# Mindanao Stinate University
# General Santos City
# Basic Programming in R
# Prepared by: Prof. Carlito O. Daarol
# Faculty
# Math Department
# Submitted by: Donnah Marielle C. Diocales
# 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] 1.74176528 1.12996428 3.76168888 4.41931251 0.87403932 1.69892588
## [7] 2.68988326 0.73554678 3.40952631 0.45486769 1.99718099 1.60968897
## [13] 1.53277782 1.02279667 0.08891834 4.30819969 0.50985256 4.84467355
## [19] 0.78715018 -0.57558302
## [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] 1.741765280 1.129964280 3.761688884 4.419312508 0.874039317
## [6] 1.698925881 2.689883260 0.735546779 3.409526306 0.454867693
## [11] 1.997180985 1.609688974 1.532777817 1.022796671 0.088918336
## [16] 4.308199692 0.509852561 4.844673546 0.787150184 -0.575583019
## [21] 2.801301023 6.905336822 1.382638993 1.532735378 0.513251171
## [26] 1.794026251 0.893255941 0.262612246 5.097496956 -0.360820942
## [31] -1.785949411 2.325859039 5.042730702 1.560550049 1.293754050
## [36] 2.703056083 6.428543919 4.230822644 0.070079963 1.729149627
## [41] 3.014568416 2.593608544 2.314950880 4.350016454 2.516668412
## [46] 2.797230099 1.682739383 2.968209203 1.864355382 2.723638561
## [51] 1.581243693 1.124744801 2.044300086 0.916194520 1.658705583
## [56] 3.758544044 1.964007709 3.046007302 2.945754534 2.684947831
## [61] 1.719497193 0.084412108 2.269120147 3.375253059 3.566323532
## [66] 2.382197165 -1.278539926 1.376769939 1.448000069 3.077682304
## [71] 1.099368943 0.358018439 2.278547370 1.351684361 1.725504259
## [76] 1.997767354 1.693554621 0.907175138 3.108522142 3.247247759
## [81] 1.165256342 2.133005982 1.332191872 3.094012755 0.126615023
## [86] 2.564047211 -1.430986514 -0.500707047 4.260490564 4.102505694
## [91] 2.245528305 1.614886164 1.490007894 1.991104069 1.739901040
## [96] 0.304742780 -1.247474449 2.856178522 1.133969628 4.350527280
## [101] 1.546792229 2.338727496 2.826879333 1.338678562 -0.168311033
## [106] 1.425625572 3.225140483 1.845827607 0.726735250 -0.798729875
## [111] 1.390036707 1.375853850 2.727339334 0.361308826 4.215315503
## [116] 0.986838786 1.181422285 2.523034064 0.426376492 0.455997114
## [121] -1.167664474 1.170399985 2.085012601 2.032699559 1.506567647
## [126] 1.473494026 2.380040920 4.819959747 7.248467331 2.373655312
## [131] 0.652569751 3.906177433 2.902435865 2.092167321 2.168841938
## [136] 3.680263560 6.131515323 4.625974123 3.050125530 1.934021283
## [141] 4.291930263 -0.008266397 2.731911751 3.256966315 1.721086985
## [146] 2.046234746 0.505443647 1.059395012 2.127353004 5.228018081
## [151] 0.060135732 3.079355884 1.636365898 1.546639166 1.642151126
## [156] 1.786811686 3.807634901 2.918972649 2.530191297 -1.582241924
## [161] 2.118335364 2.608034520 4.082423734 3.960505471 2.046386833
## [166] -0.234618210 2.395507020 1.970059888 2.075966694 5.243118106
## [171] 4.125171261 5.923744996 2.180512898 2.243158139 1.004612290
## [176] 2.426625937 1.593312351 1.175637868 -1.082138119 0.058810224
## [181] 0.923851340 1.181304359 3.033269472 1.784183758 2.535742419
## [186] 1.353865506 2.728113378 3.681108964 3.824008029 0.967204783
## [191] 0.702302859 4.529331460 1.722363964 0.578777804 3.502426969
## [196] 3.630670848 3.727097748 0.914203164 1.856876906 3.002469665
## [201] 2.211350377 -0.576398808 1.694175203 3.746304567 2.209425086
## [206] 4.502368436 -0.271486043 1.922833042 1.349027611 1.723812271
## [211] 2.593288494 1.870839159 2.010183261 1.158873065 1.325584479
## [216] 2.670454043 1.654071803 2.789200485 4.123723495 0.331964771
## [221] 2.186362977 2.384665121 3.627164572 4.028229499 1.996663423
## [226] 1.711846401 0.526269625 3.461677889 1.373003499 3.587262866
## [231] 3.195079242 0.908217404 3.162996362 1.579547354 3.438019632
## [236] 2.124113601 0.201402211 2.637011479 -0.772121517 2.563918857
## [241] -0.212169067 5.556870664 0.935694775 1.879652184 1.981885308
## [246] 0.503733809 1.606420814 1.088571544 4.032806316 -0.162999692
## [251] 0.850636428 3.330494129 0.176591499 3.355435928 2.343399237
## [256] 2.602483477 0.442530004 3.264868984 3.911305556 3.167170990
## [261] 3.381672726 2.489017506 2.293504917 0.863190480 -0.297178759
## [266] 2.945581774 3.770342016 -0.226068989 3.641369682 0.509611127
## [271] 3.606887190 0.805098409 4.022232290 2.997542352 4.335202956
## [276] 3.663008555 2.720263801 2.988403599 0.423526728 3.101584713
## [281] 2.583280321 3.016459174 5.125735301 3.880295411 3.836934278
## [286] 3.378269560 0.699924373 3.617790619 2.129616599 3.780660949
## [291] 1.220978874 2.756902482 2.141821087 3.937635645 2.268369544
## [296] 1.218355315 5.763517983 5.913518030 3.820264685 2.716407347
## [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] -3.142669916 -3.037708934 -2.932747951 -2.827786969 -2.722825987
## [6] -2.617865005 -2.512904022 -2.407943040 -2.302982058 -2.198021075
## [11] -2.093060093 -1.988099111 -1.883138129 -1.778177146 -1.673216164
## [16] -1.568255182 -1.463294199 -1.358333217 -1.253372235 -1.148411252
## [21] -1.043450270 -0.938489288 -0.833528306 -0.728567323 -0.623606341
## [26] -0.518645359 -0.413684376 -0.308723394 -0.203762412 -0.098801429
## [31] 0.006159553 0.111120535 0.216081517 0.321042500 0.426003482
## [36] 0.530964464 0.635925447 0.740886429 0.845847411 0.950808394
## [41] 1.055769376 1.160730358 1.265691340 1.370652323 1.475613305
## [46] 1.580574287 1.685535270 1.790496252 1.895457234 2.000418216
## [51] 2.105379199 2.210340181 2.315301163 2.420262146 2.525223128
## [56] 2.630184110 2.735145093 2.840106075 2.945067057 3.050028039
## [61] 3.154989022 3.259950004 3.364910986 3.469871969 3.574832951
## [66] 3.679793933 3.784754916 3.889715898 3.994676880 4.099637862
## [71] 4.204598845 4.309559827 4.414520809 4.519481792 4.624442774
## [76] 4.729403756 4.834364738 4.939325721 5.044286703 5.149247685
## [81] 5.254208668 5.359169650 5.464130632 5.569091615 5.674052597
## [86] 5.779013579 5.883974561 5.988935544 6.093896526 6.198857508
## [91] 6.303818491 6.408779473 6.513740455 6.618701438 6.723662420
## [96] 6.828623402 6.933584384 7.038545367 7.143506349 7.248467331
## [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%
## -3.142670 1.087593 2.008261 3.029697 7.248467
## 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] 1.741765280 1.129964280 3.761688884 4.419312508 0.874039317
## [6] 1.698925881 2.689883260 0.735546779 3.409526306 0.454867693
## [11] 1.997180985 1.609688974 1.532777817 1.022796671 0.088918336
## [16] 4.308199692 0.509852561 4.844673546 0.787150184 -0.575583019
## [21] 2.801301023 6.905336822 1.382638993 1.532735378 0.513251171
## [26] 1.794026251 0.893255941 0.262612246 5.097496956 -0.360820942
## [31] -1.785949411 2.325859039 5.042730702 1.560550049 1.293754050
## [36] 2.703056083 6.428543919 4.230822644 0.070079963 1.729149627
## [41] 3.014568416 2.593608544 2.314950880 4.350016454 2.516668412
## [46] 2.797230099 1.682739383 2.968209203 1.864355382 2.723638561
## [51] 1.581243693 1.124744801 2.044300086 0.916194520 1.658705583
## [56] 3.758544044 1.964007709 3.046007302 2.945754534 2.684947831
## [61] 1.719497193 0.084412108 2.269120147 3.375253059 3.566323532
## [66] 2.382197165 -1.278539926 1.376769939 1.448000069 3.077682304
## [71] 1.099368943 0.358018439 2.278547370 1.351684361 1.725504259
## [76] 1.997767354 1.693554621 0.907175138 3.108522142 3.247247759
## [81] 1.165256342 2.133005982 1.332191872 3.094012755 0.126615023
## [86] 2.564047211 -1.430986514 -0.500707047 4.260490564 4.102505694
## [91] 2.245528305 1.614886164 1.490007894 1.991104069 1.739901040
## [96] 0.304742780 -1.247474449 2.856178522 1.133969628 4.350527280
## [101] 1.546792229 2.338727496 2.826879333 1.338678562 -0.168311033
## [106] 1.425625572 3.225140483 1.845827607 0.726735250 -0.798729875
## [111] 1.390036707 1.375853850 2.727339334 0.361308826 4.215315503
## [116] 0.986838786 1.181422285 2.523034064 0.426376492 0.455997114
## [121] -1.167664474 1.170399985 2.085012601 2.032699559 1.506567647
## [126] 1.473494026 2.380040920 4.819959747 7.248467331 2.373655312
## [131] 0.652569751 3.906177433 2.902435865 2.092167321 2.168841938
## [136] 3.680263560 6.131515323 4.625974123 3.050125530 1.934021283
## [141] 4.291930263 -0.008266397 2.731911751 3.256966315 1.721086985
## [146] 2.046234746 0.505443647 1.059395012 2.127353004 5.228018081
## [151] 0.060135732 3.079355884 1.636365898 1.546639166 1.642151126
## [156] 1.786811686 3.807634901 2.918972649 2.530191297 -1.582241924
## [161] 2.118335364 2.608034520 4.082423734 3.960505471 2.046386833
## [166] -0.234618210 2.395507020 1.970059888 2.075966694 5.243118106
## [171] 4.125171261 5.923744996 2.180512898 2.243158139 1.004612290
## [176] 2.426625937 1.593312351 1.175637868 -1.082138119 0.058810224
## [181] 0.923851340 1.181304359 3.033269472 1.784183758 2.535742419
## [186] 1.353865506 2.728113378 3.681108964 3.824008029 0.967204783
## [191] 0.702302859 4.529331460 1.722363964 0.578777804 3.502426969
## [196] 3.630670848 3.727097748 0.914203164 1.856876906 3.002469665
## [201] 2.211350377 -0.576398808 1.694175203 3.746304567 2.209425086
## [206] 4.502368436 -0.271486043 1.922833042 1.349027611 1.723812271
## [211] 2.593288494 1.870839159 2.010183261 1.158873065 1.325584479
## [216] 2.670454043 1.654071803 2.789200485 4.123723495 0.331964771
## [221] 2.186362977 2.384665121 3.627164572 4.028229499 1.996663423
## [226] 1.711846401 0.526269625 3.461677889 1.373003499 3.587262866
## [231] 3.195079242 0.908217404 3.162996362 1.579547354 3.438019632
## [236] 2.124113601 0.201402211 2.637011479 -0.772121517 2.563918857
## [241] -0.212169067 5.556870664 0.935694775 1.879652184 1.981885308
## [246] 0.503733809 1.606420814 1.088571544 4.032806316 -0.162999692
## [251] 0.850636428 3.330494129 0.176591499 3.355435928 2.343399237
## [256] 2.602483477 0.442530004 3.264868984 3.911305556 3.167170990
## [261] 3.381672726 2.489017506 2.293504917 0.863190480 -0.297178759
## [266] 2.945581774 3.770342016 -0.226068989 3.641369682 0.509611127
## [271] 3.606887190 0.805098409 4.022232290 2.997542352 4.335202956
## [276] 3.663008555 2.720263801 2.988403599 0.423526728 3.101584713
## [281] 2.583280321 3.016459174 5.125735301 3.880295411 3.836934278
## [286] 3.378269560 0.699924373 3.617790619 2.129616599 3.780660949
## [291] 1.220978874 2.756902482 2.141821087 3.937635645 2.268369544
## [296] 1.218355315 5.763517983 5.913518030 3.820264685 2.716407347
## [301] 4.913187047 -1.178971460 2.307967024 4.749927718 1.397646749
## [306] 5.510096392 -0.374943484 3.470776098 2.114875973 2.058345322
## [311] 1.588723290 5.661680343 0.825984599 -0.381414595 3.769511173
## [316] 4.417992123 0.897269349 4.751270029 1.146974773 1.683883260
## [321] 2.111668668 1.724190109 1.371746221 2.681069387 2.325353036
## [326] 2.962323115 0.164204326 0.003842234 2.020522987 1.148455715
## [331] 1.996007420 4.224885233 1.856664480 1.128999742 -0.994339418
## [336] 1.490919770 1.482919422 3.472749946 2.442010686 2.159283426
## [341] 4.690744866 -0.021763459 4.338363630 2.928354555 2.406029670
## [346] 1.908153311 -1.127518098 0.313340039 -0.630241357 3.588245793
## [351] 1.650858919 0.020144844 2.632411528 1.756633000 2.135356776
## [356] 0.405247883 0.589811349 1.361505376 3.389413108 -0.130758513
## [361] 2.222184997 3.173870424 0.804774226 1.087770521 3.669004693
## [366] 3.017792030 1.619776458 1.243515192 -0.059513032 2.319565090
## [371] -0.525522892 2.213766501 -2.181255530 0.710433122 0.758302188
## [376] 2.067866543 2.943009891 4.226364655 1.649795704 2.335550821
## [381] 2.947879377 2.474728381 2.434086542 1.154263670 2.132715484
## [386] 4.972955975 1.955160816 1.184967531 1.479141856 3.367002541
## [391] 2.691622977 4.270767349 4.205092923 3.770080321 2.272059997
## [396] 1.436342744 3.776447252 2.886747647 1.544252632 2.490356982
## [401] 1.950074052 -0.005848462 3.238992065 0.715692356 0.339441502
## [406] 3.180745205 2.955591957 2.278481525 2.636693687 2.597644935
## [411] 2.202573597 1.662787166 0.971559896 1.900717924 0.456424570
## [416] 4.193044492 2.740098285 0.673101841 4.069558174 0.381286900
## [421] 1.580153939 1.587323488 3.997069068 3.502705926 2.195252663
## [426] 4.513843593 2.498329219 2.934206015 1.473174912 1.874600234
## [431] 2.898413003 2.227834208 4.282185282 3.622630274 2.838002278
## [436] 0.807627130 -0.128200202 2.021021317 2.196624432 4.503463582
## [441] 3.362942351 2.026116278 -1.322723911 2.052108677 5.291621584
## [446] 3.646810285 -0.233232641 3.336405864 2.078818223 0.489846568
## [451] 3.332230736 3.988614891 1.709877975 0.282140481 3.189029438
## [456] 4.731830427 5.357675354 -1.169313996 -0.051902273 -0.595122968
## [461] 1.750997521 4.702863993 0.415866248 3.461868034 1.375042744
## [466] 4.000471629 3.547555212 3.524509101 0.634070352 1.562479225
## [471] 1.839108112 1.956880322 2.527540652 0.332715774 3.839144853
## [476] 2.023316585 3.299735574 1.549585400 3.268492942 4.267881234
## [481] 1.577045362 2.451182736 -0.137881687 2.524460703 1.456321309
## [486] -1.056163882 3.611568490 1.986839367 0.664952606 3.169298993
## [491] 1.194922174 4.440761591 1.448655312 2.248646560 1.463872272
## [496] 3.074386740 2.236447524 3.039922886 3.726066554 -0.082591065
## [501] 0.677920837 2.132444970 1.723095006 0.675474324 0.941950007
## [506] 1.528896802 1.076367258 2.577442589 1.893396950 0.738613607
## [511] 5.001942307 -0.093985465 3.327320335 1.461875506 1.841831273
## [516] 5.743786546 1.398613141 1.936639099 1.044436559 1.060743532
## [521] 2.413579424 1.692399824 2.877416009 2.006339526 1.872305142
## [526] -0.354665686 3.250560679 1.241490438 2.338277409 2.225675119
## [531] 3.307987154 1.575683370 2.567718275 3.623491618 1.237066606
## [536] 1.345647700 3.128946421 1.024394489 1.453729676 2.865972250
## [541] 4.243436534 0.795627617 1.969909591 1.644250135 4.377862976
## [546] 3.021357372 3.176772909 1.662978922 0.100530062 2.689257825
## [551] 2.093043810 1.239017085 2.090624451 0.722050781 0.329123279
## [556] 2.342139028 1.889658339 3.059127119 2.105189374 2.331303901
## [561] 2.038331781 0.649924241 1.606403726 3.702757608 0.766896034
## [566] -1.293187476 3.071326640 1.475993360 0.452622113 1.414731867
## [571] 1.315715948 0.301818191 3.630064927 0.140349913 3.508671361
## [576] 1.545515200 1.330013842 2.509733699 0.335713199 2.826931205
## [581] -0.457178888 2.235949259 3.674800935 1.411260812 0.470724240
## [586] 5.831998821 2.191904503 2.274211320 3.369184904 3.388747753
## [591] 1.690962202 2.925225873 0.363980768 1.263480614 1.341431465
## [596] 4.441652342 1.662489269 0.696110460 -0.404474602 4.737018426
## [601] 2.626925812 3.318104675 2.861606107 3.208761292 1.359593443
## [606] 4.218977612 -0.811947895 0.889926011 1.621927706 0.295773670
## [611] 0.381936853 1.972064945 2.223681944 2.886528745 1.854375294
## [616] 0.505006138 0.945062391 1.328309869 2.680877230 4.651312923
## [621] -0.716437429 2.053882599 -0.487081852 1.107016309 0.883088921
## [626] -0.540376565 2.993416226 3.202757839 0.258145688 2.439228721
## [631] 2.551451874 1.573168127 2.110401638 2.437200723 0.763279911
## [636] 1.289289256 4.351310227 3.218264722 1.087058593 2.146173634
## [641] 0.468753830 0.457695968 2.159473207 1.734821910 3.401863353
## [646] 4.050725300 3.046510421 1.546193698 2.284107088 3.234010774
## [651] -0.819643142 2.587533577 0.650425665 2.900349136 1.447508891
## [656] 2.599346212 1.074247085 0.649527093 2.828848755 1.701186537
## [661] 1.617598809 3.439875525 2.022574150 1.501693222 0.438420124
## [666] 2.391569463 1.662214288 2.843763074 3.027577585 -0.968896528
## [671] 2.223062230 5.301884082 0.581686623 -0.401757287 1.580373834
## [676] 1.648480561 2.200723143 1.050341439 2.193615242 3.912991870
## [681] 4.365646141 0.232824703 4.403002109 1.920368454 4.160346574
## [686] -0.125554408 -0.015079024 1.616516622 0.771023888 3.891450719
## [691] 1.779212348 0.627679755 2.037862646 2.220813844 1.719226830
## [696] 1.071055843 3.476050154 2.627207790 2.438338359 3.725888993
## [701] 1.692329786 1.535452856 2.019786940 2.158178214 3.617952530
## [706] 3.985775371 3.591441569 2.835574078 1.542233607 0.892646523
## [711] -0.596650084 3.898656310 2.075407606 2.945853260 1.717756300
## [716] 1.229821450 0.671411253 -0.826785308 2.003882213 3.238414378
## [721] 0.097742615 4.014176050 4.274884988 0.566129906 3.106564957
## [726] 3.335114432 -0.682808731 4.072753629 0.356951451 2.407721757
## [731] 0.794466222 1.420215568 3.167387033 1.903379563 3.463421154
## [736] -0.023377226 1.018787706 2.723225582 3.330216442 2.440985319
## [741] -1.647980085 1.160256911 1.472715895 2.114238329 2.608115386
## [746] -0.534899448 1.288675738 2.549964462 2.286476762 -0.491439015
## [751] 3.402928802 2.918933300 1.952412709 0.865380701 0.653421041
## [756] 2.236832950 0.832789385 0.002464977 0.994140024 1.716331534
## [761] 0.621481722 -0.466339588 0.541166478 1.145035126 1.878511145
## [766] 2.060086933 2.264996565 3.070361438 6.050942307 1.613248170
## [771] 2.419001414 0.813029401 3.454522051 3.564442047 1.799784549
## [776] 2.303237921 2.986839966 1.354666537 0.103526072 5.012010414
## [781] 3.470334842 0.744204285 1.372093357 2.404970792 0.179463997
## [786] -1.297544614 1.981677891 3.593775549 2.568078430 1.647360667
## [791] 1.503495749 1.661175539 2.215301015 1.754451964 3.087483149
## [796] 2.744999787 -0.147083954 -0.536066142 3.786250882 -0.456816832
## [801] 0.245964368 1.466335911 0.907627511 4.540074508 3.183357510
## [806] 3.310278575 3.699645134 3.693901744 0.755181871 3.232177356
## [811] 1.643655219 0.024114387 1.245418638 3.196251168 1.763434194
## [816] 1.156158675 2.387284503 2.236409682 3.265828028 1.698812143
## [821] 2.758914344 1.211136911 0.142265599 3.178751655 1.670675370
## [826] 4.827722886 2.818339530 1.018086868 1.743342831 0.217331400
## [831] 2.108285808 1.271601150 3.124219672 -1.023409321 3.028506275
## [836] -0.094809243 1.136902471 0.857326501 2.492631905 0.076697055
## [841] -0.309467994 1.287645969 2.339998721 0.462604718 1.212366369
## [846] 2.602022805 4.598213425 1.991407059 3.627637836 2.084070985
## [851] 4.782109201 2.908753311 2.915920059 1.806193132 1.083524139
## [856] 2.454958631 -0.117272430 1.796927509 2.167499934 1.885169173
## [861] 1.622889356 2.024668806 2.558293011 0.736833241 3.526637673
## [866] 1.948107956 1.054411448 1.277576914 5.164525787 3.109991731
## [871] 2.332272316 1.851078256 3.134405279 -0.090546582 0.689748239
## [876] 1.321456550 0.284681249 1.164211948 3.537217615 1.443376513
## [881] 0.183388667 6.992204404 4.355584542 1.273515108 2.581514859
## [886] 0.488387899 2.380326436 1.279162836 -0.025431545 1.872797167
## [891] 1.118118863 2.326697299 3.613633246 3.021597725 1.080641491
## [896] 0.442905469 1.203704450 0.654994650 3.510259817 2.501166394
## [901] 1.311799654 3.122377847 1.846789731 -1.492398772 2.303414526
## [906] 2.051893188 0.947767217 1.743582524 -0.078603346 1.342064132
## [911] 2.558470689 4.625356675 0.480661731 0.368499463 2.338459193
## [916] 2.795844257 1.298431009 3.488643420 2.976448000 1.321081199
## [921] 3.197478090 0.605513413 3.263054266 2.225277046 3.877104347
## [926] 2.668275523 0.889760261 1.036624833 1.079007754 1.013406763
## [931] 3.227127281 1.806837698 2.896798763 1.807552406 4.129634180
## [936] 0.918719954 0.399618458 3.168434697 1.703381795 5.362561675
## [941] 3.904262768 2.116817277 -0.313859536 3.320948383 0.743870319
## [946] -1.870641616 1.724360680 1.506408380 2.194305164 4.131628206
## [951] 1.791161242 1.829084334 2.496582662 -0.538498358 2.127327123
## [956] -1.091267137 4.059321866 1.646446434 2.137068385 2.967215367
## [961] 2.781081106 2.256415395 1.467818504 2.388184807 -3.142669916
## [966] 1.497544980 2.397931826 2.068096255 2.558234702 0.197478728
## [971] 2.508615916 1.974937310 2.180504486 1.605271747 2.483223960
## [976] 0.322569683 1.526474800 4.329676535 6.172652958 1.310238195
## [981] 5.386567248 3.072266054 3.367097460 4.040236359 2.507724692
## [986] 2.974831099 2.646189290 1.524076742 3.826711920 1.757084558
## [991] 4.206289558 2.915510317 0.302385619 0.763818616 0.435931719
## [996] 3.063840513 1.726209028 1.330768272 0.055721149 -0.338328760
## [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.
## -3.143 1.088 2.008 2.043 3.030 7.248
## 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%
## -0.3615271
## 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%
## 4.440806
## 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%
## -0.3615271
## 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
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## [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
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -0.5755830 -1.7859494 -1.2785399 -1.4309865 -0.5007070 -1.2474744
## [7] -0.7987299 -1.1676645 -1.5822419 -1.0821381 -0.5763988 -0.7721215
## [13] -1.1789715 -0.3749435 -0.3814146 -0.9943394 -1.1275181 -0.6302414
## [19] -0.5255229 -2.1812555 -1.3227239 -1.1693140 -0.5951230 -1.0561639
## [25] -1.2931875 -0.4571789 -0.4044746 -0.8119479 -0.7164374 -0.4870819
## [31] -0.5403766 -0.8196431 -0.9688965 -0.4017573 -0.5966501 -0.8267853
## [37] -0.6828087 -1.6479801 -0.5348994 -0.4914390 -0.4663396 -1.2975446
## [43] -0.5360661 -0.4568168 -1.0234093 -1.4923988 -1.8706416 -0.5384984
## [49] -1.0912671 -3.1426699
## [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%
## 4.440806
## 95%
## 4.539426
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [37] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
## [301] TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [313] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [445] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [457] TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
## [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
## [1] 50
data[Top5Percent==TRUE]
## [1] 4.844674 6.905337 5.097497 5.042731 6.428544 4.819960 7.248467 6.131515
## [9] 4.625974 5.228018 5.243118 5.923745 4.529331 4.502368 5.556871 5.125735
## [17] 5.763518 5.913518 4.913187 4.749928 5.510096 5.661680 4.751270 4.690745
## [25] 4.972956 4.513844 4.503464 5.291622 4.731830 5.357675 4.702864 5.001942
## [33] 5.743787 5.831999 4.441652 4.737018 4.651313 5.301884 6.050942 5.012010
## [41] 4.540075 4.827723 4.598213 4.782109 5.164526 6.992204 4.625357 5.362562
## [49] 6.172653 5.386567
## [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