## [701] 0.959470551 -1.171813586 5.149246634 1.526920342 0.985093007
## [706] 3.451097603 3.167493828 2.728335154 2.401262483 3.215177912
## [711] 3.281341269 1.382848106 1.391302878 1.626263370 1.763322645
## [716] 5.366444273 0.276069864 1.905307462 4.840065699 3.733801709
## [721] 4.438203775 3.185899540 1.878276826 2.637632044 0.176425865
## [726] 2.841049136 2.044755781 0.877724905 2.591220291 2.640110088
## [731] 2.910537064 0.855646401 2.522232249 2.969488464 2.087639574
## [736] 2.226568271 0.399482863 2.239270833 3.187259925 2.523356283
## [741] 5.451679946 2.922271742 2.526499953 -0.602010200 5.051859546
## [746] 2.813145488 3.286458570 3.096925084 4.232031411 -1.431535341
## [751] 1.612631479 2.226280871 2.406609858 2.312823402 3.380811987
## [756] 2.788087938 1.776713767 -0.166583551 3.050179212 2.179958828
## [761] -1.686752459 1.788674305 2.495131033 1.834726667 3.236889368
## [766] 3.219386051 1.403455805 0.865602625 2.742065955 2.657597681
## [771] 1.774616363 1.360933266 4.993363907 2.598899539 2.466343926
## [776] 1.195005704 0.863993202 1.550097069 1.210122339 3.074478533
## [781] -0.261988032 2.739478703 3.973940765 0.431756670 1.284861284
## [786] 2.150268996 2.776496323 -0.314294629 1.233878321 2.222717551
## [791] 1.301022092 2.949528214 0.796709904 0.806088336 3.399621356
## [796] 1.026929158 2.956321181 2.031297246 0.713305651 2.347865924
## [801] -0.331473335 0.735342817 0.035310693 3.750526890 1.747708544
## [806] 1.631256794 6.914927348 3.598109686 2.299557421 -0.496642627
## [811] 2.343447865 1.365548460 -2.106430383 0.126337201 0.040461171
## [816] 4.473814988 4.782141146 0.812040435 1.966031233 3.838423362
## [821] 2.284023396 1.708435559 -0.212632968 4.451610322 0.866143574
## [826] 2.758496942 4.731972988 1.524670198 5.430937629 1.019419444
## [831] 1.243030815 1.350460195 1.380219528 0.353803281 -1.446095453
## [836] 1.941772431 1.122631205 3.150500791 0.443344396 1.871297897
## [841] 1.978503192 4.049006589 3.605989484 2.793715627 5.681092223
## [846] 4.510185804 2.429949985 4.244155882 2.280570289 1.358353560
## [851] 4.881207885 1.814945731 3.366893812 0.225602349 3.140000826
## [856] 1.317941789 1.479892142 1.463976034 1.651714398 2.272989580
## [861] 2.946845167 0.791216048 2.492654546 3.320758236 2.396611207
## [866] -0.085140835 1.202333447 0.846850515 3.609449938 0.245453702
## [871] 1.850980288 3.965191909 2.465775635 4.203688144 3.561415436
## [876] 3.564735110 0.595400465 3.854848397 1.601406320 3.605949532
## [881] 4.593568608 0.502974489 -1.779577133 2.977156335 3.337122013
## [886] 1.630899684 2.102328029 2.571945702 3.575070810 2.478694700
## [891] 1.614230650 0.228259652 1.949447336 1.486693431 2.358827614
## [896] 2.884023455 2.067428358 1.086513838 1.398820267 0.843654800
## [901] 3.103522324 2.122580508 2.685890727 1.069691771 2.260541949
## [906] 2.072993392 3.369336692 5.643493332 5.698388337 1.912541756
## [911] 0.845295365 1.761777211 1.509597880 1.277120592 0.565607732
## [916] 0.627463348 3.420679859 -0.373666153 2.685763968 0.387807883
## [921] 2.198797363 3.021282980 1.478790757 1.186410967 1.646888627
## [926] 2.689001484 0.375593209 3.137941950 -0.337787271 0.022858611
## [931] 2.946110945 0.205452380 1.901610549 1.210761213 3.733490465
## [936] 3.884131720 2.750222811 -0.595883797 1.880742709 2.754384783
## [941] 2.845859244 2.885235357 3.990890015 -1.030105172 2.679693831
## [946] 5.919426754 2.186756351 1.608103681 1.466853161 1.113741685
## [951] 4.738159101 1.877525200 1.396816702 3.265137953 2.309838988
## [956] 2.627907613 2.154514547 2.316690314 2.947013997 0.551635911
## [961] 2.526882313 4.368995082 2.606056788 1.808904038 2.233930842
## [966] 2.160513953 3.924549048 2.656557475 3.330593839 1.107914558
## [971] 4.352847347 1.157047106 -0.593327050 4.919644119 1.662115382
## [976] 2.307233912 2.868940868 4.289463983 1.422488003 4.386860576
## [981] 0.236458050 3.878313527 0.468106020 1.512801967 2.209468588
## [986] -0.526037502 2.158515102 0.817233758 2.004559813 4.688678737
## [991] 3.994174947 1.136051951 0.016738077 1.482096967 2.016242849
## [996] 1.093357960 0.746532273 2.465985147 3.534393461 3.028251130
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.2143 0.9534 1.9864 1.9793 2.9476 6.9149
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.884 1.133 2.123 2.066 3.033 7.494
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%
## -0.4981124
## 5%
## -0.3792859
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%
## 4.491517
## 95%
## 4.454798
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%
## -0.4981124
## 5%
## -0.3792859
# 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [37] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE TRUE FALSE FALSE 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 TRUE FALSE FALSE TRUE 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 TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE TRUE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [397] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [421] FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [745] FALSE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE TRUE 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
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -0.9565346 -0.7472071 -0.6773094 -0.9217593 -1.2501434 -0.9347781
## [7] -0.6889298 -0.6834190 -1.1290262 -0.9947618 -0.5384360 -2.2143059
## [13] -1.1221112 -0.7211686 -1.2430637 -0.9056214 -0.7462291 -0.5321641
## [19] -1.2283043 -0.6244800 -0.5898646 -1.6412423 -0.8896190 -0.9308048
## [25] -1.4896814 -0.5686405 -0.5896239 -1.7525072 -1.5033818 -0.7429639
## [31] -0.6386334 -0.5914814 -1.0908562 -0.8698004 -1.3033436 -1.0810934
## [37] -0.6531093 -1.4503895 -0.8395134 -1.1718136 -0.6020102 -1.4315353
## [43] -1.6867525 -2.1064304 -1.4460955 -1.7795771 -0.5958838 -1.0301052
## [49] -0.5933271 -0.5260375
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.491517
## 95%
## 4.454798
(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 TRUE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] TRUE 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 TRUE FALSE FALSE FALSE
## [181] TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE 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 TRUE
## [469] TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [649] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [745] TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [829] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.775455 4.703107 4.874097 4.873076 5.913998 4.632390 5.224713 5.362811
## [9] 4.516423 4.862413 5.257592 4.780883 4.538932 4.495930 4.720734 4.888151
## [17] 4.768563 4.807445 5.509955 4.827542 5.361822 4.593865 4.989797 5.795097
## [25] 4.608673 5.530772 4.607058 5.066809 5.058112 4.846976 5.149247 5.366444
## [33] 4.840066 5.451680 5.051860 4.993364 6.914927 4.782141 4.731973 5.430938
## [41] 5.681092 4.510186 4.881208 4.593569 5.643493 5.698388 5.919427 4.738159
## [49] 4.919644 4.688679