# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Zandra Marie Delgado
# Prepared by: 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
data[1:20] # display first 20 elements
## [1] 4.7708866 -0.3371247 -0.2316465 1.4929579 2.6232902 2.4323118
## [7] 1.9275441 -0.6013027 -0.2268779 2.6495123 2.9307323 3.6296406
## [13] 0.4332276 2.7302470 3.1119717 3.1019810 3.7105853 1.8416602
## [19] 2.8523276 2.8575038
data[1:300] # display the first 300 elements
## [1] 4.77088656 -0.33712465 -0.23164649 1.49295788 2.62329017 2.43231184
## [7] 1.92754406 -0.60130267 -0.22687795 2.64951230 2.93073230 3.62964062
## [13] 0.43322764 2.73024702 3.11197167 3.10198102 3.71058532 1.84166022
## [19] 2.85232763 2.85750382 4.27760079 -0.76699393 4.02368720 1.66532908
## [25] 1.77497485 2.97099839 3.17438831 0.75399333 -0.61121064 0.90828118
## [31] 1.27902311 3.29945542 1.78295034 1.34167251 4.26160033 0.13704194
## [37] 1.34074575 0.75744008 0.65914503 -0.25510467 3.91035313 1.46914220
## [43] 2.60051613 1.57513985 3.33783608 -0.37681592 3.45265393 4.08312304
## [49] 0.10075747 1.68679809 3.58754738 2.95258689 2.61675948 3.11705834
## [55] 2.22625339 -1.39370181 0.85911705 1.96574371 1.16333696 6.38556312
## [61] 3.64705882 0.41560660 2.69153054 1.76592353 0.64608978 3.16463018
## [67] 0.78393056 0.27835756 0.29473057 1.72316199 -0.20140222 1.68960045
## [73] 2.02141268 1.01746915 0.19588281 1.20718582 -2.41172845 1.04842128
## [79] 0.37479813 3.33268135 4.07726398 4.60178303 0.18138305 1.96474782
## [85] 2.28655049 2.24204147 -0.01985719 2.15302673 3.25965478 0.74468488
## [91] 0.84045939 4.03916144 3.80042421 2.89105119 3.63166834 0.38874463
## [97] 3.00733970 -0.88920895 2.38997663 4.36909677 0.82718973 2.40239742
## [103] 1.09121806 3.20108276 2.57587828 3.50018970 1.51629462 3.27973972
## [109] 0.38496710 2.29221463 -0.13894604 4.78312423 3.31534019 2.04401799
## [115] 1.09800858 5.60486456 3.18259642 2.14967593 1.15176258 1.33824768
## [121] 2.97675173 1.18094874 3.69902811 3.11271111 3.96669640 5.52503270
## [127] 2.49251745 2.17758807 3.97542745 0.33658835 1.07238312 2.67599853
## [133] 2.31366118 0.34936914 4.34371576 1.89744562 1.42782263 3.29047537
## [139] 1.08182617 1.61574050 0.20606189 2.28305488 3.05606986 -0.02549068
## [145] 1.84691238 5.00467775 0.96036692 0.47924065 -0.19167721 0.55569701
## [151] 3.11418171 0.60560736 2.50599556 1.91675758 1.85056297 2.34185653
## [157] 1.91516049 2.85383388 1.45840848 3.16378759 1.45379195 0.98957532
## [163] 1.70471527 3.05532508 3.00338887 0.63344131 2.46189262 3.54130655
## [169] 3.02536436 0.38957360 3.65176894 3.26771864 3.64699544 2.64218710
## [175] 3.02347869 2.77571181 3.64825988 2.53325887 3.86325904 1.70421475
## [181] -1.17160288 2.04045573 4.96129262 2.78299156 2.41698262 2.55288734
## [187] 3.67732897 0.57295098 4.27397926 1.20027267 4.27930853 2.68261855
## [193] 1.56873607 5.19434222 4.81020588 4.46833983 0.92080400 0.29261418
## [199] 2.75297178 1.19661910 1.14039838 -0.97570595 3.53359815 4.13450173
## [205] 2.04310500 -0.24930428 2.56125595 2.56802380 1.11644772 3.13677042
## [211] 2.83577128 1.58804686 2.35283003 4.41928758 2.77268385 2.56605922
## [217] 0.42261086 2.72086945 4.60923765 -0.68421430 1.75433767 0.31290146
## [223] 3.20672615 1.09443740 3.46742747 2.42088019 2.71379960 0.98626147
## [229] 1.73630006 3.99336346 4.23736218 4.97238784 2.62355198 0.72645273
## [235] 0.67564044 1.37814665 2.80039536 2.43412224 2.75743773 1.52744826
## [241] 2.57256206 0.46422385 4.83337566 -0.10149172 3.39377392 0.95817819
## [247] 2.13043781 3.21529739 1.55213421 1.02043289 2.81999517 2.31319222
## [253] 1.81623079 2.21097614 2.34530539 0.82402534 1.47123490 1.49796728
## [259] 1.95072667 -1.19388981 2.09443377 0.89407866 -0.61725597 2.84158803
## [265] 1.59510975 -0.01519995 1.68974190 -1.19723006 2.38529913 2.82836365
## [271] 4.51622505 3.10701235 3.45995339 3.50025797 0.52414386 1.79602126
## [277] 2.51913771 0.42007680 3.54089328 2.17376688 2.84614177 0.30271783
## [283] 3.64462912 3.43359438 0.74606652 2.38028591 -0.61910969 4.30897391
## [289] 2.60670502 4.51223311 1.97826961 1.32494144 1.63069100 4.35372346
## [295] 2.81746250 1.89450799 1.26048416 3.29014882 3.99169262 0.62740456
# 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] -3.89224113 -3.78499632 -3.67775150 -3.57050669 -3.46326188 -3.35601707
## [7] -3.24877225 -3.14152744 -3.03428263 -2.92703781 -2.81979300 -2.71254819
## [13] -2.60530338 -2.49805856 -2.39081375 -2.28356894 -2.17632412 -2.06907931
## [19] -1.96183450 -1.85458969 -1.74734487 -1.64010006 -1.53285525 -1.42561043
## [25] -1.31836562 -1.21112081 -1.10387600 -0.99663118 -0.88938637 -0.78214156
## [31] -0.67489674 -0.56765193 -0.46040712 -0.35316231 -0.24591749 -0.13867268
## [37] -0.03142787 0.07581695 0.18306176 0.29030657 0.39755138 0.50479620
## [43] 0.61204101 0.71928582 0.82653064 0.93377545 1.04102026 1.14826507
## [49] 1.25550989 1.36275470 1.46999951 1.57724433 1.68448914 1.79173395
## [55] 1.89897876 2.00622358 2.11346839 2.22071320 2.32795802 2.43520283
## [61] 2.54244764 2.64969245 2.75693727 2.86418208 2.97142689 3.07867171
## [67] 3.18591652 3.29316133 3.40040614 3.50765096 3.61489577 3.72214058
## [73] 3.82938540 3.93663021 4.04387502 4.15111983 4.25836465 4.36560946
## [79] 4.47285427 4.58009909 4.68734390 4.79458871 4.90183352 5.00907834
## [85] 5.11632315 5.22356796 5.33081278 5.43805759 5.54530240 5.65254721
## [91] 5.75979203 5.86703684 5.97428165 6.08152647 6.18877128 6.29601609
## [97] 6.40326090 6.51050572 6.61775053 6.72499534
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%
## -3.892241 1.060075 1.952105 3.098399 6.724995
# 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] 4.770886555 -0.337124654 -0.231646495 1.492957884 2.623290171
## [6] 2.432311842 1.927544064 -0.601302667 -0.226877949 2.649512295
## [11] 2.930732304 3.629640623 0.433227642 2.730247016 3.111971668
## [16] 3.101981017 3.710585317 1.841660222 2.852327634 2.857503819
## [21] 4.277600785 -0.766993929 4.023687199 1.665329077 1.774974853
## [26] 2.970998394 3.174388314 0.753993329 -0.611210641 0.908281180
## [31] 1.279023114 3.299455423 1.782950342 1.341672514 4.261600330
## [36] 0.137041938 1.340745746 0.757440079 0.659145029 -0.255104674
## [41] 3.910353129 1.469142202 2.600516127 1.575139851 3.337836085
## [46] -0.376815920 3.452653930 4.083123037 0.100757471 1.686798086
## [51] 3.587547382 2.952586894 2.616759484 3.117058343 2.226253394
## [56] -1.393701815 0.859117049 1.965743706 1.163336958 6.385563123
## [61] 3.647058824 0.415606604 2.691530542 1.765923528 0.646089781
## [66] 3.164630181 0.783930556 0.278357561 0.294730566 1.723161993
## [71] -0.201402223 1.689600450 2.021412680 1.017469154 0.195882814
## [76] 1.207185818 -2.411728450 1.048421278 0.374798126 3.332681348
## [81] 4.077263981 4.601783028 0.181383052 1.964747816 2.286550486
## [86] 2.242041469 -0.019857191 2.153026726 3.259654778 0.744684878
## [91] 0.840459387 4.039161437 3.800424207 2.891051186 3.631668343
## [96] 0.388744629 3.007339704 -0.889208950 2.389976632 4.369096775
## [101] 0.827189726 2.402397419 1.091218055 3.201082763 2.575878285
## [106] 3.500189699 1.516294625 3.279739722 0.384967104 2.292214627
## [111] -0.138946040 4.783124229 3.315340192 2.044017995 1.098008584
## [116] 5.604864560 3.182596419 2.149675931 1.151762579 1.338247682
## [121] 2.976751729 1.180948742 3.699028111 3.112711105 3.966696397
## [126] 5.525032696 2.492517446 2.177588068 3.975427445 0.336588347
## [131] 1.072383118 2.675998526 2.313661176 0.349369139 4.343715757
## [136] 1.897445621 1.427822635 3.290475371 1.081826169 1.615740498
## [141] 0.206061887 2.283054880 3.056069857 -0.025490684 1.846912381
## [146] 5.004677748 0.960366920 0.479240651 -0.191677211 0.555697014
## [151] 3.114181706 0.605607357 2.505995557 1.916757578 1.850562973
## [156] 2.341856528 1.915160486 2.853833876 1.458408478 3.163787590
## [161] 1.453791947 0.989575321 1.704715274 3.055325084 3.003388874
## [166] 0.633441310 2.461892623 3.541306555 3.025364358 0.389573599
## [171] 3.651768945 3.267718641 3.646995438 2.642187097 3.023478693
## [176] 2.775711810 3.648259880 2.533258867 3.863259037 1.704214753
## [181] -1.171602878 2.040455726 4.961292618 2.782991562 2.416982624
## [186] 2.552887343 3.677328975 0.572950979 4.273979257 1.200272673
## [191] 4.279308530 2.682618551 1.568736073 5.194342220 4.810205877
## [196] 4.468339826 0.920804002 0.292614182 2.752971782 1.196619098
## [201] 1.140398379 -0.975705954 3.533598146 4.134501731 2.043104999
## [206] -0.249304278 2.561255947 2.568023800 1.116447715 3.136770422
## [211] 2.835771284 1.588046857 2.352830029 4.419287577 2.772683848
## [216] 2.566059221 0.422610858 2.720869448 4.609237654 -0.684214296
## [221] 1.754337670 0.312901456 3.206726150 1.094437404 3.467427469
## [226] 2.420880191 2.713799603 0.986261470 1.736300057 3.993363465
## [231] 4.237362176 4.972387843 2.623551982 0.726452725 0.675640442
## [236] 1.378146654 2.800395359 2.434122238 2.757437735 1.527448262
## [241] 2.572562061 0.464223849 4.833375659 -0.101491717 3.393773919
## [246] 0.958178186 2.130437810 3.215297388 1.552134206 1.020432889
## [251] 2.819995167 2.313192223 1.816230790 2.210976142 2.345305395
## [256] 0.824025341 1.471234895 1.497967275 1.950726666 -1.193889810
## [261] 2.094433771 0.894078658 -0.617255969 2.841588034 1.595109747
## [266] -0.015199950 1.689741901 -1.197230061 2.385299130 2.828363646
## [271] 4.516225049 3.107012346 3.459953393 3.500257970 0.524143864
## [276] 1.796021256 2.519137714 0.420076800 3.540893277 2.173766883
## [281] 2.846141768 0.302717829 3.644629116 3.433594379 0.746066519
## [286] 2.380285914 -0.619109688 4.308973914 2.606705024 4.512233107
## [291] 1.978269606 1.324941444 1.630691000 4.353723461 2.817462495
## [296] 1.894507990 1.260484155 3.290148820 3.991692624 0.627404563
## [301] 0.569767686 2.545253958 -0.279368860 2.279364759 2.085278621
## [306] 2.280873021 1.637169455 2.340390110 3.119038955 1.519899240
## [311] 0.324248727 3.949190911 5.442682256 1.567583404 1.512439589
## [316] 1.859170600 1.184405270 4.564247493 2.258164411 1.662661664
## [321] 3.097205534 1.875017353 0.498247950 2.081207206 1.898518171
## [326] 2.618951176 1.156025958 3.007269552 1.869202936 0.680727402
## [331] 4.974499610 1.620642585 5.325095879 1.839046168 1.093594909
## [336] 4.748774416 1.506606180 0.462492194 1.764115912 2.604112243
## [341] 5.657844799 2.264346631 2.649160629 0.466761277 1.710318787
## [346] 3.769953821 0.633786978 0.742676099 2.176024816 -0.315645751
## [351] 3.514018628 1.574110712 4.483971341 5.073936889 0.370268691
## [356] 1.535243922 1.597586857 -0.159420998 2.194448092 1.382118529
## [361] 4.239256373 2.044358664 -0.050273176 2.762352353 1.059057596
## [366] 2.569651303 5.425940718 2.363058516 4.699411559 0.223531216
## [371] 1.829218536 0.780183331 0.382890611 3.204732348 0.522350661
## [376] 1.831718860 1.400166486 1.530388425 0.663437752 3.774466227
## [381] 3.142576490 1.978993070 1.231696726 0.589479977 0.615102533
## [386] 4.347717563 -1.232642914 -0.137058509 1.980578335 0.127606022
## [391] 2.426192305 0.781864950 1.936524544 1.236606619 0.020087422
## [396] 1.717250742 3.173460917 3.089424417 0.274918674 2.323776449
## [401] 1.554129345 0.375523186 -0.232465044 3.872756226 2.449428552
## [406] 3.705610810 2.185274473 -0.145860809 0.364752782 2.410624743
## [411] 0.745635190 1.342904808 1.219889229 1.912390619 0.026652115
## [416] 3.587850143 1.280824961 1.888888612 2.963386989 3.154067102
## [421] 1.826102056 -0.417151873 3.423120964 2.332589670 0.389198845
## [426] 2.796630233 3.475163844 3.731457975 0.962335744 1.983167990
## [431] 2.571736598 -0.239832581 3.596985159 1.396096527 -0.614422317
## [436] 5.257419602 1.651182404 1.216321796 1.689697657 2.312504953
## [441] 1.370978155 1.012018738 4.382209272 3.904207402 2.502963867
## [446] 3.110994379 3.210028619 0.161650908 4.011372647 4.274873834
## [451] -0.170531388 -0.972922732 5.759421149 0.697667347 3.317990971
## [456] 5.394241522 2.560209063 1.947121658 1.054179645 2.438852722
## [461] 0.995464089 1.205794851 4.197145226 0.761063294 3.502489941
## [466] 1.333389892 0.953076114 2.797966054 0.682483731 1.645832126
## [471] 2.115764878 1.241820712 0.015590010 -0.001490219 0.789477691
## [476] 5.197960308 4.928665504 2.423145330 1.820771204 0.754404107
## [481] 1.775848742 1.171838030 1.252889112 0.430159283 1.493489756
## [486] 0.284096088 3.786464777 3.318022596 0.290541286 2.904340474
## [491] 1.482087856 -0.681207664 1.959313376 1.910127212 0.038856139
## [496] 2.575286326 1.965823897 4.262095776 0.300758307 1.214600123
## [501] 1.142274431 3.719695699 1.313719989 2.875930482 4.458807095
## [506] -0.486428885 1.942585541 0.686985948 4.040930145 1.449126288
## [511] -1.329617881 0.377510004 1.404433650 2.001130763 -0.619431655
## [516] 4.990492993 2.087902190 3.293986530 1.856720208 4.000118063
## [521] 1.011235444 4.303406743 1.376034449 1.153436118 2.296451729
## [526] 1.125377834 0.949654120 3.636360080 3.032098922 -0.368657967
## [531] 1.099194235 1.843104356 3.169209212 0.777755002 6.072870317
## [536] 1.788182521 4.847752994 1.784162772 1.975627239 1.630794894
## [541] 1.937355949 -0.397876353 1.180805363 1.143064841 4.589849999
## [546] 1.904131102 -1.520122188 -0.319539576 1.525558568 -1.048065705
## [551] 1.805439560 2.906636456 3.845292567 5.268156131 0.705506847
## [556] 2.386596431 2.606425232 3.111818780 1.716375855 1.237546131
## [561] 3.888589938 1.896146898 3.171296288 1.596780181 3.540869329
## [566] 1.513841327 3.831593995 2.789237222 1.193267625 0.448955292
## [571] 1.726594119 2.509754789 0.897539776 1.149576433 1.850476007
## [576] 3.363322073 0.914928582 -0.314057797 3.059576081 2.564720313
## [581] 1.334093940 3.416466986 2.769755097 3.577197003 1.302764102
## [586] 1.469611293 3.726225685 3.552524647 0.957249342 0.187587491
## [591] 1.762561242 3.648537872 0.441121927 2.889204845 1.425256314
## [596] 2.152097240 1.613925852 -0.128414470 0.018969288 2.532159368
## [601] 1.760468556 2.441215520 1.763555061 1.263723728 3.547090972
## [606] 3.862215691 1.556981124 1.368619637 0.225651859 3.262437267
## [611] 2.055477321 3.545645515 2.545006285 -0.229626216 3.883123442
## [616] 2.909091101 -0.669795646 2.131836948 2.412888395 -1.219094952
## [621] -0.012711480 1.497171550 2.963360688 2.957940662 1.694320124
## [626] 0.279746327 2.291542774 2.669123892 1.826230023 4.376483494
## [631] 3.147821280 2.851327282 3.276205967 6.724995343 -0.309237016
## [636] 1.596517614 3.698279577 4.512821715 0.330539528 4.751426785
## [641] 1.903578221 0.023997999 3.214011010 3.303487753 -3.574316938
## [646] 1.367875984 4.700227069 1.062751370 0.645105237 2.889731965
## [651] 1.365458040 1.450313227 2.580808565 0.709110712 -0.123919224
## [656] 0.771622228 2.735889714 2.239087380 1.956552631 -0.453185417
## [661] 1.820151037 -0.236902801 0.671243379 4.297615352 2.200579582
## [666] 1.885672303 2.676829790 3.952622093 0.510808214 0.851712631
## [671] 2.683367938 2.178962131 2.059685464 0.283466322 1.098079194
## [676] 1.755243369 1.399953393 1.515483438 3.549141214 1.646528863
## [681] 3.615481325 2.032356456 1.723537805 3.750793730 2.584158566
## [686] 6.344379467 1.102912472 0.951156215 2.849549769 -0.195913229
## [691] 6.328349974 2.986346206 1.456894291 3.619292618 0.480293896
## [696] 2.029268832 4.121349385 4.254791004 1.308228427 1.532312147
## [701] 2.456329566 1.232834289 1.244395669 -0.142015353 1.896194324
## [706] 0.822721969 1.512792272 -0.900548266 1.029880967 2.863402901
## [711] 1.425550614 3.836621376 1.767809604 0.193598070 0.839215289
## [716] 3.602919427 0.998398972 0.843259053 -1.145583783 3.036461664
## [721] 2.379245724 3.151010504 1.595220671 0.274745913 2.575386126
## [726] -0.332144515 1.864656415 2.706217964 2.602794109 -0.739850462
## [731] 2.721575549 2.875735584 -0.105984340 2.585805177 2.423645227
## [736] 2.078537917 1.674020658 1.061308208 1.098379013 4.269619441
## [741] 4.311675120 1.290247629 2.785666047 2.439088426 2.474518747
## [746] 0.947822757 3.332616755 4.985131807 2.593127862 2.507762218
## [751] 2.857006291 1.913843147 1.753044429 1.963647002 1.016170059
## [756] 3.823981721 1.453695785 3.847844290 0.607580777 2.177651625
## [761] 5.529394667 3.317970645 1.424846237 1.617852420 2.230573599
## [766] 2.157983724 1.730774285 4.207210441 1.546672278 2.335680684
## [771] 1.922669021 3.757744261 3.816640941 1.376935666 2.268749700
## [776] 2.435455969 2.582865983 2.569306165 2.155009015 0.519636871
## [781] 3.238434856 3.377839899 2.659979415 1.061377475 0.185202726
## [786] 1.182548717 1.557551290 1.576642668 3.507002915 0.670163919
## [791] 2.922124544 1.555950683 2.850620750 3.381946348 1.577409530
## [796] 4.029123683 5.662156921 2.142732300 4.948523665 0.223955719
## [801] 2.798630221 2.088337022 3.394583320 2.550668282 1.357571462
## [806] -0.671445697 -0.650649396 4.108404720 -0.265656841 1.770556194
## [811] 1.710104500 2.319450673 3.549314962 2.643648307 -0.247539464
## [816] 0.796683048 1.805299934 3.497864873 3.267703890 3.449266646
## [821] 0.800712791 3.237057740 2.277402727 -0.116275496 -0.291905482
## [826] 3.270821475 2.896094409 0.246659038 3.339947733 -0.051589208
## [831] 2.802778338 0.431074041 1.911805191 3.430985517 2.318620795
## [836] 0.438835993 2.206116669 3.043312639 2.720799606 2.424690127
## [841] 4.164071306 -0.232115886 1.804215693 3.863900827 2.625574289
## [846] 3.711936225 0.092535457 -0.305458704 3.831697213 1.001887107
## [851] 2.992239623 0.253910234 1.051641936 2.703949281 3.163972134
## [856] 1.773668760 1.817032108 -0.336714810 3.362846553 0.455878189
## [861] 2.780682925 1.299379374 1.234699653 -1.906486495 2.824458498
## [866] 1.060413477 1.446799220 1.645182280 2.677274788 1.306186042
## [871] 2.478399224 1.778510123 1.346143483 3.683849818 2.755646802
## [876] 3.366661501 2.905483703 3.224510881 2.224325285 -0.683165432
## [881] 1.454474901 5.140742599 1.828760526 3.300345326 2.257332476
## [886] 1.782298416 2.746326780 2.547804496 1.429430143 1.494410411
## [891] 2.831828646 1.394663313 0.650927242 1.552203686 2.207602092
## [896] 2.950001494 3.234752528 1.527179055 2.963022985 3.785467131
## [901] 0.248385025 5.295247031 1.730699110 5.275994264 0.160244704
## [906] 1.533040966 3.514418039 -0.348127282 3.354783831 3.431456495
## [911] 4.837164859 2.957606664 3.142652950 4.321651132 1.753344971
## [916] 1.037777586 3.415215249 2.780881671 2.704729375 1.953483441
## [921] 5.805552424 0.431283508 -3.892241129 -1.128748038 1.678055680
## [926] 4.554435176 0.934012726 5.500642313 0.138762808 0.573308089
## [931] 4.898851835 4.663459039 3.782135459 -0.554497126 3.896725064
## [936] 3.977949181 1.809379676 0.307560621 -0.963290371 1.207856608
## [941] 1.703215190 0.976192253 0.495217093 1.750471928 2.284517057
## [946] 3.033666054 0.322846233 2.614553630 1.937960780 3.799709411
## [951] -1.039240877 2.047898627 0.583975509 3.384664928 1.908676818
## [956] 4.444378309 2.376476687 2.829597750 1.094181916 1.706167986
## [961] 5.162207302 4.117474214 2.207600379 1.210738485 2.146567432
## [966] 3.479826075 2.937070260 3.160489981 2.468522949 1.929257182
## [971] 1.831831830 -0.246105703 2.762735837 1.627123942 1.703448602
## [976] 0.763269301 1.794850638 1.920730479 2.711565553 3.339439627
## [981] -1.256859830 0.945900137 3.088418570 1.535405829 3.222943464
## [986] 2.187729761 3.385312639 0.660821519 3.183829808 1.677755283
## [991] 0.375437234 1.622221524 0.672878175 2.055718251 3.574003614
## [996] 1.003023141 1.694705533 1.230072397 1.811100805 2.993602609
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.892 1.060 1.952 2.052 3.098 6.725
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%
## -0.3094781
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%
## 4.554926
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%
## -0.3094781
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [265] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE TRUE FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE 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 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 FALSE 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 TRUE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE TRUE TRUE 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] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE TRUE 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 FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [937] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
# count all true values using the sum command
sum(Low5Percent[TRUE]) # there are 50 of them
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -0.3371247 -0.6013027 -0.7669939 -0.6112106 -0.3768159 -1.3937018
## [7] -2.4117285 -0.8892089 -1.1716029 -0.9757060 -0.6842143 -1.1938898
## [13] -0.6172560 -1.1972301 -0.6191097 -0.3156458 -1.2326429 -0.4171519
## [19] -0.6144223 -0.9729227 -0.6812077 -0.4864289 -1.3296179 -0.6194317
## [25] -0.3686580 -0.3978764 -1.5201222 -0.3195396 -1.0480657 -0.3140578
## [31] -0.6697956 -1.2190950 -3.5743169 -0.4531854 -0.9005483 -1.1455838
## [37] -0.3321445 -0.7398505 -0.6714457 -0.6506494 -0.3367148 -1.9064865
## [43] -0.6831654 -0.3481273 -3.8922411 -1.1287480 -0.5544971 -0.9632904
## [49] -1.0392409 -1.2568598
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.554926
(Top5Percent <- (data >= Cutoff))
## [1] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## [337] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE 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 TRUE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [637] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE TRUE FALSE FALSE TRUE TRUE 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] TRUE 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] 4.770887 6.385563 4.601783 4.783124 5.604865 5.525033 5.004678 4.961293
## [9] 5.194342 4.810206 4.609238 4.972388 4.833376 5.442682 4.564247 4.974500
## [17] 5.325096 4.748774 5.657845 5.073937 5.425941 4.699412 5.257420 5.759421
## [25] 5.394242 5.197960 4.928666 4.990493 6.072870 4.847753 4.589850 5.268156
## [33] 6.724995 4.751427 4.700227 6.344379 6.328350 4.985132 5.529395 5.662157
## [41] 4.948524 5.140743 5.295247 5.275994 4.837165 5.805552 5.500642 4.898852
## [49] 4.663459 5.162207