# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Jen Marie B. Talaugon
# Submitted to: Prof. Carlito O. Daarol
# Math Department
# March 23, 2023
# Processing of continuous data
# Using random number generators
# Exer1: generate data with mean 2 and standard deviation 1.5 using rnorm()command
data <- rnorm(1000,2,1.5) # 1 thousand values
length(data) # count number of elements
## [1] 1000
data[1:20] # display first 20 elements
## [1] 1.4959250 0.2727201 1.8854381 1.4972984 4.3246445 3.1098109 5.8561149
## [8] 1.3830068 4.6353211 0.4230150 5.0610136 2.1788557 1.7175754 2.7068618
## [15] 4.5963158 2.8119726 1.6884906 1.6366055 1.6138264 2.1719013
data[1:300] # display the first 300 elements
## [1] 1.49592502 0.27272006 1.88543808 1.49729840 4.32464449 3.10981094
## [7] 5.85611487 1.38300676 4.63532111 0.42301498 5.06101364 2.17885575
## [13] 1.71757540 2.70686178 4.59631585 2.81197264 1.68849065 1.63660546
## [19] 1.61382642 2.17190126 1.99805695 1.53103577 3.20984498 4.87581679
## [25] 3.63822792 0.22615004 1.91465276 2.10689492 -1.24820632 1.46986637
## [31] 0.80450187 2.15331208 2.85276519 4.31043217 2.38784676 2.08824724
## [37] 1.74564119 0.17056910 2.75701516 2.01536333 1.01680996 5.42294350
## [43] 1.20357473 3.60863773 0.65595981 0.72438535 -0.34773246 3.52083136
## [49] -0.18511918 4.58549647 2.15531275 1.77341984 2.30819536 2.67421388
## [55] 1.00511012 -0.15396848 -1.16515608 3.16596713 0.74180588 1.33361249
## [61] 1.59845663 1.95548152 1.88967293 2.16816749 0.54269997 -0.81440800
## [67] 3.81330783 4.68901362 2.70370453 0.25747165 7.04756732 2.08272154
## [73] 1.46202129 0.78795377 4.47966422 1.38192002 2.50044157 1.38118325
## [79] 0.46937936 -0.18702809 0.15906436 1.03028880 -0.31564815 3.50969581
## [85] 4.60552890 3.45457619 0.68416533 3.30547505 5.51976432 4.24253493
## [91] 0.53055761 0.82181002 3.65877682 2.69751103 1.23369241 1.14334968
## [97] -0.02002216 1.89754112 1.77668208 4.15611564 0.28825281 3.50826706
## [103] 0.73450214 3.28462618 0.50504377 3.52005010 1.43365439 1.31898452
## [109] 2.61903580 1.88757020 3.67423095 3.35003618 2.15275064 0.07716550
## [115] 2.38277084 2.36017894 2.08513382 0.75208865 3.60065606 0.68608964
## [121] 1.07852778 0.63329967 3.33565572 0.91710338 1.84044748 2.56507939
## [127] 5.02492613 4.79765911 1.84367109 4.49305338 -2.01264277 3.79634012
## [133] 4.95084107 1.44939141 2.10501757 -0.09621848 -0.55063707 3.78367874
## [139] 1.95722244 -1.16496469 1.84008134 3.18434640 1.86422449 3.05413800
## [145] 2.88241841 2.34727292 1.30950067 2.75936698 3.66305276 -0.03624156
## [151] 2.48875385 3.12925969 1.22315607 1.42407417 5.57301721 -0.47885923
## [157] 3.05389153 1.12492805 1.92789316 3.23667666 3.58455010 3.37993028
## [163] 3.13910742 4.83558765 1.41649909 1.56991582 1.69395260 2.13479020
## [169] 3.28590745 4.35250398 1.45329989 0.17292007 1.30286782 -0.68408066
## [175] 2.05208077 1.38954180 0.90003854 5.39057683 0.04594060 -0.60354676
## [181] 1.66679746 1.08419187 2.65046512 4.31081246 1.20341039 1.43400384
## [187] 1.31244487 1.97130646 1.72736064 0.49163574 3.64761695 0.34058376
## [193] -0.27006217 2.91108931 4.78078066 3.25212155 1.03361882 2.89137403
## [199] 1.71925510 0.01388928 2.24988802 3.60575867 0.70085147 0.24318487
## [205] 2.91674829 3.85883645 2.42027937 1.13157817 2.37734008 3.42218178
## [211] 3.16072897 4.86180680 2.42632571 1.43016032 5.22110132 0.74697794
## [217] 3.47088331 0.87843996 2.16193766 1.81701788 0.85495740 0.35129257
## [223] 3.07604255 1.86889882 2.45926011 3.23757222 2.96009007 2.97232353
## [229] 1.23383267 1.42343560 2.88959786 0.73765962 -0.32442438 1.17106474
## [235] -0.31048630 2.66426349 0.65503271 -2.16851878 3.94427620 2.44993063
## [241] 1.79926721 0.28781473 0.90888941 2.04508064 5.69374290 4.47002871
## [247] 2.00026180 2.39618672 3.79707025 1.41684691 3.08000229 4.78863989
## [253] 2.41432556 2.75068040 5.16386154 4.59837105 2.78776067 2.29679933
## [259] 1.99318336 1.37951084 4.42839291 1.76687919 0.92094840 4.21338826
## [265] 1.64493798 4.94811433 1.37584605 1.20837599 4.30732285 3.12010222
## [271] 2.27733478 3.40405523 1.53230073 3.34809995 1.34689734 1.87802230
## [277] 2.66201857 0.89228641 4.99443006 2.98018287 1.87656497 5.26052615
## [283] 1.64158645 -0.23750994 -0.45692300 0.46098077 1.93349224 2.05600160
## [289] 0.70201156 2.43198427 3.10083235 1.35875243 1.51774460 2.83245032
## [295] -1.13280645 3.98019723 1.76465008 4.64694996 5.32018389 0.29305790
# 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] -3.00086939 -2.89937002 -2.79787066 -2.69637130 -2.59487194 -2.49337258
## [7] -2.39187322 -2.29037386 -2.18887450 -2.08737514 -1.98587578 -1.88437642
## [13] -1.78287706 -1.68137770 -1.57987834 -1.47837898 -1.37687962 -1.27538025
## [19] -1.17388089 -1.07238153 -0.97088217 -0.86938281 -0.76788345 -0.66638409
## [25] -0.56488473 -0.46338537 -0.36188601 -0.26038665 -0.15888729 -0.05738793
## [31] 0.04411143 0.14561079 0.24711016 0.34860952 0.45010888 0.55160824
## [37] 0.65310760 0.75460696 0.85610632 0.95760568 1.05910504 1.16060440
## [43] 1.26210376 1.36360312 1.46510248 1.56660184 1.66810120 1.76960056
## [49] 1.87109993 1.97259929 2.07409865 2.17559801 2.27709737 2.37859673
## [55] 2.48009609 2.58159545 2.68309481 2.78459417 2.88609353 2.98759289
## [61] 3.08909225 3.19059161 3.29209097 3.39359034 3.49508970 3.59658906
## [67] 3.69808842 3.79958778 3.90108714 4.00258650 4.10408586 4.20558522
## [73] 4.30708458 4.40858394 4.51008330 4.61158266 4.71308202 4.81458138
## [79] 4.91608074 5.01758011 5.11907947 5.22057883 5.32207819 5.42357755
## [85] 5.52507691 5.62657627 5.72807563 5.82957499 5.93107435 6.03257371
## [91] 6.13407307 6.23557243 6.33707179 6.43857115 6.54007051 6.64156988
## [97] 6.74306924 6.84456860 6.94606796 7.04756732
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%
## -3.000869 1.003440 1.999159 2.973210 7.047567
## 0% 25% 50% 75% 100%
## -2.2512646 0.9161359 1.9863926 2.9767851 6.0366483
# 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] 1.495925023 0.272720057 1.885438084 1.497298404 4.324644492
## [6] 3.109810943 5.856114870 1.383006756 4.635321107 0.423014977
## [11] 5.061013645 2.178855745 1.717575399 2.706861779 4.596315846
## [16] 2.811972636 1.688490649 1.636605460 1.613826424 2.171901261
## [21] 1.998056948 1.531035774 3.209844981 4.875816792 3.638227925
## [26] 0.226150043 1.914652759 2.106894922 -1.248206322 1.469866372
## [31] 0.804501870 2.153312078 2.852765188 4.310432167 2.387846763
## [36] 2.088247238 1.745641191 0.170569102 2.757015158 2.015363334
## [41] 1.016809960 5.422943504 1.203574729 3.608637733 0.655959808
## [46] 0.724385354 -0.347732457 3.520831364 -0.185119180 4.585496472
## [51] 2.155312752 1.773419840 2.308195356 2.674213877 1.005110124
## [56] -0.153968478 -1.165156077 3.165967131 0.741805876 1.333612487
## [61] 1.598456630 1.955481525 1.889672929 2.168167488 0.542699973
## [66] -0.814407998 3.813307835 4.689013624 2.703704534 0.257471646
## [71] 7.047567318 2.082721536 1.462021286 0.787953772 4.479664217
## [76] 1.381920018 2.500441566 1.381183252 0.469379364 -0.187028087
## [81] 0.159064362 1.030288803 -0.315648151 3.509695813 4.605528899
## [86] 3.454576187 0.684165325 3.305475045 5.519764322 4.242534932
## [91] 0.530557613 0.821810023 3.658776815 2.697511027 1.233692409
## [96] 1.143349681 -0.020022159 1.897541125 1.776682079 4.156115638
## [101] 0.288252809 3.508267062 0.734502144 3.284626176 0.505043766
## [106] 3.520050102 1.433654395 1.318984524 2.619035800 1.887570205
## [111] 3.674230949 3.350036181 2.152750645 0.077165497 2.382770841
## [116] 2.360178944 2.085133815 0.752088651 3.600656063 0.686089640
## [121] 1.078527780 0.633299673 3.335655718 0.917103385 1.840447483
## [126] 2.565079386 5.024926126 4.797659112 1.843671091 4.493053384
## [131] -2.012642770 3.796340119 4.950841065 1.449391412 2.105017573
## [136] -0.096218479 -0.550637067 3.783678738 1.957222442 -1.164964686
## [141] 1.840081343 3.184346401 1.864224489 3.054137998 2.882418407
## [146] 2.347272923 1.309500671 2.759366984 3.663052763 -0.036241559
## [151] 2.488753847 3.129259687 1.223156069 1.424074172 5.573017206
## [156] -0.478859230 3.053891525 1.124928055 1.927893159 3.236676657
## [161] 3.584550100 3.379930282 3.139107422 4.835587652 1.416499094
## [166] 1.569915818 1.693952600 2.134790201 3.285907451 4.352503980
## [171] 1.453299886 0.172920073 1.302867825 -0.684080663 2.052080766
## [176] 1.389541804 0.900038543 5.390576828 0.045940600 -0.603546755
## [181] 1.666797462 1.084191871 2.650465119 4.310812458 1.203410389
## [186] 1.434003835 1.312444871 1.971306459 1.727360644 0.491635741
## [191] 3.647616948 0.340583758 -0.270062166 2.911089313 4.780780662
## [196] 3.252121554 1.033618815 2.891374034 1.719255100 0.013889283
## [201] 2.249888020 3.605758674 0.700851470 0.243184869 2.916748291
## [206] 3.858836452 2.420279370 1.131578168 2.377340084 3.422181775
## [211] 3.160728972 4.861806804 2.426325706 1.430160316 5.221101323
## [216] 0.746977938 3.470883307 0.878439961 2.161937659 1.817017877
## [221] 0.854957402 0.351292568 3.076042555 1.868898825 2.459260109
## [226] 3.237572220 2.960090065 2.972323530 1.233832674 1.423435598
## [231] 2.889597863 0.737659624 -0.324424378 1.171064739 -0.310486304
## [236] 2.664263491 0.655032709 -2.168518782 3.944276203 2.449930629
## [241] 1.799267205 0.287814731 0.908889410 2.045080640 5.693742899
## [246] 4.470028715 2.000261801 2.396186723 3.797070251 1.416846915
## [251] 3.080002293 4.788639892 2.414325556 2.750680397 5.163861544
## [256] 4.598371049 2.787760674 2.296799335 1.993183356 1.379510844
## [261] 4.428392910 1.766879193 0.920948399 4.213388256 1.644937980
## [266] 4.948114331 1.375846050 1.208375994 4.307322853 3.120102220
## [271] 2.277334781 3.404055231 1.532300730 3.348099949 1.346897340
## [276] 1.878022295 2.662018566 0.892286414 4.994430063 2.980182866
## [281] 1.876564967 5.260526145 1.641586455 -0.237509942 -0.456922999
## [286] 0.460980768 1.933492238 2.056001597 0.702011563 2.431984268
## [291] 3.100832347 1.358752427 1.517744602 2.832450319 -1.132806451
## [296] 3.980197233 1.764650075 4.646949958 5.320183887 0.293057897
## [301] 2.447685780 1.692973436 5.304386923 1.870028339 -0.582515708
## [306] 1.518058034 2.564437732 5.262266734 2.721041258 0.350831861
## [311] 0.582136502 2.375978693 3.457455520 -0.665793451 2.820864274
## [316] 0.938516331 1.298991136 4.860043724 1.239609891 2.793249498
## [321] 2.440720459 1.305103951 0.139429914 2.215350924 1.731173259
## [326] -0.072671270 4.716598354 -1.502474704 4.535715493 2.230577343
## [331] 4.435418282 1.796701881 2.421364826 0.414653566 4.140505577
## [336] 3.740657128 2.267530308 1.446215975 2.673831848 2.265301626
## [341] 0.337879307 0.298042150 0.983140795 -0.615149564 4.128374161
## [346] 1.039124703 0.969322449 -0.487413521 1.003772430 1.772013677
## [351] 2.710817012 4.193473116 4.622510731 2.047776341 2.869074805
## [356] -0.651413447 0.780669693 2.418152646 3.494430258 2.972277146
## [361] 2.416863060 1.665437432 0.047700988 0.698532766 3.006420044
## [366] 1.624851932 2.624894865 1.670525557 1.045761071 3.213658720
## [371] 2.232026967 1.385953920 3.699249622 2.056825092 6.522366976
## [376] 3.047024698 1.144925629 3.157630583 4.440405322 1.790709577
## [381] 1.867779995 1.002443844 3.801310399 3.184862787 2.975804959
## [386] -0.895682169 0.901634717 4.672739787 3.145538499 2.663461407
## [391] 4.801868041 1.638444202 3.825120320 -0.763649621 1.513594571
## [396] 2.457075816 3.863568461 3.989167295 2.609482529 0.077813411
## [401] 2.737856190 3.310079617 1.825701993 0.012823619 2.156632919
## [406] 1.705342750 -1.162690091 1.341850834 1.724084658 3.350085755
## [411] 5.074654768 3.802328044 1.765149177 3.099073838 3.431301182
## [416] 2.664032897 0.434324842 0.680506826 0.615466769 0.780483793
## [421] 1.490228218 0.853118068 0.150947625 1.201705566 3.714075326
## [426] 1.145153707 1.399957760 2.605834139 1.751981833 -0.350981836
## [431] 1.973478480 0.498905663 2.537771536 1.178238437 4.556932500
## [436] 3.814142590 2.408255370 0.861621562 0.450561854 3.077494217
## [441] 3.456574926 2.362620619 1.835106810 1.885384410 2.518544506
## [446] 2.583073248 -0.250467455 1.760647079 3.949892441 2.258454386
## [451] 2.623505140 2.269445495 3.318123289 2.499095302 4.040750462
## [456] 2.440685523 -0.024417106 2.937064586 -0.640954076 4.669074442
## [461] 1.945612902 0.861914495 4.573297060 1.187568915 1.816057593
## [466] 1.503647037 2.082526746 3.565251832 4.118409416 1.619513535
## [471] 2.078476435 4.165243121 5.197346276 0.502811281 1.811174878
## [476] 3.978031164 4.534984382 0.551743082 2.114651688 0.408962187
## [481] 2.266725619 0.561030564 2.867264581 -0.824117405 2.343385145
## [486] 3.511410232 2.126580840 0.994078920 1.152814621 2.522861005
## [491] 2.133029067 2.737477267 1.120056162 3.787527171 4.417002534
## [496] 1.632294602 -0.623713429 2.396262086 2.469073696 0.048038058
## [501] 2.416796896 1.848962695 1.995619349 2.190747007 1.067098829
## [506] 2.715563823 1.010880760 0.030305543 -0.629953997 0.952585802
## [511] -1.175415297 1.128373244 0.845181068 0.897221517 2.103708308
## [516] 2.873734661 2.972345564 1.047700899 0.672175233 1.252457262
## [521] 0.316981535 1.740893765 1.701359227 2.520459207 1.047391072
## [526] 2.464555782 3.410447259 1.288006980 1.311585118 2.774870853
## [531] 3.345746559 0.813729259 0.358298505 0.659303332 3.070083551
## [536] 2.348698097 2.227748671 2.713212259 0.913221509 0.802760571
## [541] 1.232647066 1.210637637 -0.303652783 3.062458902 2.031310202
## [546] 2.939347460 1.217720077 3.051759806 3.294458619 3.994173810
## [551] 1.724251452 2.320692533 0.454709300 2.279144444 0.898157470
## [556] -0.666670346 0.768720061 2.242595553 1.464308880 -0.715884704
## [561] 0.215275333 1.143986966 1.380575745 1.031310612 2.951987923
## [566] 1.334107453 -1.529760233 0.471375903 -0.065562042 3.189218608
## [571] 2.934692154 3.268927504 4.415359508 -0.061645129 3.360072098
## [576] 0.795992421 1.672141076 -2.634241346 2.715674254 0.636758408
## [581] 3.312336261 0.036361698 1.597362681 1.964066553 2.156250447
## [586] 2.862139678 3.721104014 2.708221286 2.656939165 1.383350226
## [591] 3.635244172 3.158926663 1.126154713 0.581451770 0.548105177
## [596] 2.097315017 3.982721002 1.933500745 2.001584017 3.243816050
## [601] 1.768881958 -2.160581381 -0.131549956 1.411184134 4.642588432
## [606] 2.803125468 1.881634425 2.344024592 5.244663907 -0.055618145
## [611] 2.609365064 2.792906171 0.559799771 1.659833182 0.954707244
## [616] 1.710677216 -0.724592077 1.742290607 3.162870704 -1.035194146
## [621] -0.153759481 2.263214890 5.175840930 1.945118683 2.249026904
## [626] 3.930392177 -0.091550810 2.855464504 2.059761071 3.060199546
## [631] 1.015652324 1.386743476 2.621719488 4.404545499 2.951253387
## [636] 0.550968005 3.076910298 1.382234428 2.532821004 0.693865268
## [641] -0.564915807 1.720872898 3.933851326 2.028069185 -0.342582793
## [646] 2.879160610 -3.000869385 2.815631165 2.123423106 1.160010671
## [651] 2.220951077 2.927499478 2.837886464 0.032588704 2.377124117
## [656] 3.246820400 -0.650816334 1.201633117 3.216331649 2.366307471
## [661] 3.079828133 1.040757001 0.871443646 2.094420708 2.818530744
## [666] 4.143698339 1.081454270 3.299817069 0.956211255 1.593373277
## [671] 3.163246507 0.949062018 2.106965864 2.678452939 0.699630594
## [676] 1.771096411 -0.366240746 3.831612565 2.334788623 2.423121120
## [681] -0.730866294 2.864596381 2.205529431 2.506615035 2.292557826
## [686] -0.788880033 2.701969753 2.586063036 0.866827199 0.683053556
## [691] 5.247503297 2.700400206 0.676579761 3.356498538 2.014557845
## [696] 3.257098022 0.019197987 1.746439853 -0.087213275 -2.312863590
## [701] -0.071041998 2.710812817 2.727194573 2.302570929 -0.848461092
## [706] 2.061091537 2.911200524 1.894555462 3.642901546 2.129386252
## [711] 1.407840737 2.171502182 0.561164520 3.660822721 3.183382141
## [716] 0.195866098 0.625381933 1.345813050 2.273833691 1.327496313
## [721] 2.199065168 4.117471086 2.435403532 1.955431622 2.360020141
## [726] 3.655247277 2.527004216 2.492465694 2.026797819 1.203680180
## [731] 1.981321314 3.345439767 1.750607291 2.265727075 -0.382158920
## [736] 1.523522901 2.467582519 1.368780560 0.291051117 0.401410283
## [741] 0.968831636 2.084556375 0.854842372 1.302121455 2.098676550
## [746] 2.728854108 0.811626018 2.263813151 3.756598317 -1.156041998
## [751] 2.950125773 1.118782602 2.667379150 0.326330561 4.322787307
## [756] 2.709518832 0.019360678 1.551388973 1.616716410 2.018378478
## [761] -1.007925103 4.086898074 4.166842469 0.462795512 0.242875554
## [766] 1.577398436 1.444952552 1.432738179 2.426634817 3.116151204
## [771] 1.651356808 1.340462198 2.282065249 -0.891324059 1.007550370
## [776] 3.894198200 2.314591516 1.373781957 0.503173743 -0.847759105
## [781] 4.277280800 2.934963896 4.433879613 0.972625537 -1.314342820
## [786] 0.007624295 3.756790404 3.234319919 1.181715429 0.770845089
## [791] 2.506166079 2.771517471 3.906462489 -0.007539027 2.980119164
## [796] 4.447852460 4.696946776 0.216290578 0.934300209 3.197791483
## [801] 1.672781842 2.727841386 1.800135313 1.202328518 5.207452363
## [806] 1.309791319 4.044302150 3.713015236 1.082221832 2.809388440
## [811] 1.637556419 1.729234628 3.182061241 2.181734205 -0.174208233
## [816] -1.547633549 2.506363298 -0.607404908 2.490761711 3.460849847
## [821] 0.566048035 4.106193729 1.766983707 2.679835919 0.378032883
## [826] 1.445349536 -0.780187144 0.702586519 0.955725599 -1.241162024
## [831] 1.448557648 1.086088862 2.472073660 1.046667586 2.128633207
## [836] 3.931283072 0.791874413 2.112626778 1.758017016 2.291696030
## [841] 5.439664523 2.618769533 3.209229998 2.623473421 -0.350066554
## [846] 3.068297768 2.293296750 2.367410906 0.932765769 -0.079537220
## [851] 3.074929125 3.153260891 1.822210676 -0.005772751 2.343018478
## [856] 1.051413208 1.773275545 0.763572150 2.098739654 1.526449476
## [861] 3.443869909 3.375007809 1.976655123 2.815455184 2.198082814
## [866] 3.218275460 1.230511122 2.159913803 -0.873686913 2.138258834
## [871] 1.352601130 3.176335954 -1.324477422 2.707009359 1.980107797
## [876] 1.415170515 -1.028962483 0.478081876 1.817750096 0.094682723
## [881] 2.729069974 -0.777024870 1.121992307 2.367132489 1.876108000
## [886] 2.934947495 1.972519585 0.766974977 3.025329892 3.769385536
## [891] 4.067412272 0.947928925 3.309469847 3.292017072 3.118222951
## [896] -0.980026904 3.446366974 1.659220914 2.570283431 0.611149970
## [901] 0.662552681 4.087348233 1.461509552 1.164861061 2.401122176
## [906] 6.027738517 3.376639150 2.897882650 1.306952445 0.264406419
## [911] 5.840946593 1.106296087 2.713640924 2.517727192 4.192309200
## [916] 2.372534505 2.618308939 2.019235724 2.025865187 1.156704222
## [921] 0.911899231 3.281754178 2.036778768 1.651715376 1.554469611
## [926] 3.154101522 1.263716515 3.693706815 2.908846310 0.035270244
## [931] 0.267009816 0.783072466 1.147406806 2.570085699 0.818393570
## [936] 4.474909531 1.982077443 -0.797050957 2.833003195 0.449266746
## [941] -0.105538259 0.371633929 2.392292220 2.799544481 4.117733557
## [946] 1.369391265 1.525766274 -1.980870603 2.259888498 1.026016899
## [951] 1.349337552 4.218508137 4.681458657 6.360570853 1.714514636
## [956] 1.198270704 4.304970573 3.728160464 3.349090082 -0.754876800
## [961] 3.212801127 2.541992099 0.191086364 2.669715295 1.415471188
## [966] 1.968279802 2.652956081 2.315640920 0.635842235 0.239538498
## [971] 1.092744106 1.689727714 1.166228185 3.667949851 1.426073614
## [976] 4.126090273 2.176651363 1.829865633 3.016839684 3.346627008
## [981] 3.112252684 2.753197089 1.751024512 0.072334713 0.066259427
## [986] 1.957404786 2.422276017 -1.250734484 1.158204819 0.706234427
## [991] 4.235811893 0.545822741 0.937846967 3.170729438 3.005012664
## [996] 1.188141117 4.458954622 2.111872398 2.629004878 3.561976967
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.001 1.003 1.999 1.996 2.973 7.048
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%
## -0.6077921
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%
## 4.586037
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%
## -0.6077921
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [685] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [781] FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [829] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [877] TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE 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] -1.2482063 -1.1651561 -0.8144080 -2.0126428 -1.1649647 -0.6840807
## [7] -2.1685188 -1.1328065 -0.6657935 -1.5024747 -0.6151496 -0.6514134
## [13] -0.8956822 -0.7636496 -1.1626901 -0.6409541 -0.8241174 -0.6237134
## [19] -0.6299540 -1.1754153 -0.6666703 -0.7158847 -1.5297602 -2.6342413
## [25] -2.1605814 -0.7245921 -1.0351941 -3.0008694 -0.6508163 -0.7308663
## [31] -0.7888800 -2.3128636 -0.8484611 -1.1560420 -1.0079251 -0.8913241
## [37] -0.8477591 -1.3143428 -1.5476335 -0.7801871 -1.2411620 -0.8736869
## [43] -1.3244774 -1.0289625 -0.7770249 -0.9800269 -0.7970510 -1.9808706
## [49] -0.7548768 -1.2507345
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.586037
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE TRUE FALSE
## [13] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE TRUE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] TRUE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE
## [133] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE 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 FALSE FALSE
## [193] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [253] FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
## [301] FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE 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 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE 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 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 TRUE 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] 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [841] TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.856115 4.635321 5.061014 4.596316 4.875817 5.422944 4.689014 7.047567
## [9] 4.605529 5.519764 5.024926 4.797659 4.950841 5.573017 4.835588 5.390577
## [17] 4.780781 4.861807 5.221101 5.693743 4.788640 5.163862 4.598371 4.948114
## [25] 4.994430 5.260526 4.646950 5.320184 5.304387 5.262267 4.860044 4.716598
## [33] 4.622511 6.522367 4.672740 4.801868 5.074655 4.669074 5.197346 4.642588
## [41] 5.244664 5.175841 5.247503 4.696947 5.207452 5.439665 6.027739 5.840947
## [49] 4.681459 6.360571