# Mindanao Stinate University
# General Santos City
# Basic Programming in R
# Prepared by: Prof. Carlito O. Daarol
# Faculty
# Math Department
# Submitted by: Czarina L. Genobiagon
# 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] 2.4992369 2.6263939 2.4452493 5.0732236 0.9842960 1.7288494
## [7] -0.4591114 2.6732738 3.4355202 1.6566538 0.7377926 3.2398813
## [13] 0.9250996 3.9234693 2.2230063 1.2610408 1.5714457 4.7346705
## [19] 1.5056527 1.5381212
data[1:300] # display the first 300 elements
## [1] 2.499236910 2.626393921 2.445249259 5.073223584 0.984295984
## [6] 1.728849360 -0.459111366 2.673273759 3.435520179 1.656653824
## [11] 0.737792645 3.239881286 0.925099584 3.923469299 2.223006342
## [16] 1.261040779 1.571445726 4.734670477 1.505652651 1.538121167
## [21] 2.559303551 2.392877064 3.287354899 1.273389479 0.228688644
## [26] 1.658201183 -1.104192106 1.771458159 1.879601090 0.762886018
## [31] 2.933471725 2.330208028 2.061442003 4.097833428 3.413702354
## [36] 1.213766147 1.219875055 5.055125606 4.215441252 3.063765868
## [41] 2.095384882 2.549016751 2.438057934 1.400512324 2.290715308
## [46] 4.045073048 1.058436103 1.373790479 2.569981587 2.201832012
## [51] -0.516992418 2.619781654 1.202870592 -0.475971818 -1.144161128
## [56] 1.087100551 5.225918068 2.448292064 6.151700922 2.223016786
## [61] 1.746049820 2.001820584 -0.300050806 1.996635010 2.827821590
## [66] 3.115129141 1.680983759 1.803438111 3.305061448 2.346209553
## [71] 4.112080289 1.253311425 3.156619745 1.249086963 2.581072768
## [76] -0.356644220 1.587408517 0.007459284 1.680268929 2.704352011
## [81] -1.159225457 1.977047690 1.403159626 4.307757994 -0.158365127
## [86] 0.276111993 -0.380490664 2.005763285 4.069631846 1.971166885
## [91] 4.097062014 1.781639100 2.863403200 0.207494017 3.900401284
## [96] 1.852334369 1.409621976 4.293479667 2.857601090 2.278156338
## [101] 2.985164458 3.372571456 2.355322614 0.086692249 1.874368417
## [106] 1.993587815 2.522544846 3.148410793 1.395592010 1.379894611
## [111] -0.076943268 3.807154051 0.967084577 1.814183860 3.972776587
## [116] 1.358292098 1.953277041 2.650033776 2.033663355 1.099357196
## [121] 2.009262546 2.549042106 3.084603522 3.573572488 3.201336658
## [126] 2.246657991 3.496147584 -0.029613227 1.004155857 2.935937107
## [131] 2.038547291 2.149243633 2.235199877 2.057381812 3.362959261
## [136] 3.274791078 2.508662351 2.820982877 -0.815108780 2.480811844
## [141] -0.538182769 -0.830305421 1.132853368 2.179668016 2.449158759
## [146] -0.005322721 -2.190315473 4.538548932 3.152042187 3.381200953
## [151] 2.962593504 4.388080198 -2.407851455 0.920347993 -0.264642422
## [156] 2.488381093 2.966170133 4.217025926 3.237259281 3.932411320
## [161] 3.586380855 -0.326082180 3.059998643 1.346651630 3.727368877
## [166] 2.789224804 0.637069988 2.511011691 1.221767357 3.818434772
## [171] -0.690287016 3.782970873 -0.928365542 1.075282258 0.957782007
## [176] 0.505457954 1.120980640 1.238084441 1.192364667 -0.454613305
## [181] 5.058692024 2.750563331 2.342785408 0.677026939 0.807315332
## [186] 0.115630025 0.839608060 4.487093207 0.814279286 1.252567590
## [191] 1.391606133 1.598439542 1.301023570 1.039520089 -0.519366381
## [196] 3.082055370 1.208103792 2.564309320 2.612231503 2.424859355
## [201] 1.284197331 0.278408669 5.396447755 -0.988854169 2.412222300
## [206] 3.623198202 4.114385432 1.153448412 4.370712729 4.086650533
## [211] 2.519799605 -0.018200220 3.777114440 1.919525671 4.533448948
## [216] 1.184949939 0.655496378 3.213914715 1.896702994 1.105592902
## [221] 2.384997989 1.605544794 4.428351361 3.624949447 1.076489142
## [226] 3.797287684 -0.032684322 1.133626247 1.534399307 4.037402940
## [231] 3.850671875 2.674600921 2.966792471 1.224471285 2.166681271
## [236] 1.735649716 0.609872672 3.509822861 4.069789434 2.270710679
## [241] 2.740502114 3.618513750 2.071868141 1.329874380 2.495226182
## [246] 0.354715235 2.279070155 1.162748195 3.461169335 2.259350599
## [251] 3.138964457 2.351246402 1.402151357 1.786752792 5.904376391
## [256] 1.552511466 1.706665427 2.214846255 3.623470243 1.289892345
## [261] 2.373471323 0.374674384 -0.489194614 2.511221182 2.146036662
## [266] 1.606074109 2.822620305 2.613781343 2.093517812 0.517120205
## [271] -1.594566795 0.143313429 3.464694078 1.106834058 1.330413166
## [276] 2.159897801 -1.869617392 3.471516945 2.027808177 2.815195395
## [281] 2.251484410 1.456015476 1.952716837 2.211991930 0.802156379
## [286] 1.158053863 1.522208483 0.739975316 5.552892802 1.966114847
## [291] -0.225639225 1.795209357 1.833140042 2.008098150 2.925935421
## [296] 1.642985705 3.046823022 3.094318311 1.754785455 4.194211592
# Exer2: Draw histogram with one main title and different thickness
maintitle <- "Histogram and Density Plot"
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
hist(data, breaks=300,col="gray",main = maintitle)
# Exer3: Draw histogram with one main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
# Question: What causes the subtitle to be in the second line?
# Exer4: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# # Add density curve. We define the range of the density curve
x = seq(from=min(data), to=max(data), length.out=100)
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/
20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
# Exer5: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# Add density curve and the location of the mean value
(x = seq(from=min(data), to=max(data), length.out=100))
## [1] -2.737186594 -2.642980068 -2.548773543 -2.454567017 -2.360360491
## [6] -2.266153966 -2.171947440 -2.077740915 -1.983534389 -1.889327864
## [11] -1.795121338 -1.700914813 -1.606708287 -1.512501761 -1.418295236
## [16] -1.324088710 -1.229882185 -1.135675659 -1.041469134 -0.947262608
## [21] -0.853056083 -0.758849557 -0.664643032 -0.570436506 -0.476229980
## [26] -0.382023455 -0.287816929 -0.193610404 -0.099403878 -0.005197353
## [31] 0.089009173 0.183215698 0.277422224 0.371628750 0.465835275
## [36] 0.560041801 0.654248326 0.748454852 0.842661377 0.936867903
## [41] 1.031074428 1.125280954 1.219487479 1.313694005 1.407900531
## [46] 1.502107056 1.596313582 1.690520107 1.784726633 1.878933158
## [51] 1.973139684 2.067346209 2.161552735 2.255759261 2.349965786
## [56] 2.444172312 2.538378837 2.632585363 2.726791888 2.820998414
## [61] 2.915204939 3.009411465 3.103617990 3.197824516 3.292031042
## [66] 3.386237567 3.480444093 3.574650618 3.668857144 3.763063669
## [71] 3.857270195 3.951476720 4.045683246 4.139889772 4.234096297
## [76] 4.328302823 4.422509348 4.516715874 4.610922399 4.705128925
## [81] 4.799335450 4.893541976 4.987748501 5.081955027 5.176161553
## [86] 5.270368078 5.364574604 5.458781129 5.552987655 5.647194180
## [91] 5.741400706 5.835607231 5.929813757 6.024020283 6.118226808
## [96] 6.212433334 6.306639859 6.400846385 6.495052910 6.589259436
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/
20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
abline(v = mean(data), col="black", lwd=3, lty=2)
# Add legend to top right position
legend("topright",
legend = c("Histogram", "density curve", "Average"),
col = c("lightblue", "violet", "black"),
lty = 1)
# Compute Quartile values Q1,Q2 and Q3
# These quantities divide the data into 4 equal parts
hist(data, breaks=20,col="lightblue",main = maintitle)
Quantiles = quantile(data)
Quantiles
## 0% 25% 50% 75% 100%
## -2.737187 1.079900 2.055904 3.123142 6.589259
# 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] 2.499236910 2.626393921 2.445249259 5.073223584 0.984295984
## [6] 1.728849360 -0.459111366 2.673273759 3.435520179 1.656653824
## [11] 0.737792645 3.239881286 0.925099584 3.923469299 2.223006342
## [16] 1.261040779 1.571445726 4.734670477 1.505652651 1.538121167
## [21] 2.559303551 2.392877064 3.287354899 1.273389479 0.228688644
## [26] 1.658201183 -1.104192106 1.771458159 1.879601090 0.762886018
## [31] 2.933471725 2.330208028 2.061442003 4.097833428 3.413702354
## [36] 1.213766147 1.219875055 5.055125606 4.215441252 3.063765868
## [41] 2.095384882 2.549016751 2.438057934 1.400512324 2.290715308
## [46] 4.045073048 1.058436103 1.373790479 2.569981587 2.201832012
## [51] -0.516992418 2.619781654 1.202870592 -0.475971818 -1.144161128
## [56] 1.087100551 5.225918068 2.448292064 6.151700922 2.223016786
## [61] 1.746049820 2.001820584 -0.300050806 1.996635010 2.827821590
## [66] 3.115129141 1.680983759 1.803438111 3.305061448 2.346209553
## [71] 4.112080289 1.253311425 3.156619745 1.249086963 2.581072768
## [76] -0.356644220 1.587408517 0.007459284 1.680268929 2.704352011
## [81] -1.159225457 1.977047690 1.403159626 4.307757994 -0.158365127
## [86] 0.276111993 -0.380490664 2.005763285 4.069631846 1.971166885
## [91] 4.097062014 1.781639100 2.863403200 0.207494017 3.900401284
## [96] 1.852334369 1.409621976 4.293479667 2.857601090 2.278156338
## [101] 2.985164458 3.372571456 2.355322614 0.086692249 1.874368417
## [106] 1.993587815 2.522544846 3.148410793 1.395592010 1.379894611
## [111] -0.076943268 3.807154051 0.967084577 1.814183860 3.972776587
## [116] 1.358292098 1.953277041 2.650033776 2.033663355 1.099357196
## [121] 2.009262546 2.549042106 3.084603522 3.573572488 3.201336658
## [126] 2.246657991 3.496147584 -0.029613227 1.004155857 2.935937107
## [131] 2.038547291 2.149243633 2.235199877 2.057381812 3.362959261
## [136] 3.274791078 2.508662351 2.820982877 -0.815108780 2.480811844
## [141] -0.538182769 -0.830305421 1.132853368 2.179668016 2.449158759
## [146] -0.005322721 -2.190315473 4.538548932 3.152042187 3.381200953
## [151] 2.962593504 4.388080198 -2.407851455 0.920347993 -0.264642422
## [156] 2.488381093 2.966170133 4.217025926 3.237259281 3.932411320
## [161] 3.586380855 -0.326082180 3.059998643 1.346651630 3.727368877
## [166] 2.789224804 0.637069988 2.511011691 1.221767357 3.818434772
## [171] -0.690287016 3.782970873 -0.928365542 1.075282258 0.957782007
## [176] 0.505457954 1.120980640 1.238084441 1.192364667 -0.454613305
## [181] 5.058692024 2.750563331 2.342785408 0.677026939 0.807315332
## [186] 0.115630025 0.839608060 4.487093207 0.814279286 1.252567590
## [191] 1.391606133 1.598439542 1.301023570 1.039520089 -0.519366381
## [196] 3.082055370 1.208103792 2.564309320 2.612231503 2.424859355
## [201] 1.284197331 0.278408669 5.396447755 -0.988854169 2.412222300
## [206] 3.623198202 4.114385432 1.153448412 4.370712729 4.086650533
## [211] 2.519799605 -0.018200220 3.777114440 1.919525671 4.533448948
## [216] 1.184949939 0.655496378 3.213914715 1.896702994 1.105592902
## [221] 2.384997989 1.605544794 4.428351361 3.624949447 1.076489142
## [226] 3.797287684 -0.032684322 1.133626247 1.534399307 4.037402940
## [231] 3.850671875 2.674600921 2.966792471 1.224471285 2.166681271
## [236] 1.735649716 0.609872672 3.509822861 4.069789434 2.270710679
## [241] 2.740502114 3.618513750 2.071868141 1.329874380 2.495226182
## [246] 0.354715235 2.279070155 1.162748195 3.461169335 2.259350599
## [251] 3.138964457 2.351246402 1.402151357 1.786752792 5.904376391
## [256] 1.552511466 1.706665427 2.214846255 3.623470243 1.289892345
## [261] 2.373471323 0.374674384 -0.489194614 2.511221182 2.146036662
## [266] 1.606074109 2.822620305 2.613781343 2.093517812 0.517120205
## [271] -1.594566795 0.143313429 3.464694078 1.106834058 1.330413166
## [276] 2.159897801 -1.869617392 3.471516945 2.027808177 2.815195395
## [281] 2.251484410 1.456015476 1.952716837 2.211991930 0.802156379
## [286] 1.158053863 1.522208483 0.739975316 5.552892802 1.966114847
## [291] -0.225639225 1.795209357 1.833140042 2.008098150 2.925935421
## [296] 1.642985705 3.046823022 3.094318311 1.754785455 4.194211592
## [301] 1.532659823 3.005292052 4.697094447 -0.628450045 5.106799565
## [306] 0.970235615 0.965250027 3.654909357 2.184646421 2.139159110
## [311] 2.349428293 2.949296285 2.857906112 1.830165368 4.648347604
## [316] 0.757039697 2.375699488 1.345269432 2.103169849 1.948426912
## [321] 3.312459299 2.193203334 0.502662878 1.104706973 2.780055050
## [326] 2.440507181 2.077012769 1.828909261 2.495555844 5.315159989
## [331] 5.243115424 2.896827334 -0.640883679 -0.660510575 2.046897615
## [336] 1.000484504 -0.197312447 3.188391906 1.097375431 -0.631916274
## [341] 1.580797667 1.648138137 3.399124313 2.032317133 3.214116433
## [346] 3.609435707 0.948793608 0.850601466 2.290336309 1.389706823
## [351] 0.290348833 3.189125783 -0.439321587 1.473674583 0.397639583
## [356] 4.747402543 2.242470590 1.172242726 3.535848452 3.828940985
## [361] 0.508596019 -0.094837135 3.664494800 3.819669491 0.323803216
## [366] 1.319215132 1.987543827 3.939257093 5.599033985 1.899798859
## [371] 2.662903653 3.363077785 -1.334613938 3.289719553 3.514781557
## [376] 2.900077770 -0.809464438 1.891559241 -0.074180713 -0.815137238
## [381] 3.815719988 0.472661203 1.499770206 0.317095729 2.066209694
## [386] 3.664011450 3.289230561 1.675533798 1.906366964 1.433449431
## [391] 1.373297428 -2.737186594 4.297647953 1.690792968 1.558496681
## [396] 1.254080983 1.063723046 5.095122075 2.441981351 3.528783968
## [401] 3.227477053 0.878366691 0.294609217 3.335428553 0.538837607
## [406] 0.531207230 1.176006258 1.624407399 3.352108272 -0.429982848
## [411] 2.692089763 4.351287716 1.425975505 3.033247288 1.623905742
## [416] 5.355512985 3.366973414 2.780903574 3.440823302 3.357772506
## [421] 2.982402417 3.589168544 2.155017216 3.520358488 2.061384653
## [426] 4.225251909 2.619849908 2.333349985 0.875614684 2.456190154
## [431] 3.521291248 2.628825242 1.458096535 2.913788188 2.057467690
## [436] 2.132993858 -0.527941134 2.931007326 3.196774640 3.818893978
## [441] 0.127883557 1.527341655 0.330040845 2.246771284 5.835631544
## [446] -0.866824019 2.134336398 2.793613058 -0.101820772 3.669375232
## [451] 2.763162383 0.782371915 1.212541029 1.405966296 -1.095454815
## [456] -0.916746150 4.314794532 0.591164280 1.188760992 1.084559155
## [461] 1.953537576 -0.393023571 1.298448643 2.149735536 -0.267293997
## [466] 0.830156961 3.453825534 1.099889452 2.866695286 5.584749967
## [471] 0.529543241 2.736266167 2.931740256 1.814093110 1.673411981
## [476] 1.347193536 1.802790436 2.747237516 2.418778541 -0.877612385
## [481] 1.985254595 5.019336141 2.653658313 4.884445885 2.332781672
## [486] 0.594390651 0.501686255 -0.231671186 -1.986277055 4.024613450
## [491] 1.573601350 0.651157369 2.047860588 0.142270753 -0.139873361
## [496] 2.823677112 1.138491885 0.289392216 0.775014716 5.698073116
## [501] 0.930461112 6.589259436 3.843960944 0.742017437 2.123173896
## [506] 4.018953339 2.954721901 3.106043333 1.562136374 1.217787388
## [511] 3.158085275 5.181076719 1.766608193 2.661716248 1.007707959
## [516] 0.498994387 1.512275769 1.181784437 3.526077180 3.790482631
## [521] 0.599416584 1.005679262 -0.360675503 1.204795190 2.161189310
## [526] 1.527269571 2.596454649 -0.003751898 2.665686010 3.694977115
## [531] -1.127741768 -0.561399179 3.124716950 1.646317501 1.439797817
## [536] 4.997275613 4.165253572 3.325053118 -0.657464357 1.776122761
## [541] 0.957351023 0.297446854 -0.073851962 3.327496502 3.400899691
## [546] 0.576574508 5.648287034 2.792164927 1.221679742 1.786215426
## [551] 0.001155235 1.402729913 1.425230360 1.689302995 0.190006639
## [556] 3.125430448 3.269761854 0.054724885 5.195829747 0.720543137
## [561] -0.440496260 0.704644602 2.427867194 0.944259656 2.717791028
## [566] 2.183330735 2.566548860 1.643803227 2.236562610 0.826942956
## [571] 0.380575503 3.130325367 0.494507475 3.895391354 3.233633274
## [576] 4.274910789 1.040078139 2.984171654 5.381407613 3.920636718
## [581] 4.971094869 -2.230414313 3.165741313 4.340298477 1.240959847
## [586] 1.045209727 2.429720811 1.141471558 0.825186441 1.166040658
## [591] 0.954861613 5.169790396 2.151442821 3.788255318 2.836437284
## [596] 4.010013263 3.111149366 0.545529976 2.091400443 3.935974761
## [601] 3.119433683 0.306883551 3.481353858 3.038387847 2.112096621
## [606] 3.896202513 1.776379089 0.315934602 4.120567654 4.490119868
## [611] -1.294396334 0.849109417 0.923649502 0.142266925 3.335264379
## [616] 0.851564459 3.186532218 6.439571580 1.534550408 2.896738751
## [621] 2.282886603 0.562740051 1.325507699 1.789796156 1.191597154
## [626] 2.329273257 3.935992480 0.557337058 1.358121967 1.832015152
## [631] 2.931389049 2.606872137 -1.854233081 5.434942576 2.145889629
## [636] 1.627308604 -0.470060682 5.197782433 2.378083462 3.896406580
## [641] 1.207240429 3.574100251 0.093131351 2.761264178 3.078455532
## [646] 5.284031698 2.228770876 -0.897082287 -0.243969818 1.936383443
## [651] 3.202569498 1.632067290 2.038398445 5.732535953 1.342616559
## [656] 4.368475869 0.989647070 0.474548814 3.503228517 4.073602960
## [661] 0.914260060 2.653981031 3.836096880 3.593807953 2.283158474
## [666] -1.342183480 2.379871300 4.519458087 4.487392676 1.317129339
## [671] 0.494971376 2.015093774 3.386450514 2.177097727 0.638449450
## [676] 2.733173245 3.973633340 0.476230519 4.526298166 1.872793804
## [681] 1.476511961 1.186604939 1.694703951 2.067465050 1.123507680
## [686] 2.415944446 2.810782118 2.451254923 3.015394423 2.631979647
## [691] 1.599082325 0.509620670 0.620786953 3.679150745 1.177209215
## [696] 3.952682232 2.703978798 2.449175951 3.676331558 2.424733325
## [701] 1.684434198 3.790241141 2.973609621 2.197102063 1.054208153
## [706] 5.051670967 4.147209799 0.467571338 2.335005808 1.727176902
## [711] 4.274012848 0.153691781 3.487915795 3.807009504 4.065186730
## [716] -0.490082352 0.854911430 2.952300066 0.660336624 0.590722486
## [721] 0.542281239 1.588240077 3.094415247 4.530558805 2.877234677
## [726] 2.775129296 1.332918421 1.295891151 0.658936664 3.557316136
## [731] 2.953758375 3.587616718 2.917102647 0.282205408 1.520552908
## [736] 1.705551576 0.188024740 4.272267868 3.789428796 3.034328380
## [741] -0.609195370 2.262581861 0.969172906 0.648976153 -0.552929325
## [746] 0.874250772 3.443214940 3.192124659 4.033086691 2.417005476
## [751] 0.543096288 2.554326959 0.093826430 2.494580081 0.967774303
## [756] 4.222977338 3.172260334 1.870452251 4.247560220 0.632813624
## [761] 1.599360191 1.881097616 1.836909212 2.699228742 -0.325762839
## [766] 1.712352835 3.508218454 2.632917192 3.043776261 0.417947109
## [771] 2.973434925 0.065752032 0.173735906 0.427489675 1.380565778
## [776] 1.473830897 3.788770865 3.237064738 3.303230628 1.614720778
## [781] 2.641875380 5.426132593 5.069770215 3.433260146 1.176965611
## [786] 3.859017372 2.200684071 4.110453986 2.820314458 2.583253726
## [791] 2.667473946 1.714665180 5.800689246 0.686485688 1.880892078
## [796] 1.597501136 3.107720092 2.665682277 1.335810129 4.139165799
## [801] 3.124675207 2.203388627 4.061585289 2.341368289 1.405200592
## [806] 4.306956764 4.282408373 0.374496524 0.774229793 3.984346483
## [811] 1.763009065 3.522406258 0.958052783 -1.209045534 4.862665248
## [816] 0.409274788 0.509516708 2.376490508 1.583758741 1.758850826
## [821] 4.304448468 1.961622742 4.887711687 2.011210847 2.757012842
## [826] 4.292831788 1.474779115 4.394515534 2.756235322 1.181848191
## [831] 1.473301947 1.244617192 2.644442143 3.939951631 1.793498700
## [836] 1.115690208 2.150458288 2.059088731 0.815699593 0.391310709
## [841] 1.286008721 2.740202972 2.660743861 1.572108218 2.287627739
## [846] 2.252387249 -0.800164266 -1.615807786 3.792868373 1.477973934
## [851] 4.088097850 2.417788999 2.578176079 2.629410559 2.554084089
## [856] 1.408371776 5.878675624 3.959970347 3.445269939 3.228712536
## [861] 2.054425944 0.445800521 2.746143799 1.020912249 4.004944305
## [866] 0.529033472 1.252510084 3.263944135 2.827252633 0.362208879
## [871] 3.122630637 1.601938365 1.950215443 2.479779546 0.087216360
## [876] 2.980726667 5.367004739 0.866273486 4.135194477 -0.813390961
## [881] -0.700427156 1.507786736 0.787224323 2.385135864 3.030655175
## [886] -0.213000765 -0.146655246 1.163939414 1.735227451 4.602976759
## [891] 2.126202069 5.872736504 0.768866018 3.231637885 1.468557093
## [896] 1.529973110 2.516334100 2.801502751 0.327953521 0.039051519
## [901] 2.868867172 0.985155796 3.774500059 1.215810262 1.698281800
## [906] 3.964349733 -0.054417207 3.348940226 1.926255097 2.162386015
## [911] 2.037422601 2.961928750 1.895281736 1.788834623 -1.074489335
## [916] 4.106662016 -0.581959456 1.693407885 0.702245429 0.471737019
## [921] 2.558177193 1.139074765 1.280951439 1.684073724 2.040634669
## [926] 2.800091833 0.853566593 2.634939334 3.063850859 2.790501378
## [931] 2.698340135 1.557100590 0.175329998 -0.640794421 1.323461413
## [936] -0.402467295 2.695649088 1.043967391 3.957832778 2.232027702
## [941] 3.150134763 -0.304199211 1.568494753 -0.478716549 -0.395009765
## [946] 1.270775266 5.159589427 3.214741346 4.556094618 0.020212975
## [951] 3.571609269 2.770602336 0.631087836 0.640376564 2.179366268
## [956] 1.966023569 2.083302498 3.811775350 2.238863108 0.213606467
## [961] 3.325063343 0.070474408 0.904915160 3.223563391 1.278037410
## [966] 0.276921244 3.059745904 5.211495015 1.112504239 1.819050575
## [971] 4.087344951 -0.105104001 1.853126556 1.770170410 3.260635029
## [976] 1.576985482 0.388993611 2.752402577 2.474787129 2.201684582
## [981] 1.311175467 2.355139539 2.568172776 1.729867826 1.149241254
## [986] 1.746465084 1.757472683 3.680398133 2.615331988 2.576975284
## [991] 0.698639688 1.143123546 0.500006806 0.940692600 1.081036300
## [996] 3.524581857 4.606586711 0.217375872 1.509369138 1.975269989
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.737 1.080 2.056 2.073 3.123 6.589
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%
## -0.4761091
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%
## 4.539426
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%
## -0.4761091
# 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 TRUE 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 TRUE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE FALSE FALSE
## [145] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [277] TRUE 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 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 FALSE TRUE TRUE FALSE FALSE
## [337] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## [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 TRUE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE 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 TRUE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE 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 TRUE 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 FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [937] FALSE FALSE 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] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
# count all true values using the sum command
sum(Low5Percent[TRUE]) # there are 50 of them
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -1.1041921 -0.5169924 -1.1441611 -1.1592255 -0.8151088 -0.5381828
## [7] -0.8303054 -2.1903155 -2.4078515 -0.6902870 -0.9283655 -0.5193664
## [13] -0.9888542 -0.4891946 -1.5945668 -1.8696174 -0.6284500 -0.6408837
## [19] -0.6605106 -0.6319163 -1.3346139 -0.8094644 -0.8151372 -2.7371866
## [25] -0.5279411 -0.8668240 -1.0954548 -0.9167461 -0.8776124 -1.9862771
## [31] -1.1277418 -0.5613992 -0.6574644 -2.2304143 -1.2943963 -1.8542331
## [37] -0.8970823 -1.3421835 -0.4900824 -0.6091954 -0.5529293 -1.2090455
## [43] -0.8001643 -1.6158078 -0.8133910 -0.7004272 -1.0744893 -0.5819595
## [49] -0.6407944 -0.4787165
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.539426
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] TRUE FALSE FALSE FALSE 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 TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE TRUE TRUE 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 TRUE FALSE FALSE 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 FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE
## [445] TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [637] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE TRUE FALSE TRUE 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 FALSE TRUE FALSE
## [949] TRUE 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 FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] TRUE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.073224 4.734670 5.055126 5.225918 6.151701 5.058692 5.396448 5.904376
## [9] 5.552893 4.697094 5.106800 4.648348 5.315160 5.243115 4.747403 5.599034
## [17] 5.095122 5.355513 5.835632 5.584750 5.019336 4.884446 5.698073 6.589259
## [25] 5.181077 4.997276 5.648287 5.195830 5.381408 4.971095 5.169790 6.439572
## [33] 5.434943 5.197782 5.284032 5.732536 5.051671 5.426133 5.069770 5.800689
## [41] 4.862665 4.887712 5.878676 5.367005 4.602977 5.872737 5.159589 4.556095
## [49] 5.211495 4.606587