# Mindanao State University
# General Santos
# Introduction to R base commands
# Prepared by: Prof. Carlito O. Daarol
# Faculty
# Math Department
# Submitted by: Jeshryl R. Sabang
# 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] 1.03208329 2.53583806 1.60119428 -1.21621192 2.06695395 2.35171756
## [7] 1.92474216 0.48097444 3.25956074 2.40243075 2.14812670 2.14797927
## [13] 3.90697366 4.36212850 2.58790490 6.15408426 -0.01262737 -1.37295193
## [19] 2.82205901 -1.32059771
data[1:300] # display the first 300 elements
## [1] 1.032083286 2.535838057 1.601194280 -1.216211915 2.066953955
## [6] 2.351717557 1.924742163 0.480974445 3.259560737 2.402430750
## [11] 2.148126700 2.147979273 3.906973662 4.362128502 2.587904900
## [16] 6.154084257 -0.012627366 -1.372951928 2.822059006 -1.320597709
## [21] 1.825324626 0.908474133 3.388603992 2.201739303 2.201936545
## [26] 2.843383198 -0.188192931 0.016633437 1.820689855 5.023393950
## [31] 3.188538809 -0.302732966 3.020999106 5.113728866 0.345181578
## [36] 3.269750279 2.040707574 3.481917526 0.895165970 3.237599072
## [41] 2.897967388 1.144009964 3.642858498 2.709113508 2.535409115
## [46] 3.657916772 2.728584003 2.063453427 0.491746117 2.538787813
## [51] 0.781705681 1.680620629 -0.171772829 2.808721675 -0.588882041
## [56] -2.645512943 1.069628013 3.443603953 2.223628661 0.510383008
## [61] 3.569621887 2.930821795 4.212399790 1.364570365 -0.095401125
## [66] 4.437584127 2.070920951 2.168843045 3.607242352 0.189052463
## [71] 1.248863620 2.933109392 1.014642099 3.020458876 -0.815996368
## [76] 2.252713713 1.793552337 2.136776536 2.602298080 2.523182928
## [81] 3.364208982 0.840105110 3.446899266 0.175425186 2.927437168
## [86] 0.536146905 1.818691926 2.200209386 2.860852038 4.306657772
## [91] -0.516261550 2.296234692 1.582792194 5.307391822 -0.515957901
## [96] 2.219148006 3.129658516 4.541460834 2.781980545 1.470541873
## [101] 2.253763370 4.467628971 1.302349735 1.997879230 0.873749966
## [106] 1.857553714 2.135446100 1.024611807 2.290991012 2.996657261
## [111] 2.190938993 2.214534223 1.904437937 3.085952305 -1.275123003
## [116] 0.423698923 0.845003348 -1.825610529 4.571883194 2.824910392
## [121] 5.911009203 1.478665509 3.756911571 -0.911699338 1.469566306
## [126] 1.498801440 2.941481305 3.145422632 2.152376890 1.411882693
## [131] 1.100696889 2.044820651 2.878028647 0.824323561 -0.251528423
## [136] 2.659634307 4.467378702 1.424273459 4.351384296 1.146319399
## [141] 0.756368614 2.029843023 2.488592859 1.624735288 1.627819499
## [146] 1.424602901 3.727604184 2.217539290 2.468897176 -0.068050562
## [151] 1.400298828 2.032636316 4.440424480 1.648814914 2.208812959
## [156] 1.300315641 0.357289217 1.731150533 2.753100225 2.695332593
## [161] 2.760510129 0.772816984 -0.233638401 2.476855987 2.252191331
## [166] 2.527319577 -0.183188843 5.458323110 5.174280313 4.992610660
## [171] -1.085369229 -0.055460708 1.881821374 3.766117679 -0.192103845
## [176] 1.242437987 0.197650195 0.516902857 3.140149308 3.655551240
## [181] 3.470632047 1.125600067 1.777328043 -1.664710847 0.529720338
## [186] 1.800876998 3.531157081 2.475978882 3.229838925 2.924559935
## [191] 3.196871524 2.083371992 1.187614147 2.428529496 4.558903612
## [196] 4.428126811 -0.446683662 4.073917390 3.007190522 2.717757439
## [201] 3.200811307 1.906373153 2.809462982 -1.579459328 2.708936916
## [206] -0.185053820 0.897438518 2.104563928 -1.688302290 2.415662626
## [211] 3.475645541 2.671714876 2.255612223 2.586701257 -0.809012984
## [216] 1.155258493 -0.015280602 3.724501263 2.545186847 4.941078843
## [221] 4.572776780 2.058200820 -0.357640602 1.808786529 1.173422045
## [226] 3.035682221 0.714017328 1.038773648 2.499651504 0.722417078
## [231] 2.689521887 -1.059393914 0.271176350 2.225067009 0.091204829
## [236] 1.508350633 -0.442865175 1.245036995 2.884176379 2.359563851
## [241] 1.023003272 2.057650942 3.000424113 1.374315058 1.789705064
## [246] 0.559636348 2.086658529 1.940270447 1.971743270 0.254380378
## [251] 4.414734808 3.820031264 2.025307741 2.049154033 0.492038310
## [256] 2.222912605 2.063666919 3.239774761 1.670542371 -0.688692236
## [261] 2.310278012 0.653712715 3.219113815 2.594600007 0.870565808
## [266] -0.126940803 1.270050140 -1.019026110 1.090961157 1.643632598
## [271] 1.915692842 1.056004031 1.566610529 1.096060689 1.362077241
## [276] 0.972359284 5.011258627 2.041610483 -0.253416745 4.200394663
## [281] 1.648904703 4.121985040 2.607321494 2.160878899 -0.497923548
## [286] 3.315086720 -0.776347359 -0.569124876 1.867735758 -0.018212042
## [291] -0.360612787 3.119564194 1.868530871 0.535543771 2.608643141
## [296] 1.633546821 0.002257772 2.571922181 3.869511419 1.521830984
# 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] -3.137067e+00 -3.032499e+00 -2.927931e+00 -2.823363e+00 -2.718795e+00
## [6] -2.614227e+00 -2.509659e+00 -2.405092e+00 -2.300524e+00 -2.195956e+00
## [11] -2.091388e+00 -1.986820e+00 -1.882252e+00 -1.777684e+00 -1.673117e+00
## [16] -1.568549e+00 -1.463981e+00 -1.359413e+00 -1.254845e+00 -1.150277e+00
## [21] -1.045709e+00 -9.411415e-01 -8.365737e-01 -7.320058e-01 -6.274380e-01
## [26] -5.228701e-01 -4.183022e-01 -3.137344e-01 -2.091665e-01 -1.045987e-01
## [31] -3.081334e-05 1.045370e-01 2.091049e-01 3.136728e-01 4.182406e-01
## [36] 5.228085e-01 6.273763e-01 7.319442e-01 8.365120e-01 9.410799e-01
## [41] 1.045648e+00 1.150216e+00 1.254783e+00 1.359351e+00 1.463919e+00
## [46] 1.568487e+00 1.673055e+00 1.777623e+00 1.882191e+00 1.986758e+00
## [51] 2.091326e+00 2.195894e+00 2.300462e+00 2.405030e+00 2.509598e+00
## [56] 2.614166e+00 2.718733e+00 2.823301e+00 2.927869e+00 3.032437e+00
## [61] 3.137005e+00 3.241573e+00 3.346141e+00 3.450708e+00 3.555276e+00
## [66] 3.659844e+00 3.764412e+00 3.868980e+00 3.973548e+00 4.078116e+00
## [71] 4.182683e+00 4.287251e+00 4.391819e+00 4.496387e+00 4.600955e+00
## [76] 4.705523e+00 4.810091e+00 4.914658e+00 5.019226e+00 5.123794e+00
## [81] 5.228362e+00 5.332930e+00 5.437498e+00 5.542066e+00 5.646633e+00
## [86] 5.751201e+00 5.855769e+00 5.960337e+00 6.064905e+00 6.169473e+00
## [91] 6.274041e+00 6.378608e+00 6.483176e+00 6.587744e+00 6.692312e+00
## [96] 6.796880e+00 6.901448e+00 7.006016e+00 7.110583e+00 7.215151e+00
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%
## -3.137067 1.008967 2.110855 3.074867 7.215151
# 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] 1.032083286 2.535838057 1.601194280 -1.216211915 2.066953955
## [6] 2.351717557 1.924742163 0.480974445 3.259560737 2.402430750
## [11] 2.148126700 2.147979273 3.906973662 4.362128502 2.587904900
## [16] 6.154084257 -0.012627366 -1.372951928 2.822059006 -1.320597709
## [21] 1.825324626 0.908474133 3.388603992 2.201739303 2.201936545
## [26] 2.843383198 -0.188192931 0.016633437 1.820689855 5.023393950
## [31] 3.188538809 -0.302732966 3.020999106 5.113728866 0.345181578
## [36] 3.269750279 2.040707574 3.481917526 0.895165970 3.237599072
## [41] 2.897967388 1.144009964 3.642858498 2.709113508 2.535409115
## [46] 3.657916772 2.728584003 2.063453427 0.491746117 2.538787813
## [51] 0.781705681 1.680620629 -0.171772829 2.808721675 -0.588882041
## [56] -2.645512943 1.069628013 3.443603953 2.223628661 0.510383008
## [61] 3.569621887 2.930821795 4.212399790 1.364570365 -0.095401125
## [66] 4.437584127 2.070920951 2.168843045 3.607242352 0.189052463
## [71] 1.248863620 2.933109392 1.014642099 3.020458876 -0.815996368
## [76] 2.252713713 1.793552337 2.136776536 2.602298080 2.523182928
## [81] 3.364208982 0.840105110 3.446899266 0.175425186 2.927437168
## [86] 0.536146905 1.818691926 2.200209386 2.860852038 4.306657772
## [91] -0.516261550 2.296234692 1.582792194 5.307391822 -0.515957901
## [96] 2.219148006 3.129658516 4.541460834 2.781980545 1.470541873
## [101] 2.253763370 4.467628971 1.302349735 1.997879230 0.873749966
## [106] 1.857553714 2.135446100 1.024611807 2.290991012 2.996657261
## [111] 2.190938993 2.214534223 1.904437937 3.085952305 -1.275123003
## [116] 0.423698923 0.845003348 -1.825610529 4.571883194 2.824910392
## [121] 5.911009203 1.478665509 3.756911571 -0.911699338 1.469566306
## [126] 1.498801440 2.941481305 3.145422632 2.152376890 1.411882693
## [131] 1.100696889 2.044820651 2.878028647 0.824323561 -0.251528423
## [136] 2.659634307 4.467378702 1.424273459 4.351384296 1.146319399
## [141] 0.756368614 2.029843023 2.488592859 1.624735288 1.627819499
## [146] 1.424602901 3.727604184 2.217539290 2.468897176 -0.068050562
## [151] 1.400298828 2.032636316 4.440424480 1.648814914 2.208812959
## [156] 1.300315641 0.357289217 1.731150533 2.753100225 2.695332593
## [161] 2.760510129 0.772816984 -0.233638401 2.476855987 2.252191331
## [166] 2.527319577 -0.183188843 5.458323110 5.174280313 4.992610660
## [171] -1.085369229 -0.055460708 1.881821374 3.766117679 -0.192103845
## [176] 1.242437987 0.197650195 0.516902857 3.140149308 3.655551240
## [181] 3.470632047 1.125600067 1.777328043 -1.664710847 0.529720338
## [186] 1.800876998 3.531157081 2.475978882 3.229838925 2.924559935
## [191] 3.196871524 2.083371992 1.187614147 2.428529496 4.558903612
## [196] 4.428126811 -0.446683662 4.073917390 3.007190522 2.717757439
## [201] 3.200811307 1.906373153 2.809462982 -1.579459328 2.708936916
## [206] -0.185053820 0.897438518 2.104563928 -1.688302290 2.415662626
## [211] 3.475645541 2.671714876 2.255612223 2.586701257 -0.809012984
## [216] 1.155258493 -0.015280602 3.724501263 2.545186847 4.941078843
## [221] 4.572776780 2.058200820 -0.357640602 1.808786529 1.173422045
## [226] 3.035682221 0.714017328 1.038773648 2.499651504 0.722417078
## [231] 2.689521887 -1.059393914 0.271176350 2.225067009 0.091204829
## [236] 1.508350633 -0.442865175 1.245036995 2.884176379 2.359563851
## [241] 1.023003272 2.057650942 3.000424113 1.374315058 1.789705064
## [246] 0.559636348 2.086658529 1.940270447 1.971743270 0.254380378
## [251] 4.414734808 3.820031264 2.025307741 2.049154033 0.492038310
## [256] 2.222912605 2.063666919 3.239774761 1.670542371 -0.688692236
## [261] 2.310278012 0.653712715 3.219113815 2.594600007 0.870565808
## [266] -0.126940803 1.270050140 -1.019026110 1.090961157 1.643632598
## [271] 1.915692842 1.056004031 1.566610529 1.096060689 1.362077241
## [276] 0.972359284 5.011258627 2.041610483 -0.253416745 4.200394663
## [281] 1.648904703 4.121985040 2.607321494 2.160878899 -0.497923548
## [286] 3.315086720 -0.776347359 -0.569124876 1.867735758 -0.018212042
## [291] -0.360612787 3.119564194 1.868530871 0.535543771 2.608643141
## [296] 1.633546821 0.002257772 2.571922181 3.869511419 1.521830984
## [301] 3.454847124 5.404142341 0.407222415 4.783830524 3.370739692
## [306] 1.417138178 0.758505395 1.303667826 -0.408923543 3.538426285
## [311] 2.238557889 2.716175168 2.315732788 3.946740822 3.506242731
## [316] 2.137063659 0.113087248 3.199680961 5.233916668 2.579165390
## [321] 1.735854914 3.232144573 1.691435823 1.776302723 4.396102727
## [326] 0.917357995 4.347889849 4.480912002 0.028247494 3.301610376
## [331] 4.088799530 2.861465570 2.125734046 0.872264073 2.444006244
## [336] 2.961723571 1.748046394 -0.123583589 1.180220547 0.650642169
## [341] 2.145563867 0.141541964 4.993235032 -0.135351649 2.238662704
## [346] 1.017011889 4.105051375 2.448334609 1.894356114 2.895537985
## [351] 2.382656041 0.441832163 1.928794341 1.315926976 0.189323880
## [356] 2.151016385 1.752295316 2.260381205 4.046115589 3.538435138
## [361] 0.796808287 3.013029438 -1.139546307 2.554657933 2.590971858
## [366] -0.889812491 2.104077793 2.473430790 2.492272158 -0.104333351
## [371] 1.062735927 5.894565696 0.818424262 2.501492228 4.011207450
## [376] -0.455287752 0.128648474 1.717383994 1.845029988 1.730962943
## [381] 0.673883131 2.036443492 0.586864911 1.349915240 3.082909554
## [386] 2.138047926 1.353651255 4.320362131 4.572277394 3.269965736
## [391] 4.123848383 4.272083763 2.522331415 1.980970736 4.737547782
## [396] 2.987197779 -0.215655315 3.310501860 4.303378219 2.745489660
## [401] 1.367893368 2.842033527 2.485518113 2.396168711 0.102197759
## [406] 1.189658080 3.038801359 0.901224043 2.713532501 3.026318204
## [411] 0.067598756 3.124942020 0.600367132 0.743838377 0.859633237
## [416] 0.976568252 0.309796535 4.361047913 0.824556265 3.114213946
## [421] 1.554325226 2.631580295 3.937128273 4.328262928 0.843330308
## [426] 1.955906876 1.263561928 -0.200375470 3.678985826 1.452906090
## [431] 1.340513356 1.790183888 0.910352829 1.782162574 0.320456406
## [436] 4.073941022 1.502344796 1.396328751 3.298886039 4.647895369
## [441] 2.320188254 2.607234731 1.340985245 2.785692560 4.606804199
## [446] 0.070996821 0.651794127 3.145204126 1.645672180 3.352377188
## [451] 1.983565086 1.315733031 2.801292007 2.109538666 -0.770383472
## [456] 1.759728523 0.941845949 -2.089971819 0.534959075 3.178501599
## [461] 3.556883946 1.108260122 1.497004685 2.358679373 0.861436931
## [466] 1.833473593 3.285556337 2.239056174 4.531058626 0.392526721
## [471] 2.404765373 2.836264455 1.993504538 0.420857306 3.697225739
## [476] 2.015194563 0.159027644 3.028818950 2.225644329 0.904295803
## [481] 1.870214987 0.637634499 2.808851200 3.332514137 3.979496252
## [486] 5.017083273 2.237329203 3.326367781 2.903899136 2.715346666
## [491] 2.497997089 1.225684224 2.858858948 2.580727925 2.809418935
## [496] 3.504203066 3.739229156 2.241377563 4.752890820 -1.215380162
## [501] 1.505282581 -0.601977369 2.085196566 0.271476870 0.817419377
## [506] 3.614934531 2.326164249 0.068796258 0.820147685 7.215151300
## [511] 1.876782264 2.807055400 5.294075823 5.899472339 1.764900371
## [516] 0.048790059 0.024721467 4.798171634 4.152200153 2.378283149
## [521] -0.146907129 3.962177110 3.364515757 -0.876488121 3.479024601
## [526] 3.860769321 5.746122160 2.377494377 2.428359427 0.719847081
## [531] 0.398449627 1.209958157 5.454094522 3.695490532 -1.315012747
## [536] 2.787943752 1.143587042 4.359844279 1.509982613 4.154641240
## [541] 2.225035259 0.998241601 3.614830034 1.904414528 2.477102755
## [546] 2.141018397 2.146842733 1.590156497 1.781498901 3.069733106
## [551] 0.227068060 1.922771145 0.943581754 -0.551300209 1.494190707
## [556] 6.787627647 4.677709034 5.630825427 1.731705310 3.511262780
## [561] 1.830692036 3.534375489 2.247500741 5.031740336 1.594169187
## [566] 2.052328214 2.433112073 0.788775523 1.576768719 4.058907337
## [571] 3.521689962 1.841664004 -1.244610143 0.527433546 2.848107213
## [576] 4.973208167 2.028944388 1.414521036 -0.076415450 4.106796268
## [581] 2.316506996 5.089212297 1.379976710 2.464469859 3.056479865
## [586] 0.946619197 4.275208086 3.828874727 1.303855563 -0.135020182
## [591] 1.418250749 2.265860207 -0.260123426 2.920606205 4.483260161
## [596] 3.604793812 1.502223482 1.264689837 1.956275469 0.577480037
## [601] 1.745637520 1.947660925 1.945225455 0.643829987 2.715496454
## [606] -0.291229615 5.139125309 2.282006813 2.758286926 -0.551329535
## [611] 1.902644946 2.394840828 2.521998826 0.462495689 1.665388392
## [616] 2.872341016 1.333576522 1.482283598 1.272752961 1.432824044
## [621] 1.785082588 3.722094951 2.140015362 2.286124964 3.894721552
## [626] 4.347292326 0.040854763 2.549152166 1.343738347 -0.377738235
## [631] 2.159461493 0.006568664 1.688158246 4.391657503 4.652579245
## [636] 2.249404959 0.560736418 3.642271514 0.295757832 -2.233807292
## [641] 3.053719702 3.246612363 4.824956666 4.455396396 2.292542653
## [646] 2.807835665 0.910708660 3.256293528 1.829499315 1.636134503
## [651] 3.173761722 3.030472961 2.212331925 1.794667479 1.360140104
## [656] 2.444481085 3.529941173 0.515760903 2.632726629 1.946670908
## [661] 0.206139507 -0.591098076 -1.887877081 1.972749318 0.911982076
## [666] 0.160083300 2.294474141 0.156892100 2.075626113 2.888628869
## [671] 0.547333852 3.345530225 1.660506998 0.194192390 1.302954020
## [676] 2.916260092 -0.242287897 3.261626155 0.994519603 3.434448008
## [681] 1.757453584 3.212688750 5.899942667 0.379931039 3.803988337
## [686] 1.161667052 -0.300030634 0.129843352 2.336567245 3.112145355
## [691] 2.666718392 2.376265139 1.545452434 3.925627865 2.634716422
## [696] 3.765487686 0.903954451 0.282281084 2.690940729 3.799143022
## [701] 0.555661541 2.839635292 1.738544894 0.249032951 2.674509698
## [706] 2.343570252 1.627173946 0.315880901 3.364750283 2.814702392
## [711] 3.514367223 -0.154536351 0.620340776 2.944389212 2.191790969
## [716] 0.114453359 -0.011140778 3.624558202 1.097983575 3.414549889
## [721] 4.951771819 2.611431724 2.286849984 2.549392768 2.576382560
## [726] 0.826732854 0.564076099 4.561630324 1.586577456 5.613479624
## [731] 3.073712385 1.442149739 3.738745292 0.898178231 4.953083370
## [736] 0.490337578 3.095950049 4.316520297 2.886847624 2.503952381
## [741] 0.814205259 1.392121857 3.711387950 1.473454316 5.356640364
## [746] 1.496368678 1.277597643 4.099857101 6.386887434 1.749402573
## [751] 1.553677417 2.841135084 2.901218338 1.953065704 1.843277553
## [756] 3.010943463 0.775474567 3.507792463 4.273603407 4.465704965
## [761] 2.277962537 2.704220290 -0.333047045 1.252616377 0.998753060
## [766] 3.146216788 2.796168699 4.728332368 3.792931121 -0.791662910
## [771] 2.777646063 1.011917104 0.919492804 3.443398604 2.779011718
## [776] 1.389771770 4.021324118 4.576486752 2.798651537 0.921158004
## [781] 3.123082346 0.172227342 0.563306680 1.623402483 2.393437549
## [786] 3.059069511 2.255622243 1.382567551 1.087636425 0.529917172
## [791] 3.117376516 3.857301767 5.011547685 3.389146817 2.470107555
## [796] 3.427891998 2.657287766 3.352576817 2.539947517 2.556183933
## [801] 4.866088768 0.154903996 1.064667575 1.661403307 -2.141541575
## [806] 1.292950081 1.416228123 -1.897368691 0.685170866 2.312225997
## [811] 3.820334615 0.576532740 1.976071482 1.494296734 3.835732744
## [816] 1.072495349 2.309352081 2.795101159 -0.446210394 2.224778943
## [821] 1.200797118 3.759078896 3.512872151 1.296204356 1.848715865
## [826] 2.188752237 4.723516114 0.029595112 3.810050378 1.683628311
## [831] 2.749865507 1.693942599 0.698444240 1.023159073 2.009557356
## [836] 2.770801194 5.267237420 1.555989941 2.445015857 3.933541296
## [841] 3.157113720 1.038880659 2.682243202 0.351465060 1.252086521
## [846] 4.023017929 3.078330824 2.243595735 3.471712360 -0.390866681
## [851] 1.786196463 2.345337927 4.263766608 -0.727949690 0.822433625
## [856] 3.848036446 4.517269795 1.143732222 1.000115670 0.402434755
## [861] 2.808015217 3.185822198 0.226438136 0.925273900 0.765552090
## [866] 1.917879686 1.785636222 2.291650789 2.839015491 2.423440637
## [871] 2.391329716 1.145003045 3.805774913 2.492675945 2.425218834
## [876] 0.933668038 0.160946070 4.221362001 1.506317807 2.644095454
## [881] 4.232336092 1.596874858 3.073319925 -0.472081842 3.961584402
## [886] 1.072928819 4.887183541 0.839866931 3.878690278 0.452712936
## [891] -3.137066515 0.238661490 2.112170986 0.761633894 0.183986119
## [896] 1.311518018 2.793001724 4.942078019 1.138680700 2.627538073
## [901] 4.060625065 3.574450783 2.166384771 1.837590593 0.334252049
## [906] 0.512201356 3.775698377 3.233729358 0.059428592 2.912613860
## [911] 3.626702301 2.136527145 1.376580123 3.327305301 1.817848083
## [916] 1.549691652 0.039961229 2.390268018 0.245913530 1.431850703
## [921] 1.107794214 -0.239703156 4.280622454 2.589459593 0.100289491
## [926] 0.393639177 3.653196127 0.014982142 2.755921361 1.163109146
## [931] 3.243016002 1.194565518 2.729264858 3.141482337 0.576663872
## [936] 2.337201974 0.234353750 1.037345633 -0.932179968 1.883050279
## [941] 4.692885865 4.350866821 4.782577342 4.488208823 1.334804007
## [946] 2.898312665 2.021934386 3.975134665 0.226583557 1.248641666
## [951] 3.176407618 2.556462463 2.668576663 3.753023820 1.738627262
## [956] -0.108032013 1.076201993 1.121802950 1.745114465 -0.194009981
## [961] 0.836983184 1.073076941 1.518346816 3.620718327 1.917491635
## [966] 3.278862907 0.047170633 -1.537298327 2.888546751 0.410060109
## [971] 2.170305536 2.515141786 1.923314802 3.714144441 3.684416496
## [976] -2.203220595 4.380291176 -0.125515701 1.801995970 2.330558909
## [981] 1.172728008 1.756468888 2.987864912 0.140424594 2.955078467
## [986] 0.063815720 0.421758024 2.930046248 4.584096236 1.668517702
## [991] 2.600753989 0.420364489 2.428111597 3.080690275 2.466627128
## [996] 1.835459204 2.976373588 1.936513251 3.403106626 -0.568586108
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.137 1.009 2.111 2.063 3.075 7.215
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%
## -0.4106206
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%
## 4.585232
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%
## -0.4106206
# 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 TRUE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
## [121] FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [205] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## [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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [457] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE 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 TRUE 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 TRUE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE TRUE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE TRUE 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 TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE TRUE 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 TRUE
# 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] -1.2162119 -1.3729519 -1.3205977 -0.5888820 -2.6455129 -0.8159964
## [7] -0.5162615 -0.5159579 -1.2751230 -1.8256105 -0.9116993 -1.0853692
## [13] -1.6647108 -0.4466837 -1.5794593 -1.6883023 -0.8090130 -1.0593939
## [19] -0.4428652 -0.6886922 -1.0190261 -0.4979235 -0.7763474 -0.5691249
## [25] -1.1395463 -0.8898125 -0.4552878 -0.7703835 -2.0899718 -1.2153802
## [31] -0.6019774 -0.8764881 -1.3150127 -0.5513002 -1.2446101 -0.5513295
## [37] -2.2338073 -0.5910981 -1.8878771 -0.7916629 -2.1415416 -1.8973687
## [43] -0.4462104 -0.7279497 -0.4720818 -3.1370665 -0.9321800 -1.5372983
## [49] -2.2032206 -0.5685861
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.585232
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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] 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 FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [169] TRUE TRUE 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 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 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 FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] TRUE 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 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [445] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE
## [517] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [529] FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [577] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [733] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 6.154084 5.023394 5.113729 5.307392 5.911009 5.458323 5.174280 4.992611
## [9] 4.941079 5.011259 5.404142 4.783831 5.233917 4.993235 5.894566 4.737548
## [17] 4.647895 4.606804 5.017083 4.752891 7.215151 5.294076 5.899472 4.798172
## [25] 5.746122 5.454095 6.787628 4.677709 5.630825 5.031740 4.973208 5.089212
## [33] 5.139125 4.652579 4.824957 5.899943 4.951772 5.613480 4.953083 5.356640
## [41] 6.386887 4.728332 5.011548 4.866089 4.723516 5.267237 4.887184 4.942078
## [49] 4.692886 4.782577