# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Davy D. Dongosa, 1-BSMATH
# Mat108
# 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] 2.9049275 1.3876107 3.1480268 -2.0621630 1.2486144 3.7059548
## [7] 0.2845072 0.3270488 3.6353144 3.8858037 2.5849810 0.2147757
## [13] 3.0207445 5.2269723 1.1556143 2.7407491 3.5784498 0.7043262
## [19] 0.8241489 3.3757809
data[1:300] # display the first 300 elements
## [1] 2.90492750 1.38761070 3.14802675 -2.06216304 1.24861438 3.70595478
## [7] 0.28450720 0.32704882 3.63531438 3.88580369 2.58498099 0.21477574
## [13] 3.02074445 5.22697230 1.15561433 2.74074914 3.57844979 0.70432617
## [19] 0.82414889 3.37578093 2.38686236 0.03533862 3.43927571 1.46542604
## [25] 1.15386742 1.12931673 1.33164840 0.07414281 1.28269268 3.15187779
## [31] -0.65222878 0.42902820 1.47101046 2.76330666 2.43930954 2.76584903
## [37] -0.84022516 3.19496909 2.37162530 3.70211911 1.30510321 -0.17658143
## [43] 2.09257874 2.03815983 1.56333025 2.28403730 -2.52739890 5.03132397
## [49] 3.23190636 4.06728472 3.00010893 3.15459162 2.45611862 0.49158809
## [55] 0.05779361 1.60518067 1.93180108 -0.50467321 1.98207189 2.94084761
## [61] 1.53820754 0.72038660 3.84756873 2.08147957 -0.29269297 2.66010383
## [67] 1.48890099 0.38160733 2.85204066 0.57173694 2.85893912 0.94401910
## [73] 1.31075418 3.13742807 3.51691016 -1.02950968 3.96089465 3.00988385
## [79] 2.69571890 2.33980427 1.38871126 0.58976420 -0.82904396 1.21987569
## [85] 1.94908354 3.04488736 1.77188576 1.35183013 -0.22779957 1.61753873
## [91] 1.02341321 2.56476894 2.67564919 3.34842126 0.50438041 -2.79678510
## [97] 1.59743008 2.52032890 2.87716551 1.70967867 1.46698560 0.71546022
## [103] 5.28560083 1.69379584 1.79415164 1.69277101 0.28081507 3.07662258
## [109] 0.11992506 2.11584491 1.97894830 3.25924426 0.11047847 1.66923034
## [115] -0.58452822 2.29977937 -1.03029443 -1.59068993 -0.19183534 0.46981121
## [121] -1.08616495 3.51251510 0.24252374 4.76466855 4.08360604 2.54769369
## [127] 2.75440757 2.19042020 0.51168771 2.70963623 3.91721549 0.21718924
## [133] 1.26273400 0.13158227 4.80368173 2.18056710 -0.31515089 2.87849738
## [139] -0.07932925 -0.51301856 1.31901412 2.06806054 1.45823793 0.26181790
## [145] 1.67656141 1.98230518 3.63958580 2.64452416 3.96881561 6.35603732
## [151] 3.52091545 -0.79853720 -0.61037917 1.95734751 3.34074587 2.24003221
## [157] 0.68230765 2.56452317 1.20377458 2.26387776 1.63786386 0.64409324
## [163] 2.39781650 1.86756076 0.63311748 1.13473053 1.01882872 4.19312823
## [169] 4.05486807 1.63331996 1.09310130 0.28544357 4.05483512 3.13439113
## [175] 2.08339880 2.31073336 2.88533065 2.74052596 2.93816704 1.89066360
## [181] 2.07027582 1.00312458 3.40226873 -0.67670833 3.66601154 3.23487433
## [187] 3.78443355 3.15750723 0.92118665 0.78495508 2.11177446 3.02990064
## [193] 3.41584326 1.51567389 1.21911715 5.10860227 0.55579368 4.18555570
## [199] 4.33360599 2.89461463 3.77286401 0.06065157 0.59325995 -0.75324664
## [205] 2.44413932 2.93893615 -0.13874352 2.82718176 1.25542992 1.09338428
## [211] 3.17130537 3.92805992 2.57773812 -0.46960684 0.07553946 1.04737638
## [217] 4.01533392 2.50672472 1.30779143 -0.02876411 -1.04485983 0.24667797
## [223] 1.49685660 -0.79399712 0.57449767 1.77937469 1.98877927 -0.15819797
## [229] 0.22597971 3.97995274 4.68082653 3.56883130 1.12046205 -0.50550401
## [235] 2.52943122 3.13038452 1.63228143 4.22559604 3.55385541 -0.79014422
## [241] 4.21721524 1.91840292 1.75129646 6.16820466 2.96555433 0.83118223
## [247] 3.18462406 0.86181784 0.79336812 1.06334885 1.39549685 2.89758711
## [253] 2.16127739 5.29744883 4.04801864 0.79965173 -0.11273182 4.12703572
## [259] 0.76746795 0.59051404 0.41922332 -0.84828595 1.27473400 1.33412507
## [265] 0.94684255 3.48536299 0.47731662 0.21734928 -0.83895937 0.08996992
## [271] 3.28920177 2.29039930 1.13164639 1.01697570 2.86262613 0.91378388
## [277] 1.78862717 2.40429616 -1.58849618 0.02575380 2.29346090 0.82261505
## [283] 2.27238501 1.48062403 1.09630105 0.91914983 3.01201034 2.22648136
## [289] 0.47118922 1.55006475 4.24017132 3.39391623 2.06547890 2.10079730
## [295] 1.33960368 1.64162830 2.55652004 4.11624036 2.93201498 0.57230944
# 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] -2.796785103 -2.700228105 -2.603671107 -2.507114110 -2.410557112
## [6] -2.314000114 -2.217443116 -2.120886118 -2.024329120 -1.927772122
## [11] -1.831215124 -1.734658126 -1.638101128 -1.541544130 -1.444987133
## [16] -1.348430135 -1.251873137 -1.155316139 -1.058759141 -0.962202143
## [21] -0.865645145 -0.769088147 -0.672531149 -0.575974151 -0.479417153
## [26] -0.382860156 -0.286303158 -0.189746160 -0.093189162 0.003367836
## [31] 0.099924834 0.196481832 0.293038830 0.389595828 0.486152826
## [36] 0.582709824 0.679266822 0.775823819 0.872380817 0.968937815
## [41] 1.065494813 1.162051811 1.258608809 1.355165807 1.451722805
## [46] 1.548279803 1.644836801 1.741393799 1.837950796 1.934507794
## [51] 2.031064792 2.127621790 2.224178788 2.320735786 2.417292784
## [56] 2.513849782 2.610406780 2.706963778 2.803520776 2.900077773
## [61] 2.996634771 3.093191769 3.189748767 3.286305765 3.382862763
## [66] 3.479419761 3.575976759 3.672533757 3.769090755 3.865647753
## [71] 3.962204751 4.058761748 4.155318746 4.251875744 4.348432742
## [76] 4.444989740 4.541546738 4.638103736 4.734660734 4.831217732
## [81] 4.927774730 5.024331728 5.120888725 5.217445723 5.314002721
## [86] 5.410559719 5.507116717 5.603673715 5.700230713 5.796787711
## [91] 5.893344709 5.989901707 6.086458705 6.183015702 6.279572700
## [96] 6.376129698 6.472686696 6.569243694 6.665800692 6.762357690
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%
## -2.7967851 0.9206774 1.9658405 3.0010626 6.7623577
# 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] 2.904927496 1.387610695 3.148026752 -2.062163037 1.248614385
## [6] 3.705954782 0.284507195 0.327048823 3.635314379 3.885803692
## [11] 2.584980985 0.214775742 3.020744455 5.226972303 1.155614335
## [16] 2.740749142 3.578449790 0.704326173 0.824148885 3.375780928
## [21] 2.386862358 0.035338621 3.439275714 1.465426039 1.153867423
## [26] 1.129316726 1.331648399 0.074142814 1.282692680 3.151877790
## [31] -0.652228777 0.429028205 1.471010459 2.763306658 2.439309536
## [36] 2.765849031 -0.840225157 3.194969087 2.371625303 3.702119113
## [41] 1.305103211 -0.176581429 2.092578740 2.038159828 1.563330254
## [46] 2.284037301 -2.527398898 5.031323974 3.231906362 4.067284722
## [51] 3.000108932 3.154591625 2.456118620 0.491588094 0.057793610
## [56] 1.605180669 1.931801084 -0.504673206 1.982071887 2.940847615
## [61] 1.538207542 0.720386603 3.847568725 2.081479569 -0.292692975
## [66] 2.660103833 1.488900988 0.381607333 2.852040658 0.571736938
## [71] 2.858939117 0.944019101 1.310754176 3.137428065 3.516910161
## [76] -1.029509678 3.960894649 3.009883850 2.695718898 2.339804273
## [81] 1.388711261 0.589764201 -0.829043960 1.219875688 1.949083539
## [86] 3.044887359 1.771885761 1.351830128 -0.227799573 1.617538725
## [91] 1.023413209 2.564768935 2.675649193 3.348421263 0.504380413
## [96] -2.796785103 1.597430084 2.520328895 2.877165508 1.709678666
## [101] 1.466985596 0.715460223 5.285600828 1.693795836 1.794151638
## [106] 1.692771011 0.280815069 3.076622576 0.119925062 2.115844915
## [111] 1.978948302 3.259244258 0.110478469 1.669230338 -0.584528224
## [116] 2.299779366 -1.030294434 -1.590689932 -0.191835341 0.469811207
## [121] -1.086164946 3.512515096 0.242523745 4.764668548 4.083606044
## [126] 2.547693690 2.754407573 2.190420203 0.511687711 2.709636227
## [131] 3.917215495 0.217189244 1.262734002 0.131582268 4.803681734
## [136] 2.180567100 -0.315150887 2.878497381 -0.079329250 -0.513018564
## [141] 1.319014120 2.068060543 1.458237932 0.261817897 1.676561413
## [146] 1.982305182 3.639585801 2.644524157 3.968815606 6.356037318
## [151] 3.520915449 -0.798537200 -0.610379168 1.957347507 3.340745874
## [156] 2.240032211 0.682307648 2.564523166 1.203774584 2.263877763
## [161] 1.637863858 0.644093244 2.397816496 1.867560763 0.633117479
## [166] 1.134730533 1.018828724 4.193128233 4.054868071 1.633319955
## [171] 1.093101295 0.285443567 4.054835122 3.134391134 2.083398802
## [176] 2.310733357 2.885330649 2.740525962 2.938167043 1.890663596
## [181] 2.070275818 1.003124580 3.402268729 -0.676708327 3.666011538
## [186] 3.234874325 3.784433547 3.157507228 0.921186647 0.784955083
## [191] 2.111774455 3.029900643 3.415843265 1.515673886 1.219117147
## [196] 5.108602274 0.555793679 4.185555698 4.333605988 2.894614630
## [201] 3.772864012 0.060651570 0.593259949 -0.753246639 2.444139322
## [206] 2.938936152 -0.138743519 2.827181759 1.255429917 1.093384278
## [211] 3.171305366 3.928059916 2.577738121 -0.469606836 0.075539455
## [216] 1.047376380 4.015333921 2.506724721 1.307791434 -0.028764111
## [221] -1.044859826 0.246677972 1.496856597 -0.793997121 0.574497669
## [226] 1.779374686 1.988779265 -0.158197975 0.225979708 3.979952741
## [231] 4.680826532 3.568831296 1.120462047 -0.505504013 2.529431222
## [236] 3.130384517 1.632281430 4.225596039 3.553855406 -0.790144218
## [241] 4.217215242 1.918402920 1.751296464 6.168204658 2.965554332
## [246] 0.831182227 3.184624059 0.861817837 0.793368122 1.063348845
## [251] 1.395496854 2.897587106 2.161277385 5.297448834 4.048018644
## [256] 0.799651733 -0.112731823 4.127035717 0.767467950 0.590514044
## [261] 0.419223320 -0.848285954 1.274734000 1.334125067 0.946842548
## [266] 3.485362987 0.477316623 0.217349282 -0.838959371 0.089969922
## [271] 3.289201770 2.290399299 1.131646388 1.016975704 2.862626133
## [276] 0.913783875 1.788627167 2.404296161 -1.588496185 0.025753799
## [281] 2.293460896 0.822615050 2.272385006 1.480624031 1.096301048
## [286] 0.919149833 3.012010342 2.226481357 0.471189219 1.550064752
## [291] 4.240171321 3.393916233 2.065478897 2.100797295 1.339603681
## [296] 1.641628301 2.556520036 4.116240358 2.932014980 0.572309441
## [301] 1.453198153 0.031018887 2.024986407 3.231005194 2.246496119
## [306] 1.175206442 1.990447669 2.000038069 1.793257568 1.883576170
## [311] 1.833476081 -1.235359754 1.082496891 2.930486647 0.618302046
## [316] 1.137165651 4.718743951 0.267606352 -0.587671972 4.650111570
## [321] 4.099342458 0.890369218 1.509946781 3.813396923 -1.151988700
## [326] 0.718527827 3.011079968 4.246399332 -0.373592545 5.125005707
## [331] -0.122560561 1.684036573 2.833355514 0.487402463 3.230039191
## [336] 2.856932301 3.127034414 4.367457131 1.912318523 3.809422765
## [341] 4.560282471 4.900217065 2.172296038 1.649810022 1.177234273
## [346] 0.589149896 1.958821264 1.063695636 3.575368656 0.988137803
## [351] 0.799778301 3.915825140 3.260058589 1.113582298 -1.311078346
## [356] 5.303558299 5.000049476 2.048075763 0.617932674 1.681844490
## [361] 1.034707614 5.841525467 1.716808155 2.173841079 1.533911111
## [366] 3.607599560 2.171668534 3.069437141 1.902538368 2.075571783
## [371] 1.524459314 2.106940143 0.211622975 0.128085308 2.151706242
## [376] 5.152771217 -0.467030731 4.245587135 4.467864669 0.091960825
## [381] 0.619486930 1.924093115 4.055018295 3.298310890 1.653326562
## [386] 1.626558152 -0.386561189 1.024686520 1.677076791 -0.142711421
## [391] -0.142957378 3.173788960 1.846537873 3.615886324 3.255744774
## [396] 2.837314795 2.369168813 0.193430736 5.466645373 2.066762627
## [401] 2.807257428 2.855879529 3.012829260 -0.384416147 2.670980196
## [406] 1.945489893 2.566729363 1.088578436 1.818776170 3.305059868
## [411] 2.215267049 -0.630951553 3.573207823 1.576586682 0.531676776
## [416] 2.099417965 -1.168798348 1.612411546 0.223280498 3.209719546
## [421] 3.583221376 2.163962542 0.645517924 1.120191935 5.315243630
## [426] 1.350494201 2.484544676 -0.048787472 1.095700028 3.442563040
## [431] 5.009858558 1.197863387 2.473654272 3.197035346 2.953786593
## [436] 4.027163312 0.973880153 0.079332640 3.307946436 1.974345116
## [441] 0.628486993 6.762357690 4.439794754 2.777675591 4.711861927
## [446] 2.932559519 3.965146367 1.605946760 2.626758366 1.173741572
## [451] 2.154893791 3.343794587 3.091351402 -2.519599776 3.344341461
## [456] 0.453887633 3.581368389 1.269891441 1.738281215 2.228666057
## [461] 2.082840477 2.140701190 2.292120651 2.733022760 1.478477894
## [466] 0.987651451 3.396597781 -0.781594624 1.649275273 2.025960618
## [471] 1.924073912 1.092298595 2.160160284 3.470741628 3.480416190
## [476] 2.901964184 5.121637004 1.544126629 0.489517519 2.053815925
## [481] 3.162981452 1.786803692 3.083351238 1.642494535 0.737778818
## [486] 2.511384412 1.819934344 1.288948725 1.487570579 2.404244003
## [491] 4.182491437 -0.988934565 0.808753239 -0.186043582 2.946580072
## [496] 2.641692165 3.838660837 2.091819042 2.758701366 3.958747281
## [501] 1.815547123 1.556498148 0.807896357 -2.369605515 -1.226911273
## [506] 4.561742191 4.690921818 2.016405479 4.302656500 3.254557533
## [511] 0.657855685 5.058509878 2.380652624 1.914972736 0.019906023
## [516] 4.999151213 2.026340513 1.533555568 4.251880789 2.579408816
## [521] 0.944073025 0.912188426 2.178373089 3.411120888 3.458696075
## [526] 0.343755332 5.013160687 0.278982089 2.385013114 1.849940798
## [531] 3.961398481 2.131219117 2.895525097 2.786881379 3.899444796
## [536] -0.862942688 1.152705528 3.602304903 3.537701463 2.090958258
## [541] 1.899376343 2.680957454 1.309648794 1.527735152 1.510052710
## [546] 2.824179166 4.123376818 0.067763744 1.788329053 -0.159119334
## [551] 1.167608384 1.546130386 2.954458230 3.181095663 2.285467401
## [556] -0.809052529 1.472216822 3.817192295 0.233577790 3.178267729
## [561] 2.496427780 2.339128588 4.900648871 2.646699913 3.667140749
## [566] 3.271673725 1.330841940 2.574716012 -0.690418572 2.900285229
## [571] 3.461988410 2.655763435 4.058080348 2.557104366 1.949369911
## [576] 1.564372584 4.167604469 0.928620122 5.037533849 3.718526607
## [581] 2.041223179 1.912670142 0.532000854 4.212988501 2.859283069
## [586] -0.334111916 -0.588415040 3.051076803 0.853854708 0.140560898
## [591] 0.758641166 -0.017033377 0.182724756 0.106319106 1.989079211
## [596] 3.251070525 0.948701842 1.957036062 1.711061891 1.820617622
## [601] 0.883524182 2.824284924 0.793110827 3.093518443 1.419875245
## [606] 0.551283797 3.633411358 3.268720685 0.974175839 3.699363136
## [611] 1.979772973 1.834889302 3.893015185 2.310383262 1.161364331
## [616] 3.191857411 -0.571095686 1.991213500 -0.430692298 1.323722697
## [621] 0.277105287 3.768094210 1.546683011 2.783698952 3.363707486
## [626] 2.488103098 3.268834297 2.562741890 1.664291899 1.121697373
## [631] 1.344226642 2.150001667 2.692028624 2.708237554 2.999178634
## [636] 1.117580566 1.700010354 2.615059956 1.043297316 3.586522279
## [641] 0.559776218 1.001417906 2.245651188 0.928893647 -0.663812045
## [646] 1.720690508 2.313360695 2.652777727 0.366520524 2.073012534
## [651] 2.818650287 2.682441895 2.581451332 1.063444689 0.695151306
## [656] 4.059426609 -2.043685645 2.596631343 2.588039616 0.739457183
## [661] 3.710749666 4.095987421 2.951401929 2.290339521 1.778362631
## [666] 3.049621921 6.058756935 4.344044208 1.210484440 3.096315540
## [671] 3.031771591 1.727603827 0.331598398 1.236105284 0.485115526
## [676] 1.555518365 2.678115280 3.627007755 2.049911781 6.186023121
## [681] 3.301985562 3.417317058 1.421946964 1.785033950 -1.165910679
## [686] -1.685317585 1.400769474 -0.539049304 1.115189219 1.875915083
## [691] 1.659367806 1.567716579 2.025260678 3.082014854 0.885634202
## [696] 1.999342175 6.029969010 0.564958086 3.162676409 1.709686983
## [701] 2.193585921 2.591820824 1.087417438 0.681057442 1.518574253
## [706] 0.449968202 3.319055541 3.293047719 2.193169752 3.910673288
## [711] 2.701871537 1.259172421 0.412412622 1.379043905 2.417831171
## [716] 4.224734473 2.394856249 1.035521558 1.451391664 1.710861271
## [721] -0.251711912 3.184138713 0.607127287 3.994304290 0.435265330
## [726] 0.197691646 0.267093510 5.365034694 1.864056862 0.771446863
## [731] 2.258197674 2.951627219 2.086999419 3.970615095 2.738781768
## [736] 2.538895362 1.869497988 2.220937136 -0.424675033 2.943844247
## [741] 2.896633244 2.927219745 2.499597213 2.914453244 1.676670196
## [746] 3.450036171 0.851800480 3.683344152 0.454026789 1.661998105
## [751] -0.831016280 -0.677492057 -1.075516212 2.433093791 2.903650562
## [756] 1.323857886 2.809146394 3.136937223 1.596609136 2.317632497
## [761] 3.168571468 0.954346784 -0.148983637 3.868934318 0.770566767
## [766] 1.683826706 2.281640942 2.270344197 3.092902835 2.570866816
## [771] 2.154298210 3.383216253 1.421299220 0.963133514 1.131719556
## [776] 4.199361827 0.775051547 2.368402566 4.122059153 4.407582274
## [781] 2.470290937 0.566437220 3.387714107 0.567811080 0.755146001
## [786] 1.733508596 0.683420674 2.743739967 2.251442570 0.778481416
## [791] 2.549211994 0.538413896 0.730533918 2.439355086 1.772288461
## [796] 2.587030057 2.479025929 0.184281521 2.814331919 4.461030820
## [801] -0.057364874 2.002015632 2.584928879 3.287199618 1.634431997
## [806] 3.352480837 1.745534052 4.698658673 3.185119669 1.406837307
## [811] 1.908054397 0.420546958 1.452751152 0.510137048 0.807239064
## [816] 3.664483615 1.663607928 1.309761842 1.396805081 3.176792533
## [821] 1.985784903 2.704144969 1.041324186 2.365651012 0.019654692
## [826] 4.026911581 2.330424108 2.192779621 0.824368415 1.188860353
## [831] -0.120183972 4.264283551 3.698230434 3.433619634 2.753427384
## [836] 3.514190137 -1.625606079 4.043924078 1.836778801 4.859807813
## [841] 0.932149789 1.682954820 1.868391333 1.803467088 1.178833434
## [846] 0.390626195 3.712003159 0.543724409 -0.165634986 1.004848568
## [851] 1.959544801 2.095925592 1.583452671 1.956609645 3.395602995
## [856] 3.721642423 -0.206488704 1.363415556 1.972136127 1.267884628
## [861] 4.526572055 2.595546285 0.925797290 0.220912921 4.512459057
## [866] 2.495368614 0.674021219 0.705583908 0.007040286 2.936199608
## [871] -0.216631345 1.179345809 2.220634339 4.302209406 1.418751516
## [876] 2.304394710 1.081844554 1.333174946 2.907727856 2.390775492
## [881] 1.592813726 0.290358234 2.789640816 3.187243515 1.177118232
## [886] 4.962961706 1.085463117 1.865594710 2.618794675 2.885200846
## [891] 0.622158597 2.424951115 2.752738264 3.376738479 2.236142409
## [896] -2.255246462 2.006710257 0.193154258 5.089865429 -0.512879313
## [901] 1.075443212 1.665859331 3.837646923 0.057779443 1.293992738
## [906] 0.939137763 3.082751625 1.126302592 1.575622266 0.391678775
## [911] 2.312964101 0.273993057 2.559197666 2.863033290 3.353904612
## [916] -0.157438227 -0.177958598 6.508427565 2.127890686 5.977523764
## [921] -0.280475550 3.007311675 2.551042742 3.341688332 3.517778905
## [926] 0.169836963 3.003923559 1.602167123 1.750599352 1.294358393
## [931] 1.484317920 2.852080029 2.000693640 1.370224982 1.206556258
## [936] 0.126543009 2.887028085 0.831918201 2.315437954 0.340764350
## [941] 0.344580184 2.938082211 3.434364771 1.232473864 2.764874315
## [946] 3.059330824 2.495998496 1.996939823 0.369782350 2.097128097
## [951] 2.130813221 0.035873851 2.313203913 -1.204721083 1.527249398
## [956] 1.106694715 2.636850222 0.227529448 2.090004786 -0.029781083
## [961] 3.039885876 2.713809810 3.238641834 2.190138677 1.673133444
## [966] -0.833353139 0.251368852 -0.086000384 0.580192787 -0.097651715
## [971] 2.654820507 -1.947054126 4.217289360 0.309209010 3.606490571
## [976] 0.113299389 0.336824827 2.250463309 3.548493647 1.259245968
## [981] 0.544918262 1.826181591 2.301358421 1.320629629 2.501701733
## [986] 2.320671989 -1.460857703 -0.790636626 0.743792898 1.117947631
## [991] 1.417623722 3.489751655 0.831792397 3.577422580 4.502578238
## [996] 3.875680661 3.017801451 1.859202531 -0.081511404 4.549532521
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.7968 0.9207 1.9658 1.9494 3.0011 6.7624
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%
## -0.5717673
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%
## 4.369463
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%
## -0.5717673
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [37] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE FALSE FALSE
## [121] TRUE 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 TRUE TRUE 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 FALSE FALSE FALSE TRUE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE TRUE 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 TRUE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [325] TRUE 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 FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE
## [505] TRUE 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 TRUE 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 FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 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 FALSE FALSE FALSE FALSE
## [685] TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE 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 FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE TRUE 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
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -2.0621630 -0.6522288 -0.8402252 -2.5273989 -1.0295097 -0.8290440
## [7] -2.7967851 -0.5845282 -1.0302944 -1.5906899 -1.0861649 -0.7985372
## [13] -0.6103792 -0.6767083 -0.7532466 -1.0448598 -0.7939971 -0.7901442
## [19] -0.8482860 -0.8389594 -1.5884962 -1.2353598 -0.5876720 -1.1519887
## [25] -1.3110783 -0.6309516 -1.1687983 -2.5195998 -0.7815946 -0.9889346
## [31] -2.3696055 -1.2269113 -0.8629427 -0.8090525 -0.6904186 -0.5884150
## [37] -0.6638120 -2.0436856 -1.1659107 -1.6853176 -0.8310163 -0.6774921
## [43] -1.0755162 -1.6256061 -2.2552465 -1.2047211 -0.8333531 -1.9470541
## [49] -1.4608577 -0.7906366
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.369463
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE TRUE 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 TRUE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE TRUE 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] FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE
## [361] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
## [445] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] TRUE 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 TRUE 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 TRUE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE TRUE 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 TRUE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [865] TRUE FALSE FALSE 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 TRUE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE
## [997] FALSE FALSE FALSE TRUE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.226972 5.031324 5.285601 4.764669 4.803682 6.356037 5.108602 4.680827
## [9] 6.168205 5.297449 4.718744 4.650112 5.125006 4.560282 4.900217 5.303558
## [17] 5.000049 5.841525 5.152771 4.467865 5.466645 5.315244 5.009859 6.762358
## [25] 4.439795 4.711862 5.121637 4.561742 4.690922 5.058510 4.999151 5.013161
## [33] 4.900649 5.037534 6.058757 6.186023 6.029969 5.365035 4.407582 4.461031
## [41] 4.698659 4.859808 4.526572 4.512459 4.962962 5.089865 6.508428 5.977524
## [49] 4.502578 4.549533