# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Ron Christian D. Falle
# Submitted to: Prof. Carlito O. Daarol
# Faculty
# Math Department
# March 16, 2023
# Processing of continuous data
# Using random number generators
# Exer1: generate data with mean 2 and standard deviation 1.5 using rnorm() command
data <- rnorm(1000,2,1.5) # 1 thousand values
length(data) # count number of elements
## [1] 1000
## [1] 1000
data[1:20] # display first 20 elements
## [1] 2.5499043 3.1883268 1.9844243 1.8031629 -0.7285658 0.8245075
## [7] 3.7066563 1.6709524 3.6909404 2.9010682 -2.3337546 2.7205016
## [13] 2.5176481 4.1194972 3.2967789 -0.2312551 4.0119651 2.5919325
## [19] 4.5264088 1.3162209
## [1] 6.7950501 2.9971858 0.5114664 3.7472543 -1.0568895 0.1344303
## [7] 2.2099518 3.6546881 0.1161034 4.6784938 3.6113647 2.0999132
## [13] 1.4003658 0.2159255 3.0074956 0.6181636 3.3564768 0.9145459
## [19] -0.1743168 4.3279270
data[1:300] # display the first 300 elements
## [1] 2.54990427 3.18832683 1.98442431 1.80316288 -0.72856577 0.82450746
## [7] 3.70665632 1.67095240 3.69094044 2.90106821 -2.33375463 2.72050158
## [13] 2.51764815 4.11949724 3.29677893 -0.23125508 4.01196512 2.59193249
## [19] 4.52640876 1.31622091 0.57002010 2.41695415 1.09223576 2.36943222
## [25] 2.44574222 2.30210169 1.54304640 0.17016992 4.54059633 1.74126323
## [31] 0.73927159 4.17935960 3.48689518 1.51511465 1.83750357 2.35001981
## [37] 1.93487446 0.34705028 5.58131090 3.72427333 1.11359396 -0.24292836
## [43] 3.30221891 -0.24664807 2.57990744 2.77753397 -0.34582734 0.95782262
## [49] 1.70919139 2.50984840 1.85755997 0.77944172 -0.26844850 3.39904673
## [55] -0.18704503 3.67011359 1.04033571 5.82185803 0.21648543 1.51688711
## [61] 2.23790709 3.41664891 3.24947302 1.24732538 -0.03434474 4.38450901
## [67] 1.02066346 -0.05142967 2.39253120 2.07411467 3.83874251 -0.19790395
## [73] 0.88403395 0.09663877 3.14226082 3.87410277 2.82807722 -1.62714866
## [79] 0.82689661 3.09948493 0.92664388 2.01799608 -0.72429149 1.63994570
## [85] -0.88372553 -0.89120005 2.11073704 1.26084059 1.39000824 3.14144056
## [91] 3.54480875 2.05294397 1.87224972 4.09547383 3.18717830 3.84017441
## [97] 3.20337882 2.95204762 3.15515458 4.01236384 1.18448190 0.46883603
## [103] 2.71966822 2.38208654 3.42840376 1.23685291 -1.60036106 3.37737447
## [109] 2.18921490 1.01249230 2.40601474 4.61214391 2.00353492 0.45532346
## [115] 5.07014509 2.04282997 4.51186959 -0.31083047 4.38274608 2.31505514
## [121] 4.17650739 4.22718278 3.13832165 2.64762741 2.65927462 -0.03102264
## [127] 3.07106638 -1.88596918 2.87245915 1.49865376 1.33156475 0.91847581
## [133] 0.11965789 1.24657078 1.18596029 3.46745196 3.80724045 4.09284058
## [139] 1.96138104 2.93600104 1.42434263 0.49784322 2.76651102 1.84497980
## [145] 2.94618740 4.26034511 4.24090086 2.79462925 1.62878267 3.90219924
## [151] 4.13146805 1.40118074 1.60420078 1.91023360 4.90561627 1.33048146
## [157] 3.45724475 1.62946495 3.09465068 0.91328700 2.65155645 4.03541279
## [163] 3.16162948 2.90142748 1.44314801 3.60441279 0.31437251 2.10836962
## [169] 5.09297584 2.13870434 0.22981428 2.02153623 3.95768991 2.22639549
## [175] 2.07630635 -1.18100820 0.53931663 3.51495017 3.62156454 2.16105201
## [181] 4.03201581 2.34902481 2.13737175 4.51830852 0.64668992 0.44822269
## [187] 2.50842423 -0.21311530 1.12447188 -0.21870225 6.50926373 0.58291616
## [193] 2.12569806 2.10538231 3.61641725 1.83454932 1.20657075 4.06648353
## [199] 2.64364256 1.21201578 2.48769984 0.90316754 2.70672721 1.44685853
## [205] 2.15684539 1.97206654 2.48463685 3.86773075 1.68672399 2.59813935
## [211] 2.18421604 1.36063069 1.29755500 3.68932541 1.19975059 -0.55744026
## [217] 1.29320093 1.61708454 1.56888327 1.02774253 2.44039847 1.02378241
## [223] 7.02310169 3.05448247 1.13994366 1.97218754 3.40602675 4.89774572
## [229] 3.81728735 1.38746365 2.01218113 3.51864657 2.10993521 2.02123879
## [235] -0.56869964 0.01462643 1.57609285 3.09838853 2.15461428 1.41777982
## [241] 2.96368301 -0.38925994 1.14619402 4.85337727 1.35877014 1.19649002
## [247] 2.00474706 0.49859076 4.29025574 4.24297890 -0.82984675 1.86893230
## [253] 1.90636896 2.02936449 2.13319979 3.68466471 2.05460661 3.01404446
## [259] 2.94214428 0.31674607 4.50273850 2.95235628 1.63934736 2.70738643
## [265] 2.17511443 4.07318887 3.08230496 2.49051144 1.37292542 4.98079660
## [271] 3.94453488 -0.51377690 0.60480949 4.61627969 1.28144355 1.49918502
## [277] 2.69751895 2.10753706 2.72507377 -1.38534520 2.29187156 0.10588044
## [283] 2.10894812 1.65582998 3.29231852 2.02203261 1.49116210 -1.71211614
## [289] 5.38297948 1.16193728 0.70104743 2.28073625 3.08108955 -1.42053632
## [295] 0.03183731 1.74313971 2.93873281 2.68408834 2.97154013 2.59799312
## [1] 6.795050140 2.997185793 0.511466423 3.747254252 -1.056889512
## [6] 0.134430261 2.209951813 3.654688092 0.116103382 4.678493805
## [11] 3.611364718 2.099913215 1.400365762 0.215925543 3.007495604
## [16] 0.618163649 3.356476832 0.914545900 -0.174316824 4.327926985
## [21] 0.151049885 0.279433234 1.273728401 1.893149093 -1.226388963
## [26] 1.602769253 2.472274938 1.707579631 0.421872923 1.525518828
## [31] 4.696390334 1.535573912 4.345618480 1.227820815 -0.607101052
## [36] 2.831963560 2.404229519 2.509695348 -0.583091111 5.568949199
## [41] 1.119368833 2.111837858 0.665506408 -0.620966233 1.960926319
## [46] 1.807994709 0.517271207 2.692412408 3.737708819 1.019551835
## [51] 0.353007120 1.628221232 -0.373567030 2.162220262 1.256420979
## [56] 3.230860975 0.527688137 3.430307311 1.599772884 1.907436761
## [61] -0.006102183 2.606483788 3.352963337 3.987781161 1.179723639
## [66] 3.002797128 1.061177927 1.800204756 0.384008538 1.197958720
## [71] 0.897165627 2.310465216 3.077940173 2.118584349 1.141214465
## [76] 1.016396574 -1.887644721 3.051540786 2.025936304 5.499328788
## [81] 2.663324021 1.246812266 2.280258064 1.616529449 -0.057673659
## [86] 2.429690661 -0.179536320 3.228365534 0.017335783 4.776673816
## [91] 1.798836542 0.215230399 -0.395454981 0.361934574 1.627433546
## [96] 3.786168664 4.151159393 -0.967524400 0.773678889 2.617100312
## [101] 2.185146308 2.499219574 2.216669853 0.334296188 3.348163366
## [106] -0.150050898 1.608062070 3.030498559 0.824991536 -0.154034150
## [111] 0.937714816 -0.466886077 2.256372290 0.669470894 2.932525462
## [116] 3.478287425 1.391616168 2.118326109 2.386965644 1.228486533
## [121] -0.413528032 3.300248906 1.875707863 2.554864587 2.819341062
## [126] 0.227161757 -1.452228004 4.025204696 2.168795746 1.937025403
## [131] 0.021424613 4.980938162 2.797625897 0.787023015 0.964162992
## [136] 1.241074510 1.285468412 1.977582910 0.167900297 0.270895064
## [141] 1.395779159 3.591536082 4.058971580 2.539896498 0.647103708
## [146] -0.205524325 -0.300788502 1.398177934 -0.122276472 2.229300024
## [151] 1.197424526 5.026313700 0.001975712 2.411165881 1.408139069
## [156] 3.549472740 -0.412302858 3.362745931 -0.998544580 2.362031429
## [161] 1.890737159 2.003650673 -0.664821990 1.878542912 -1.195843558
## [166] 2.339436716 1.739921476 4.194267582 2.056000110 4.171889672
## [171] 1.407019752 1.017248943 2.728342383 3.110178969 3.708601598
## [176] 3.798673768 3.603001115 -0.852651403 0.584732627 2.963363107
## [181] 0.707380439 2.777706189 2.141100853 4.608066706 1.248204687
## [186] 1.111529125 0.869009492 0.761559882 3.200158922 3.264505863
## [191] -1.079178002 2.963826608 3.280293544 0.867398583 1.127536268
## [196] 1.369006521 3.098055661 0.135720012 0.515333658 3.396114928
## [201] 5.247966333 2.688101575 0.842640514 3.265464254 2.529634791
## [206] 1.037064104 0.398775259 2.908166835 1.001596048 -0.514667194
## [211] 0.880574149 0.800895432 -0.224082422 2.544632159 1.823455971
## [216] -0.224335693 1.073669908 0.073960031 4.273908071 6.196415207
## [221] 5.676410225 3.363331284 -0.936296982 4.000668971 1.622985540
## [226] 0.068404191 1.176475142 3.429656055 3.416952572 2.291611836
## [231] 2.602141854 2.415200497 1.300414768 3.439331358 4.020001443
## [236] 1.106696812 -0.594560209 0.501360852 4.247218607 2.523731638
## [241] 2.707108680 3.752511370 2.894097741 2.647523784 3.807279354
## [246] 3.319387411 2.306003543 1.049012665 1.823571653 5.094663747
## [251] 1.893538112 2.136748072 1.291566619 0.765436698 1.379277281
## [256] 2.963045567 -0.695473564 2.566529941 4.273584784 3.460452702
## [261] 5.117364949 0.664109717 -1.020939135 1.087650152 3.373515165
## [266] 2.071374452 0.583851842 0.379234169 2.905616978 1.873881735
## [271] 5.171919307 -0.335591042 3.940047797 0.775103809 2.635183135
## [276] -0.459101548 3.281434927 2.826557111 -0.451146704 1.575828160
## [281] 0.925787880 3.674247135 1.858296997 1.771919716 0.703224132
## [286] 2.579438717 3.803453744 2.087316387 3.600449160 3.679330445
## [291] 4.270884357 2.989631244 3.952852862 3.559064935 2.354399796
## [296] 0.914442244 2.191114092 2.138425921 1.967064876 2.273726383
# 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] -2.86743438 -2.75929608 -2.65115778 -2.54301948 -2.43488117 -2.32674287
## [7] -2.21860457 -2.11046627 -2.00232797 -1.89418967 -1.78605137 -1.67791306
## [13] -1.56977476 -1.46163646 -1.35349816 -1.24535986 -1.13722156 -1.02908326
## [19] -0.92094496 -0.81280665 -0.70466835 -0.59653005 -0.48839175 -0.38025345
## [25] -0.27211515 -0.16397685 -0.05583854 0.05229976 0.16043806 0.26857636
## [31] 0.37671466 0.48485296 0.59299126 0.70112956 0.80926787 0.91740617
## [37] 1.02554447 1.13368277 1.24182107 1.34995937 1.45809767 1.56623598
## [43] 1.67437428 1.78251258 1.89065088 1.99878918 2.10692748 2.21506578
## [49] 2.32320408 2.43134239 2.53948069 2.64761899 2.75575729 2.86389559
## [55] 2.97203389 3.08017219 3.18831050 3.29644880 3.40458710 3.51272540
## [61] 3.62086370 3.72900200 3.83714030 3.94527860 4.05341691 4.16155521
## [67] 4.26969351 4.37783181 4.48597011 4.59410841 4.70224671 4.81038502
## [73] 4.91852332 5.02666162 5.13479992 5.24293822 5.35107652 5.45921482
## [79] 5.56735313 5.67549143 5.78362973 5.89176803 5.99990633 6.10804463
## [85] 6.21618293 6.32432123 6.43245954 6.54059784 6.64873614 6.75687444
## [91] 6.86501274 6.97315104 7.08128934 7.18942765 7.29756595 7.40570425
## [97] 7.51384255 7.62198085 7.73011915 7.83825745
## [1] -3.57541165 -3.47065951 -3.36590737 -3.26115523 -3.15640309 -3.05165095
## [7] -2.94689881 -2.84214667 -2.73739453 -2.63264239 -2.52789025 -2.42313811
## [13] -2.31838597 -2.21363384 -2.10888170 -2.00412956 -1.89937742 -1.79462528
## [19] -1.68987314 -1.58512100 -1.48036886 -1.37561672 -1.27086458 -1.16611244
## [25] -1.06136030 -0.95660816 -0.85185602 -0.74710389 -0.64235175 -0.53759961
## [31] -0.43284747 -0.32809533 -0.22334319 -0.11859105 -0.01383891 0.09091323
## [37] 0.19566537 0.30041751 0.40516965 0.50992179 0.61467392 0.71942606
## [43] 0.82417820 0.92893034 1.03368248 1.13843462 1.24318676 1.34793890
## [49] 1.45269104 1.55744318 1.66219532 1.76694746 1.87169960 1.97645173
## [55] 2.08120387 2.18595601 2.29070815 2.39546029 2.50021243 2.60496457
## [61] 2.70971671 2.81446885 2.91922099 3.02397313 3.12872527 3.23347741
## [67] 3.33822955 3.44298168 3.54773382 3.65248596 3.75723810 3.86199024
## [73] 3.96674238 4.07149452 4.17624666 4.28099880 4.38575094 4.49050308
## [79] 4.59525522 4.70000736 4.80475949 4.90951163 5.01426377 5.11901591
## [85] 5.22376805 5.32852019 5.43327233 5.53802447 5.64277661 5.74752875
## [91] 5.85228089 5.95703303 6.06178517 6.16653730 6.27128944 6.37604158
## [97] 6.48079372 6.58554586 6.69029800 6.79505014
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%
## -2.867434 1.110925 2.039455 3.115990 7.838257
## 0% 25% 50% 75% 100%
## -3.5754116 0.8513114 1.9366460 3.0049901 6.7950501
# 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] 2.54990427 3.18832683 1.98442431 1.80316288 -0.72856577 0.82450746
## [7] 3.70665632 1.67095240 3.69094044 2.90106821 -2.33375463 2.72050158
## [13] 2.51764815 4.11949724 3.29677893 -0.23125508 4.01196512 2.59193249
## [19] 4.52640876 1.31622091 0.57002010 2.41695415 1.09223576 2.36943222
## [25] 2.44574222 2.30210169 1.54304640 0.17016992 4.54059633 1.74126323
## [31] 0.73927159 4.17935960 3.48689518 1.51511465 1.83750357 2.35001981
## [37] 1.93487446 0.34705028 5.58131090 3.72427333 1.11359396 -0.24292836
## [43] 3.30221891 -0.24664807 2.57990744 2.77753397 -0.34582734 0.95782262
## [49] 1.70919139 2.50984840 1.85755997 0.77944172 -0.26844850 3.39904673
## [55] -0.18704503 3.67011359 1.04033571 5.82185803 0.21648543 1.51688711
## [61] 2.23790709 3.41664891 3.24947302 1.24732538 -0.03434474 4.38450901
## [67] 1.02066346 -0.05142967 2.39253120 2.07411467 3.83874251 -0.19790395
## [73] 0.88403395 0.09663877 3.14226082 3.87410277 2.82807722 -1.62714866
## [79] 0.82689661 3.09948493 0.92664388 2.01799608 -0.72429149 1.63994570
## [85] -0.88372553 -0.89120005 2.11073704 1.26084059 1.39000824 3.14144056
## [91] 3.54480875 2.05294397 1.87224972 4.09547383 3.18717830 3.84017441
## [97] 3.20337882 2.95204762 3.15515458 4.01236384 1.18448190 0.46883603
## [103] 2.71966822 2.38208654 3.42840376 1.23685291 -1.60036106 3.37737447
## [109] 2.18921490 1.01249230 2.40601474 4.61214391 2.00353492 0.45532346
## [115] 5.07014509 2.04282997 4.51186959 -0.31083047 4.38274608 2.31505514
## [121] 4.17650739 4.22718278 3.13832165 2.64762741 2.65927462 -0.03102264
## [127] 3.07106638 -1.88596918 2.87245915 1.49865376 1.33156475 0.91847581
## [133] 0.11965789 1.24657078 1.18596029 3.46745196 3.80724045 4.09284058
## [139] 1.96138104 2.93600104 1.42434263 0.49784322 2.76651102 1.84497980
## [145] 2.94618740 4.26034511 4.24090086 2.79462925 1.62878267 3.90219924
## [151] 4.13146805 1.40118074 1.60420078 1.91023360 4.90561627 1.33048146
## [157] 3.45724475 1.62946495 3.09465068 0.91328700 2.65155645 4.03541279
## [163] 3.16162948 2.90142748 1.44314801 3.60441279 0.31437251 2.10836962
## [169] 5.09297584 2.13870434 0.22981428 2.02153623 3.95768991 2.22639549
## [175] 2.07630635 -1.18100820 0.53931663 3.51495017 3.62156454 2.16105201
## [181] 4.03201581 2.34902481 2.13737175 4.51830852 0.64668992 0.44822269
## [187] 2.50842423 -0.21311530 1.12447188 -0.21870225 6.50926373 0.58291616
## [193] 2.12569806 2.10538231 3.61641725 1.83454932 1.20657075 4.06648353
## [199] 2.64364256 1.21201578 2.48769984 0.90316754 2.70672721 1.44685853
## [205] 2.15684539 1.97206654 2.48463685 3.86773075 1.68672399 2.59813935
## [211] 2.18421604 1.36063069 1.29755500 3.68932541 1.19975059 -0.55744026
## [217] 1.29320093 1.61708454 1.56888327 1.02774253 2.44039847 1.02378241
## [223] 7.02310169 3.05448247 1.13994366 1.97218754 3.40602675 4.89774572
## [229] 3.81728735 1.38746365 2.01218113 3.51864657 2.10993521 2.02123879
## [235] -0.56869964 0.01462643 1.57609285 3.09838853 2.15461428 1.41777982
## [241] 2.96368301 -0.38925994 1.14619402 4.85337727 1.35877014 1.19649002
## [247] 2.00474706 0.49859076 4.29025574 4.24297890 -0.82984675 1.86893230
## [253] 1.90636896 2.02936449 2.13319979 3.68466471 2.05460661 3.01404446
## [259] 2.94214428 0.31674607 4.50273850 2.95235628 1.63934736 2.70738643
## [265] 2.17511443 4.07318887 3.08230496 2.49051144 1.37292542 4.98079660
## [271] 3.94453488 -0.51377690 0.60480949 4.61627969 1.28144355 1.49918502
## [277] 2.69751895 2.10753706 2.72507377 -1.38534520 2.29187156 0.10588044
## [283] 2.10894812 1.65582998 3.29231852 2.02203261 1.49116210 -1.71211614
## [289] 5.38297948 1.16193728 0.70104743 2.28073625 3.08108955 -1.42053632
## [295] 0.03183731 1.74313971 2.93873281 2.68408834 2.97154013 2.59799312
## [301] 0.63534751 3.65221471 4.02683136 0.78521697 0.79641413 1.61708674
## [307] 2.78993660 1.89704804 0.44466702 0.09035282 2.90904873 -0.64146246
## [313] 2.34968538 2.11005485 3.30788497 4.01867724 4.01441248 -0.30040196
## [319] 2.08515207 3.93753066 0.57513290 2.23747856 1.41696553 1.38560109
## [325] 3.47263497 1.77208894 1.39431483 0.54053669 0.31919504 1.76511757
## [331] 4.60005836 2.40262884 0.78514095 2.38866089 -0.49352433 2.48091430
## [337] 5.13118581 2.25118157 1.84264102 1.69356962 -0.90504109 2.17894722
## [343] 1.56886062 5.11727165 1.18197595 0.56352142 1.58581594 -0.09071419
## [349] 1.24475389 2.68131846 2.47009443 3.50922319 3.07837587 2.67803550
## [355] 1.21629359 1.46049535 1.48740286 2.00664185 3.50321138 4.07654953
## [361] 0.61359504 2.52452945 1.89233792 1.74540434 1.03616605 1.88055296
## [367] 0.54287358 2.57847914 2.56296999 4.04710389 2.18669651 3.25803746
## [373] 4.99835209 1.13009503 1.97888609 3.01893826 -0.22894450 1.15753261
## [379] 1.95010642 0.99924598 4.24696298 1.92005355 1.03627159 0.10808652
## [385] 2.45970223 0.63406061 1.54665729 3.36330409 1.68805925 1.31971762
## [391] 2.25664022 2.48480358 2.13095337 1.87018065 3.11246049 4.27780362
## [397] 1.14662100 2.24384340 1.98172080 2.29538036 4.97307713 2.07254631
## [403] 4.88208478 3.24908079 3.37189702 1.16575939 2.60799745 2.81961595
## [409] 5.07679238 2.69044757 2.49589592 1.41736935 2.31257530 2.86324880
## [415] 4.53231271 0.60188784 0.10272649 -1.15244321 1.33988793 3.49122563
## [421] 2.06317788 0.45286713 1.98277813 1.50486067 2.20664746 1.54471946
## [427] 2.56629272 0.23570975 3.14913964 3.81466452 1.31215962 0.41145529
## [433] 0.55356855 3.15024185 -0.07648630 0.63928581 3.80837060 3.96611915
## [439] 3.60947969 4.45272351 2.77034330 1.74461903 2.13883982 -0.02608860
## [445] 1.72855631 1.70097037 2.48767894 0.30562985 3.50713087 1.95717072
## [451] 2.87219639 3.09559425 1.37940697 3.22795864 -0.71550807 1.12414602
## [457] 1.10561125 4.53866273 3.31554694 1.44859102 3.91091467 -0.55747963
## [463] 2.59925860 1.93650509 2.37757126 1.54704782 1.14838085 2.54144712
## [469] 1.85006502 1.05895155 2.95117283 3.80489825 0.05848031 1.43066665
## [475] 3.98106533 2.28984331 1.32750073 4.35345571 1.59459183 0.45493889
## [481] 1.79523210 1.16225368 -0.03661001 1.57659408 1.46573183 1.87216819
## [487] 0.89680974 3.65498484 4.51407770 1.82914205 2.87238421 0.84362781
## [493] 1.68169748 0.79178148 4.27449664 1.83845186 2.96945572 2.82210852
## [499] 2.98952235 3.89075819 4.70092203 1.40507050 1.31295755 2.14737945
## [505] 2.01934266 4.47004919 3.68016734 0.36835869 2.16009062 1.06225350
## [511] 1.88507287 0.68909754 0.10654785 2.23115672 -0.85029389 -1.44522718
## [517] 3.60399137 0.26349026 2.98491238 2.35012998 -1.46899365 2.20042314
## [523] 1.22899673 -0.59087513 3.72381595 -1.67470680 5.26817042 5.12168759
## [529] 1.71737838 1.71959705 -1.04078639 -0.04894720 1.21328142 2.80310526
## [535] 2.86848988 0.60234786 0.36687139 0.20608249 2.50772168 0.87922158
## [541] 0.47767820 0.89884274 2.01143751 3.04382466 2.38121461 2.05663535
## [547] 2.11608448 2.29696060 1.62126020 3.57986713 3.14171955 2.44800517
## [553] 2.53545919 1.13641876 -1.98331839 2.25066440 2.64057315 4.76460176
## [559] 1.97690649 3.82569570 4.09812582 4.04036698 -0.12368510 1.83486087
## [565] 1.04930371 3.25061959 0.51132180 4.40351032 0.97969917 0.48386843
## [571] 3.47487168 3.35650300 2.08839373 -0.62660215 0.24757398 5.28546097
## [577] 2.84348279 0.26212154 3.49622255 0.48845416 1.38383054 2.03607943
## [583] -0.02130788 2.23720030 5.18931898 0.63614748 0.75957310 3.67362131
## [589] -2.86743438 0.65089746 0.46392514 1.39921782 3.02000382 0.58078740
## [595] 2.11080073 0.42014577 1.54865505 2.86266962 3.55178895 5.64471726
## [601] -0.30245953 1.42099611 2.20567779 -0.07975835 1.62122770 0.75535950
## [607] 0.10107766 4.42864040 5.44500696 1.32552670 3.39641927 0.12305807
## [613] 2.59752389 2.07994109 2.73151127 2.24047694 1.33472861 0.53306571
## [619] 2.76924189 3.32474013 4.47294327 1.59585185 -0.57996194 0.68143530
## [625] 0.76558589 3.90940162 1.18429134 1.04872623 1.35967739 3.89622092
## [631] 3.48855977 1.42480987 3.29387583 1.76114688 3.11782703 4.32330810
## [637] 0.15018296 4.05334685 3.86439311 0.26090204 3.10581801 0.37980910
## [643] 5.49488892 0.92542907 2.02658948 1.16460327 2.73995495 0.31793925
## [649] 2.00546704 1.29947118 1.75560062 1.26389658 0.55532044 4.64033113
## [655] 4.19906928 1.57927666 1.93488276 0.76353947 1.79672856 -2.26346160
## [661] 1.24202417 3.10075493 -1.50966961 0.82670759 2.50557758 2.00050567
## [667] 1.97843608 2.32009051 2.43259705 1.07079426 -0.87556126 3.00055563
## [673] 0.21076324 -0.38546115 1.56261504 0.11947283 2.56021278 3.04283147
## [679] 3.48643384 2.85393154 3.73290832 0.44818705 1.96210490 2.02037148
## [685] 2.17992313 1.15817471 1.37837009 1.01886627 2.49933199 2.91498687
## [691] 1.29706033 3.34181368 3.20565198 2.93954951 0.30862241 4.22268629
## [697] 1.51029137 1.12415255 1.31663032 -0.95301907 -1.53753828 2.15822765
## [703] 0.88722942 2.73970334 3.63394679 1.37249227 1.28885234 3.41434571
## [709] 3.81602551 4.49901176 -1.77756857 2.57145635 1.45575137 1.39392088
## [715] 3.21902703 0.25099490 1.26369719 2.65478490 1.81313923 4.24293228
## [721] 3.21181453 0.87768508 3.27842995 1.75864222 4.33634662 1.22899168
## [727] 2.00716418 -1.35584910 0.98227971 0.84208863 1.52706350 2.45175629
## [733] 2.79147244 4.64073477 2.38858030 0.83178388 2.51096884 1.12355422
## [739] 1.78833713 1.90298663 2.73913255 0.26210077 3.24482022 7.83825745
## [745] 0.93229700 3.70813583 2.74453738 0.38367892 -0.57004805 1.34449658
## [751] 2.17743873 1.33012577 0.61247104 1.32870258 1.64464092 3.82617945
## [757] 2.45132388 0.55777136 2.45618735 4.91595814 2.78231947 1.99977909
## [763] 2.42667181 1.43432209 0.95333152 1.33607252 1.06226073 4.83503239
## [769] 1.69206691 1.90520583 3.42949535 2.76877293 3.80727451 3.14645960
## [775] 4.12272962 2.13044928 2.29849930 2.92780782 1.12393623 -0.46911983
## [781] 3.89386294 3.37307488 4.22035277 3.17218749 3.11537717 2.43053838
## [787] 0.13580078 1.31401154 4.07334736 4.17703453 3.48172855 -0.92945010
## [793] 0.65196620 -0.77393812 1.70912463 2.20565838 2.70889518 2.82540956
## [799] 3.31118777 2.87764926 1.83285595 5.98885026 3.35880138 3.36582022
## [805] 0.63214976 3.82877763 2.51895031 4.21522825 3.29189411 2.38118303
## [811] 2.20337779 2.44267166 -0.82283321 1.85828367 3.19675676 2.47138595
## [817] 1.04428854 2.25862849 3.42114591 3.71937743 1.66429332 0.27764948
## [823] 3.09740402 3.03966150 4.64917315 1.87267374 1.89491893 1.89259411
## [829] 1.66258410 3.72858041 1.11269649 1.98337445 2.00652311 1.84161604
## [835] 2.92472870 2.16516415 3.91253959 2.11756910 2.32067244 0.50521495
## [841] 2.47004887 1.26396701 3.45525808 0.97134525 2.64687819 3.42516279
## [847] 0.54173986 3.79189058 0.68531773 -0.57461580 2.39221596 2.68194166
## [853] 2.88572333 3.55185612 1.14489983 2.43985548 2.76542937 1.91668023
## [859] 1.46779229 1.15009080 1.98795716 -1.48276693 0.78143745 0.61520660
## [865] 3.55111595 0.60578608 0.67044879 3.59476661 1.19216324 3.60610429
## [871] 3.05409819 1.13804264 0.75221696 1.91480118 1.69006278 0.20453210
## [877] 3.16994315 3.02721369 -0.66320609 -0.88104909 -0.79595464 2.86430748
## [883] 3.80745935 4.18596184 2.46418258 -0.30292177 0.98112153 0.90649388
## [889] 3.19147262 0.90182216 4.70759874 0.37772251 1.45008632 4.28746499
## [895] 1.61811212 4.23547297 3.64379524 0.38242529 3.35719923 4.22920751
## [901] 1.23668406 5.43214276 -1.01670366 3.98847611 1.17127887 1.49698190
## [907] 2.31912822 2.59766474 0.60407768 2.65769562 2.71210944 1.09589983
## [913] 3.03455808 -0.44914389 4.34001175 0.29286692 1.59285716 3.70227998
## [919] 1.35202136 2.89701226 4.39637939 0.72619812 3.01084114 3.02300680
## [925] 2.02865679 3.18567967 -1.46010494 5.55121033 -0.82070846 0.43547203
## [931] 2.26355092 -1.87044970 2.42441102 5.81782208 3.02527439 2.78512158
## [937] 1.41520538 2.02260879 1.57399071 -1.05681697 1.35428413 4.52310145
## [943] 1.57663182 0.66811057 4.62074952 2.44505299 3.84217199 2.50021859
## [949] 1.79262491 2.24314185 3.31619479 2.00004856 5.14667644 3.57697920
## [955] 2.98981552 4.77546282 4.01536210 2.03435320 1.05864474 1.55885157
## [961] 1.96728993 4.09161532 0.17736814 0.66897563 -0.53152397 2.15835527
## [967] 1.79775936 3.12252351 1.40693386 -0.82843610 2.18740131 1.02418419
## [973] -0.69116016 3.96858765 0.01646454 -0.02467910 3.07680882 2.54319313
## [979] 1.10424446 3.19254349 3.38959947 2.71467506 3.31180550 3.67161211
## [985] 2.54022131 1.15365091 4.45523388 2.30248448 0.67341266 0.49583229
## [991] 2.86459437 1.22161466 3.12053197 1.10031613 2.93382191 3.71793896
## [997] 2.16015447 2.00676230 0.90263062 1.71882239
## [1] 6.795050140 2.997185793 0.511466423 3.747254252 -1.056889512
## [6] 0.134430261 2.209951813 3.654688092 0.116103382 4.678493805
## [11] 3.611364718 2.099913215 1.400365762 0.215925543 3.007495604
## [16] 0.618163649 3.356476832 0.914545900 -0.174316824 4.327926985
## [21] 0.151049885 0.279433234 1.273728401 1.893149093 -1.226388963
## [26] 1.602769253 2.472274938 1.707579631 0.421872923 1.525518828
## [31] 4.696390334 1.535573912 4.345618480 1.227820815 -0.607101052
## [36] 2.831963560 2.404229519 2.509695348 -0.583091111 5.568949199
## [41] 1.119368833 2.111837858 0.665506408 -0.620966233 1.960926319
## [46] 1.807994709 0.517271207 2.692412408 3.737708819 1.019551835
## [51] 0.353007120 1.628221232 -0.373567030 2.162220262 1.256420979
## [56] 3.230860975 0.527688137 3.430307311 1.599772884 1.907436761
## [61] -0.006102183 2.606483788 3.352963337 3.987781161 1.179723639
## [66] 3.002797128 1.061177927 1.800204756 0.384008538 1.197958720
## [71] 0.897165627 2.310465216 3.077940173 2.118584349 1.141214465
## [76] 1.016396574 -1.887644721 3.051540786 2.025936304 5.499328788
## [81] 2.663324021 1.246812266 2.280258064 1.616529449 -0.057673659
## [86] 2.429690661 -0.179536320 3.228365534 0.017335783 4.776673816
## [91] 1.798836542 0.215230399 -0.395454981 0.361934574 1.627433546
## [96] 3.786168664 4.151159393 -0.967524400 0.773678889 2.617100312
## [101] 2.185146308 2.499219574 2.216669853 0.334296188 3.348163366
## [106] -0.150050898 1.608062070 3.030498559 0.824991536 -0.154034150
## [111] 0.937714816 -0.466886077 2.256372290 0.669470894 2.932525462
## [116] 3.478287425 1.391616168 2.118326109 2.386965644 1.228486533
## [121] -0.413528032 3.300248906 1.875707863 2.554864587 2.819341062
## [126] 0.227161757 -1.452228004 4.025204696 2.168795746 1.937025403
## [131] 0.021424613 4.980938162 2.797625897 0.787023015 0.964162992
## [136] 1.241074510 1.285468412 1.977582910 0.167900297 0.270895064
## [141] 1.395779159 3.591536082 4.058971580 2.539896498 0.647103708
## [146] -0.205524325 -0.300788502 1.398177934 -0.122276472 2.229300024
## [151] 1.197424526 5.026313700 0.001975712 2.411165881 1.408139069
## [156] 3.549472740 -0.412302858 3.362745931 -0.998544580 2.362031429
## [161] 1.890737159 2.003650673 -0.664821990 1.878542912 -1.195843558
## [166] 2.339436716 1.739921476 4.194267582 2.056000110 4.171889672
## [171] 1.407019752 1.017248943 2.728342383 3.110178969 3.708601598
## [176] 3.798673768 3.603001115 -0.852651403 0.584732627 2.963363107
## [181] 0.707380439 2.777706189 2.141100853 4.608066706 1.248204687
## [186] 1.111529125 0.869009492 0.761559882 3.200158922 3.264505863
## [191] -1.079178002 2.963826608 3.280293544 0.867398583 1.127536268
## [196] 1.369006521 3.098055661 0.135720012 0.515333658 3.396114928
## [201] 5.247966333 2.688101575 0.842640514 3.265464254 2.529634791
## [206] 1.037064104 0.398775259 2.908166835 1.001596048 -0.514667194
## [211] 0.880574149 0.800895432 -0.224082422 2.544632159 1.823455971
## [216] -0.224335693 1.073669908 0.073960031 4.273908071 6.196415207
## [221] 5.676410225 3.363331284 -0.936296982 4.000668971 1.622985540
## [226] 0.068404191 1.176475142 3.429656055 3.416952572 2.291611836
## [231] 2.602141854 2.415200497 1.300414768 3.439331358 4.020001443
## [236] 1.106696812 -0.594560209 0.501360852 4.247218607 2.523731638
## [241] 2.707108680 3.752511370 2.894097741 2.647523784 3.807279354
## [246] 3.319387411 2.306003543 1.049012665 1.823571653 5.094663747
## [251] 1.893538112 2.136748072 1.291566619 0.765436698 1.379277281
## [256] 2.963045567 -0.695473564 2.566529941 4.273584784 3.460452702
## [261] 5.117364949 0.664109717 -1.020939135 1.087650152 3.373515165
## [266] 2.071374452 0.583851842 0.379234169 2.905616978 1.873881735
## [271] 5.171919307 -0.335591042 3.940047797 0.775103809 2.635183135
## [276] -0.459101548 3.281434927 2.826557111 -0.451146704 1.575828160
## [281] 0.925787880 3.674247135 1.858296997 1.771919716 0.703224132
## [286] 2.579438717 3.803453744 2.087316387 3.600449160 3.679330445
## [291] 4.270884357 2.989631244 3.952852862 3.559064935 2.354399796
## [296] 0.914442244 2.191114092 2.138425921 1.967064876 2.273726383
## [301] 0.220879177 4.082999903 1.671456432 3.195961515 1.207592942
## [306] 2.875189212 1.857190718 1.084614217 4.906765391 1.343667168
## [311] 2.032315523 2.476480179 -1.070792622 2.020971032 6.186236925
## [316] 1.138593439 0.043309479 2.643123040 0.994689548 1.888622999
## [321] 1.080057360 1.644525065 2.153317970 2.442957840 4.798494667
## [326] 1.163670125 1.348058061 4.164677285 3.826269969 1.925113405
## [331] 3.231813577 1.088646383 2.024858178 0.547109467 -0.489607061
## [336] -0.309901376 -1.581730735 4.949248212 0.068491227 2.908237304
## [341] 2.178363044 2.459361173 2.178638877 1.740774488 3.698397464
## [346] 1.533467903 0.896601845 2.302783062 3.875482802 1.267143494
## [351] -1.275594605 1.423002596 3.992722900 1.603951948 1.318473683
## [356] 2.619657820 4.629449224 2.563049528 2.630892816 2.743201800
## [361] 4.115788134 1.459013505 2.729805458 0.949905576 2.425971915
## [366] 3.769413950 1.439217960 -0.107846992 -1.316618571 1.622461164
## [371] 0.050267712 1.005908204 1.013830687 2.356625013 2.949415017
## [376] 2.419453385 3.555284265 2.281199490 1.225283126 -0.585133676
## [381] 0.945452145 4.582033460 0.542360140 3.911150176 1.372389495
## [386] 0.446155013 0.966667218 4.579783303 0.743109326 0.801345528
## [391] 1.171484752 1.874731349 2.129289797 0.519047519 2.485590596
## [396] 0.430349118 2.398755145 3.223449261 0.351903472 1.676357318
## [401] 1.694215402 3.213743486 1.477893515 2.050495511 0.826578822
## [406] 3.052117622 0.768667441 2.682874309 2.263838812 2.159695842
## [411] 2.423292793 1.668600112 1.655704478 1.952707918 2.830999537
## [416] 1.289467147 2.069350208 3.981261607 4.461629303 0.885217324
## [421] -1.000522134 4.727642410 3.203293240 -0.119996675 3.485061128
## [426] 2.875660433 1.884146311 2.187822607 1.293867247 1.604578698
## [431] 1.214136516 0.076391492 -1.375950312 4.905165395 0.151170923
## [436] 2.807384753 1.655845750 3.038619123 5.173248210 2.450901088
## [441] 5.871866602 1.485345748 1.513342255 1.460967255 2.162043500
## [446] 3.453910073 2.824242021 2.006432226 0.219350190 1.947260781
## [451] 3.904376096 3.076547385 0.895933964 2.885090663 3.432678389
## [456] 2.467654190 -0.309343140 0.411438610 0.668180670 -0.249866193
## [461] 4.125051888 0.406004489 -1.518594308 3.076504685 3.461789479
## [466] 2.141568571 2.519208042 1.530850258 2.068421482 3.495426912
## [471] 3.522961496 1.326560892 1.615080922 1.188746739 4.549208443
## [476] 2.600803242 2.206499565 2.678741728 3.709414226 2.360060202
## [481] -0.447019627 1.218309391 -0.105587315 0.170505443 1.504964369
## [486] -1.298939150 3.404916953 0.803177473 -0.298411375 2.434916767
## [491] 5.141913206 3.724655757 0.601177526 3.169820501 0.883370835
## [496] 0.727378670 0.498719820 0.480091499 -0.631062634 2.432687598
## [501] 3.706545074 3.677513578 1.224027274 3.113150202 0.750769038
## [506] -0.301181061 2.250694938 2.219217935 1.977742786 2.597814723
## [511] -0.131138480 1.623764959 1.395725615 1.656500801 1.491236585
## [516] 3.486321194 2.971195807 4.198588644 3.771777750 3.774450382
## [521] 0.692904857 2.471132795 2.934745524 0.064860154 1.742114586
## [526] 2.926401793 4.437657223 3.020597844 0.337597041 4.189059180
## [531] 1.711568139 -0.425900220 0.801755266 0.186310709 3.705099926
## [536] 1.435737117 1.185118073 2.257769481 3.407767771 2.849783013
## [541] 2.992534017 1.178175770 2.361699770 2.056208437 1.963282502
## [546] 2.674198081 1.413175111 1.171207926 0.961810184 3.562846689
## [551] 0.001426836 3.596475227 -1.655739050 0.427573403 1.795434721
## [556] 4.762212076 0.991994118 3.277619888 0.995769527 4.980927125
## [561] -0.452281620 0.648884615 2.079987530 2.076727813 1.182485741
## [566] 1.873811502 2.007571021 1.882434511 3.254327739 -0.170096009
## [571] 3.044520782 0.549099392 0.793326706 -0.324500209 -0.374584060
## [576] 2.771876306 4.088093419 1.564986777 1.577381866 1.853214755
## [581] 0.777356561 2.637903644 0.747007199 -0.339107305 2.979966846
## [586] 2.127998150 2.192451448 2.193779509 2.022839501 0.085484092
## [591] 0.559737910 4.109813321 -2.095299906 4.601292342 0.315577419
## [596] 0.449076192 0.809628474 1.586657322 2.124452955 3.275283094
## [601] 1.849713514 1.002829277 1.823378994 -0.624164340 3.829338711
## [606] -0.613596411 1.674633812 0.834201865 2.466366711 -0.655043180
## [611] 0.564251186 4.789306612 0.445343387 5.696914808 3.627024607
## [616] 2.835437773 1.131054338 3.682889822 2.856937115 1.758801284
## [621] 4.312855495 1.460316592 3.223820266 1.309562290 3.389119803
## [626] 1.908329477 0.846784673 2.357666541 -0.192927748 2.538130654
## [631] 4.197891741 1.413608844 -0.525329086 1.499710994 2.906618869
## [636] 1.717995855 0.538062527 1.960436077 1.646467474 1.850500170
## [641] 1.604813063 4.190557323 0.811225173 1.588543547 4.173425897
## [646] 2.618060289 4.171309623 2.614054244 1.865698725 3.365848288
## [651] 2.226845191 3.264591113 -0.325397333 1.055424752 0.375334260
## [656] 3.020184514 2.521406704 1.543412285 2.550969607 -0.606162613
## [661] -0.656644329 2.462253208 -1.666150393 1.386371287 3.290618392
## [666] 1.095412110 1.400150333 1.244357560 0.831328579 4.520641709
## [671] -1.000364433 3.788260599 0.722632048 1.531094160 1.726640457
## [676] 1.340683855 1.183896990 2.919382193 1.102226846 4.162641720
## [681] 3.491886943 2.261490517 4.798242119 1.971833866 3.902422510
## [686] 1.482955956 -0.644399751 1.972067776 4.063046313 0.196186999
## [691] 2.626947098 -0.984860714 3.321227718 1.936266560 2.075171541
## [696] 1.354901244 1.933936205 0.252627061 2.953882468 1.070892082
## [701] 2.172754280 3.405652172 1.487034369 2.394833090 2.350080757
## [706] 3.598330220 -0.188118404 1.717818434 2.301609934 1.610906636
## [711] 2.497365191 0.944813637 1.578107242 -1.391068822 2.363070687
## [716] 2.754318331 1.963866550 0.522656479 -0.932336963 4.529820567
## [721] 4.535804796 5.789012033 1.823586017 0.599283398 1.087248063
## [726] -1.739174232 1.742781179 -0.134534184 -0.014040832 -0.646363199
## [731] 2.289784523 2.891792144 3.174212576 2.007737082 1.331272998
## [736] 3.101431107 2.727126352 2.201573495 3.042505391 1.699238585
## [741] 3.695679969 3.846874301 3.916611540 3.067523911 3.459379087
## [746] 5.372152587 2.128862802 1.942682407 -0.957937451 1.533144227
## [751] 1.131658858 1.111289619 0.712329765 3.449536040 3.165923211
## [756] -1.749404788 -0.928863720 2.820332950 2.487001075 2.922057555
## [761] 1.887473492 0.671591446 2.099569531 2.016107197 2.643881568
## [766] 3.173742111 0.617294677 0.382916623 0.781165170 -1.054597602
## [771] -0.528957192 3.835674559 4.674451289 2.886821211 4.368170914
## [776] 0.341337659 1.863294963 1.629965115 4.024879480 -0.532005051
## [781] 1.117950828 1.069379422 1.767143171 1.267085341 2.593013428
## [786] 2.583741464 1.622874771 0.143041715 3.919337728 -0.134919585
## [791] 3.478836016 1.373205836 2.587106412 2.837114035 2.661576789
## [796] 0.505212812 2.179293390 4.411258156 2.312644063 3.535971708
## [801] 2.121551782 1.304466954 1.873287149 0.971330545 0.877567585
## [806] 3.694901529 -0.244056140 3.812443598 -0.511530803 1.259393899
## [811] 2.314123334 2.761530557 -1.491407671 -0.109694871 0.590782341
## [816] 0.102176057 1.441105349 0.542550785 3.051805899 1.974227870
## [821] 0.541514026 3.576460355 0.425754130 1.746449142 2.224129970
## [826] 3.999578143 2.023381700 2.664380717 2.540384336 2.353327711
## [831] 1.647424439 1.824024295 2.643755799 2.385605497 4.715161185
## [836] 3.386408332 2.242501216 4.982648701 1.109108743 -0.235646483
## [841] 1.266297539 1.973624192 0.482516476 -1.019954204 4.545408473
## [846] 1.037887728 3.882095058 0.988240390 2.494925146 0.112544344
## [851] 5.568664642 3.659286935 0.484807165 3.379451382 2.800361173
## [856] 5.917450215 1.008408112 2.462593682 0.754330731 0.438003150
## [861] -1.005298691 1.671907747 2.673073499 4.386200916 2.341044447
## [866] 0.333835368 4.811512152 -0.087761439 3.351551395 3.375684391
## [871] 0.867658787 2.134196947 4.522708000 3.646964053 3.428545312
## [876] 0.474797506 2.383965154 0.687332284 0.222278834 1.714769824
## [881] 1.990791457 1.499365842 0.617535213 2.445947144 4.073301202
## [886] 5.191535378 1.850631510 2.530039885 3.342985648 -1.854672217
## [891] 3.404274671 1.496633075 2.484258215 2.718972935 -1.319544397
## [896] 0.092780585 1.481163698 3.394798518 2.418212617 3.302158314
## [901] 1.953194260 1.310317509 2.034332240 2.068468522 2.973729094
## [906] 4.480464078 1.259660759 1.269998669 3.796272942 1.631736041
## [911] 2.850235095 1.435978899 2.121162379 4.117027175 3.076959428
## [916] -0.400745134 0.009857423 2.596362300 1.384884009 1.322564780
## [921] 4.137896853 2.956121536 0.240440974 -0.274277026 2.304079014
## [926] 0.319907793 1.561897735 -0.514680213 1.171866307 0.729465814
## [931] 3.589326431 1.535755486 4.199680177 0.093265292 2.441985930
## [936] 3.279735723 3.004154917 6.252110140 0.540363036 0.153472880
## [941] 4.447217194 3.130428054 0.284222771 1.538933607 3.893861088
## [946] 0.835160106 3.361086444 1.807312009 0.916601053 0.344144407
## [951] 2.953598813 0.262050009 4.038659150 3.561131903 3.661436811
## [956] 2.479456041 0.939512202 3.369168859 1.926401680 2.233581522
## [961] 3.233826831 0.844089870 3.238901640 5.083396890 0.768924952
## [966] 3.648814610 4.186953209 0.638222878 1.322371097 4.377999827
## [971] 0.171002110 1.637723642 3.810481239 1.613217592 2.674855341
## [976] 3.648562743 2.034957532 0.852820346 1.469414786 3.483417841
## [981] 0.494425023 2.269006233 4.901418352 2.069647629 2.200726851
## [986] 0.898501513 4.753990827 1.163342293 1.981031874 2.754153385
## [991] 4.030990209 2.269479027 0.822790758 1.436812408 0.586205384
## [996] -3.575411645 2.893262542 2.756701543 0.525447365 1.441007718
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.867 1.111 2.039 2.066 3.116 7.838
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.5754 0.8513 1.9366 1.9371 3.0050 6.7950
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%
## -0.5687671
## 5%
## -0.585605
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%
## 4.51198
## 95%
## 4.523064
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%
## -0.5687671
## 5%
## -0.585605
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE
## [85] TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [289] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## [517] FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE
## [529] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [661] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [793] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE TRUE 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 TRUE 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 TRUE FALSE TRUE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [973] TRUE 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
## [1] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE TRUE 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 TRUE 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 TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE 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 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [661] TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [757] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE TRUE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE
## [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] -0.7285658 -2.3337546 -1.6271487 -0.7242915 -0.8837255 -0.8912001
## [7] -1.6003611 -1.8859692 -1.1810082 -0.8298468 -1.3853452 -1.7121161
## [13] -1.4205363 -0.6414625 -0.9050411 -1.1524432 -0.7155081 -0.8502939
## [19] -1.4452272 -1.4689936 -0.5908751 -1.6747068 -1.0407864 -1.9833184
## [25] -0.6266021 -2.8674344 -0.5799619 -2.2634616 -1.5096696 -0.8755613
## [31] -0.9530191 -1.5375383 -1.7775686 -1.3558491 -0.5700481 -0.9294501
## [37] -0.7739381 -0.8228332 -0.5746158 -1.4827669 -0.6632061 -0.8810491
## [43] -0.7959546 -1.0167037 -1.4601049 -0.8207085 -1.8704497 -1.0568170
## [49] -0.8284361 -0.6911602
## [1] -1.0568895 -1.2263890 -0.6071011 -0.6209662 -1.8876447 -0.9675244
## [7] -1.4522280 -0.9985446 -0.6648220 -1.1958436 -0.8526514 -1.0791780
## [13] -0.9362970 -0.5945602 -0.6954736 -1.0209391 -1.0707926 -1.5817307
## [19] -1.2755946 -1.3166186 -1.0005221 -1.3759503 -1.5185943 -1.2989391
## [25] -0.6310626 -1.6557390 -2.0952999 -0.6241643 -0.6135964 -0.6550432
## [31] -0.6061626 -0.6566443 -1.6661504 -1.0003644 -0.6443998 -0.9848607
## [37] -1.3910688 -0.9323370 -1.7391742 -0.6463632 -0.9579375 -1.7494048
## [43] -0.9288637 -1.0545976 -1.4914077 -1.0199542 -1.0052987 -1.8546722
## [49] -1.3195444 -3.5754116
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.51198
## 95%
## 4.523064
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
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## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
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## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [925] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE
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## [997] FALSE FALSE FALSE FALSE
## [1] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
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## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE TRUE TRUE 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 TRUE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [313] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [385] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [613] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [721] TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [853] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [985] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
## [1] 50
data[Top5Percent==TRUE]
## [1] 4.526409 4.540596 5.581311 5.821858 4.612144 5.070145 4.905616 5.092976
## [9] 4.518309 6.509264 7.023102 4.897746 4.853377 4.980797 4.616280 5.382979
## [17] 4.600058 5.131186 5.117272 4.998352 4.973077 4.882085 5.076792 4.532313
## [25] 4.538663 4.514078 4.700922 5.268170 5.121688 4.764602 5.285461 5.189319
## [33] 5.644717 5.445007 5.494889 4.640331 4.640735 7.838257 4.915958 4.835032
## [41] 5.988850 4.649173 4.707599 5.432143 5.551210 5.817822 4.523101 4.620750
## [49] 5.146676 4.775463
## [1] 6.795050 4.678494 4.696390 5.568949 5.499329 4.776674 4.980938 5.026314
## [9] 4.608067 5.247966 6.196415 5.676410 5.094664 5.117365 5.171919 4.906765
## [17] 6.186237 4.798495 4.949248 4.629449 4.582033 4.579783 4.727642 4.905165
## [25] 5.173248 5.871867 4.549208 5.141913 4.762212 4.980927 4.601292 4.789307
## [33] 5.696915 4.798242 4.529821 4.535805 5.789012 5.372153 4.674451 4.715161
## [41] 4.982649 4.545408 5.568665 5.917450 4.811512 5.191535 6.252110 5.083397
## [49] 4.901418 4.753991