# Mindanao State University
# General Santos City
# Introduction to R base commands
# Prepared by: Ehjie Bob A. Jumaway
# Student
# Math Department
# March 21, 2023
# Processing of continuous data
# Using random number generators
# Exer1: generate data with mean 2 and standard deviation 1.5 using rnorm() command
data <- rnorm(1000,2,1.5) # 1 thousand values
length(data) # count number of elements
## [1] 1000
## [1] 1000
data[1:20] # display first 20 elements
## [1] 0.8212292 3.8373775 2.3933322 1.5995944 1.1666721 4.0535308
## [7] 0.5932258 3.2851322 3.6770145 2.9249392 3.2627255 5.0057901
## [13] -0.6576320 3.9336992 2.8590366 0.5692789 2.0992101 -0.4168984
## [19] 2.1147834 2.3624817
## [1] 2.5301773 2.1433329 2.7461992 0.7191137 3.2323958 3.5984216
## [7] 0.1271980 -1.5035094 1.0505412 1.1516095 -0.5724505 3.0382656
## [13] 0.1978632 4.8605855 1.7109003 1.4850920 0.8958760 0.9233573
## [19] 1.9103658 3.1534402
data[1:300] # display the first 300 elements
## [1] 0.821229172 3.837377527 2.393332222 1.599594424 1.166672068
## [6] 4.053530752 0.593225820 3.285132191 3.677014501 2.924939195
## [11] 3.262725480 5.005790149 -0.657632004 3.933699165 2.859036588
## [16] 0.569278862 2.099210139 -0.416898398 2.114783386 2.362481680
## [21] 2.756634873 3.124686812 -0.002088106 0.782613625 1.833376961
## [26] 2.646547918 -2.206918118 3.367529997 2.094360435 4.447022686
## [31] 3.218956683 1.558977029 1.788248084 5.219907260 3.636560868
## [36] 3.313760326 1.425370117 2.641995232 0.339195347 4.654836653
## [41] 2.502123992 3.594602396 2.851749520 2.797659167 1.067314311
## [46] 3.276952638 -0.803047452 3.915062080 1.739429059 -0.081190896
## [51] 3.012392842 1.819204022 -0.619395120 3.488878158 2.283913653
## [56] 3.307519575 -0.367422047 -1.745441588 -0.442531620 0.531535119
## [61] 1.417800807 -1.974664175 3.628294391 3.978784643 2.647974839
## [66] 1.262603879 1.534395202 1.188757193 2.294355433 3.580550863
## [71] -0.403678432 -0.726070370 2.641968470 5.327918540 2.414307190
## [76] 2.995458197 1.855873836 1.275345487 1.496817009 1.273108882
## [81] 2.469768752 3.059223355 0.556097244 2.677023323 0.238609570
## [86] 1.314147238 3.621290350 -0.084699111 0.170200358 2.358064798
## [91] 0.856090755 -2.116907652 0.712541217 1.701862056 1.682213056
## [96] 2.240958667 1.371168246 2.620158363 -0.285188293 2.790153982
## [101] 2.687072775 -1.980080019 0.204291978 2.720255854 3.447957871
## [106] 1.060286615 0.946419659 0.993391576 4.955671438 4.654328774
## [111] 1.606253102 4.718575884 0.531694703 3.855480734 3.049354532
## [116] 2.254468061 4.156862001 2.621037017 1.733721782 2.430890446
## [121] 0.234922208 1.805676173 2.601917124 1.883286733 0.374434707
## [126] 2.216380723 5.549166311 4.023406774 3.662294390 2.697344308
## [131] 4.342555137 -1.139645590 3.630250517 4.143436955 2.175813430
## [136] 1.444428667 -0.316573211 2.155898463 3.241868394 1.333997731
## [141] 3.427736860 2.785605543 1.052682623 2.210117079 2.903835498
## [146] 2.521468452 0.079563228 2.190689247 1.369082479 3.368724266
## [151] 3.212812698 1.094765684 1.396173395 2.039918311 3.691632391
## [156] 0.373745747 2.706188161 2.334990758 -1.190578157 0.056721379
## [161] 2.955582575 0.189104557 1.763113960 2.678547035 -0.509829496
## [166] 3.253045023 1.634019783 1.582134177 1.026194857 3.923583996
## [171] 4.804582269 3.951372875 2.026965567 3.363294724 2.135214757
## [176] 0.237686762 5.423394530 2.867888446 6.099057668 0.665062234
## [181] 4.975725484 2.059326456 3.498997715 3.110910844 3.057571971
## [186] 3.537403565 1.924119452 3.818760854 5.228674355 1.439267255
## [191] 2.589687592 2.518985630 0.227321006 2.514675882 2.731027216
## [196] 3.875905822 3.302706452 -0.518637578 1.217286212 -0.431147824
## [201] 0.619033241 5.307734404 1.442496782 3.752997254 0.631264694
## [206] 0.050544262 5.452915684 -0.581581268 3.804120775 2.114346082
## [211] 3.089953593 0.494220239 3.000950809 0.281694081 3.750178062
## [216] 5.052645303 3.959705101 3.599971308 2.988651350 3.884106603
## [221] 3.018222756 -1.020517332 1.660169793 3.248641645 0.853775358
## [226] 3.431870088 1.552940813 2.656618348 2.573240892 2.770242764
## [231] 5.101064696 2.951055529 2.395515840 2.261005793 3.799198385
## [236] -1.693287506 2.041695485 2.396292810 2.590017285 1.003923408
## [241] 3.503347136 1.041710815 1.850892212 -4.048816523 2.686322408
## [246] 3.613285170 0.721114698 3.523996740 1.331075522 1.138947667
## [251] 1.542041543 1.455160721 2.257322561 1.305537300 3.150189150
## [256] 5.014890015 0.796422030 4.209090580 3.287697457 2.935797890
## [261] 3.151953667 1.873029548 2.241232985 4.261498174 2.996296076
## [266] -0.094307909 1.242206949 0.620982100 2.822070417 -1.135914235
## [271] 1.446925603 2.700423031 2.311281441 3.246191774 1.778366181
## [276] 3.354676670 3.966433758 1.798351827 3.507876567 1.786710854
## [281] 2.234861601 2.619632686 1.285543033 3.659130576 3.320445372
## [286] 1.903271614 -0.168679144 5.005573038 3.409899544 4.423734470
## [291] 2.135520034 1.500676149 1.319288759 0.541255941 3.274995088
## [296] 2.232171677 0.708355272 0.197206895 -1.124595635 3.818604132
## [1] 2.53017729 2.14333287 2.74619917 0.71911371 3.23239577 3.59842156
## [7] 0.12719804 -1.50350940 1.05054122 1.15160954 -0.57245047 3.03826556
## [13] 0.19786324 4.86058548 1.71090027 1.48509205 0.89587598 0.92335733
## [19] 1.91036581 3.15344023 5.01095876 0.75518489 1.15872555 1.82397581
## [25] 1.50632586 1.70451599 1.71363965 3.16092542 1.41424246 2.70767519
## [31] 2.34194604 1.12922626 4.18295372 3.41712818 3.25516589 3.05053743
## [37] 2.47589292 0.47143164 -0.35358646 0.94239599 2.19532992 -0.34707714
## [43] 0.72822654 2.30719960 4.60896771 -0.38553970 1.51808335 1.75324622
## [49] 3.54546895 2.54469933 3.68790809 1.62037411 1.80931174 3.21205768
## [55] 3.64204633 3.87653431 1.59626534 0.03258597 4.06113852 0.08584966
1
## [1] 1
## [61] 2.40483453 3.08791868 5.87272754 2.28367265 1.19629550 1.23368431
## [67] 2.26210886 4.45251460 3.94986536 -0.05017694 3.63721288 2.14730728
## [73] 1.22865278 -1.42413222 4.93708263 4.19257067 4.03429238 1.80774185
## [79] 2.15666292 2.76533613 1.88500634 2.42736388 0.31655924 3.22756032
## [85] 1.67470075 1.68793583 3.23808692 2.48080479 4.63653054 0.98998566
## [91] 2.53575797 2.36378688 -0.73546788 1.47872156 0.52086139 2.71338695
## [97] 1.64264726 -0.03791427 3.95907237 3.31417822 0.82689494 3.32884200
## [103] 2.53981645 2.06174817 1.02317400 3.12359841 1.88881456 2.72975600
## [109] 1.38909232 1.97472713 -0.34187563 3.70868997 1.47445785 3.30526679
## [115] 1.99389648 2.83270561 3.51509687 1.27900433 -0.27240020 3.13985177
## [121] 2.60164412 3.66566796 0.27142563 3.61860788 2.14488065 4.44576638
## [127] 2.52361200 -0.02018926 -0.25735321 -0.14514788 -0.04724710 2.05061401
## [133] 1.23601331 2.36341686 2.51724459 1.30403881 1.91736742 -1.21160814
## [139] 0.42810944 4.34646701 3.78801599 2.09373401 -1.58873917 3.90993262
## [145] 6.46316120 3.46810043 2.77923434 1.67690946 1.67591261 0.69017881
## [151] 3.25044564 2.14475244 0.61749419 3.58543756 0.20688825 3.20380741
## [157] 4.44093990 1.28085659 1.93543571 4.17826882 1.26279160 0.27243645
## [163] 2.92818134 -0.49234735 2.01833799 -0.73042899 0.99737820 1.57241572
## [169] -1.45721689 3.51880972 1.66399557 1.06835349 0.30032527 1.03057396
## [175] 0.30861280 0.69947727 -0.15339295 4.03024048 -0.19428241 1.16544111
## [181] 1.64142335 2.48844230 0.74131615 0.85648847 0.98333780 2.08331348
## [187] 1.57065808 1.90518256 0.46158262 3.49711027 0.65980659 1.35496600
## [193] 3.47621214 2.17367392 2.38684434 2.53219931 1.23622560 1.10682177
## [199] 1.03657751 -0.92355901 -0.05330628 0.61958041 1.33936637 0.47472995
## [205] 4.05561795 0.17189757 1.79880350 2.64016349 1.10200620 2.21361803
## [211] 2.90493832 2.10541709 2.67174008 2.89207565 2.39642030 0.93116301
## [217] -0.10528053 4.16901238 1.41683546 2.74381871 1.02245214 3.19642203
## [223] 4.05721867 0.41828482 4.07060640 1.56632748 1.97136238 2.21232125
## [229] 1.32515136 0.81734762 0.70201719 0.57576807 3.35980598 2.44865382
## [235] 2.62899771 1.03307040 0.50243425 1.30908838 0.14736192 1.55326124
## [241] 1.54341528 1.84158493 0.54586864 2.68452555 0.67190664 3.37086889
## [247] 3.76657256 1.45899596 -1.19260984 3.13319096 -0.25374195 3.73154570
## [253] 3.15600168 2.01901610 3.08196253 0.10009726 2.06570085 -1.34419441
## [259] 1.10782841 1.29243410 -0.24975947 1.67180825 0.87073013 2.75159933
## [265] 4.56599691 2.55598017 1.37452517 3.43774643 0.51216846 3.34991311
## [271] 2.07740756 2.32332660 1.68143674 0.40572880 2.85049458 2.91784367
## [277] -0.64081632 3.74438714 0.88266679 2.78489378 1.29391291 2.87166677
## [283] -1.93194656 2.57689838 2.18230703 0.40949431 2.94160025 1.96983849
## [289] 1.50542856 1.98466586 0.77916145 1.15143327 4.41782602 3.01918213
## [295] 4.82105886 0.90341428 0.77589011 2.54892354 2.02331959 -1.28331697
# Exer2: Draw histogram with one main title and different thickness
maintitle <- "Histogram and Density Plot"
hist(data, breaks=20,col="lightgreen",main = maintitle)
hist(data, breaks=40,col="lightgreen",main = maintitle)
hist(data, breaks=100,col="violet",main = maintitle)
hist(data, breaks=300,col="violet",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="brown",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="lightgreen",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="yellow",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='red',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] -4.04881652 -3.94153206 -3.83424760 -3.72696314 -3.61967868 -3.51239422
## [7] -3.40510976 -3.29782531 -3.19054085 -3.08325639 -2.97597193 -2.86868747
## [13] -2.76140301 -2.65411855 -2.54683409 -2.43954963 -2.33226517 -2.22498071
## [19] -2.11769625 -2.01041179 -1.90312733 -1.79584287 -1.68855841 -1.58127395
## [25] -1.47398949 -1.36670503 -1.25942057 -1.15213611 -1.04485165 -0.93756719
## [31] -0.83028273 -0.72299827 -0.61571381 -0.50842935 -0.40114489 -0.29386043
## [37] -0.18657597 -0.07929151 0.02799295 0.13527741 0.24256187 0.34984633
## [43] 0.45713079 0.56441525 0.67169971 0.77898417 0.88626862 0.99355308
## [49] 1.10083754 1.20812200 1.31540646 1.42269092 1.52997538 1.63725984
## [55] 1.74454430 1.85182876 1.95911322 2.06639768 2.17368214 2.28096660
## [61] 2.38825106 2.49553552 2.60281998 2.71010444 2.81738890 2.92467336
## [67] 3.03195782 3.13924228 3.24652674 3.35381120 3.46109566 3.56838012
## [73] 3.67566458 3.78294904 3.89023350 3.99751796 4.10480242 4.21208688
## [79] 4.31937134 4.42665580 4.53394026 4.64122472 4.74850918 4.85579364
## [85] 4.96307810 5.07036255 5.17764701 5.28493147 5.39221593 5.49950039
## [91] 5.60678485 5.71406931 5.82135377 5.92863823 6.03592269 6.14320715
## [97] 6.25049161 6.35777607 6.46506053 6.57234499
## [1] -2.31383083 -2.22004644 -2.12626204 -2.03247765 -1.93869325 -1.84490885
## [7] -1.75112446 -1.65734006 -1.56355567 -1.46977127 -1.37598687 -1.28220248
## [13] -1.18841808 -1.09463369 -1.00084929 -0.90706489 -0.81328050 -0.71949610
## [19] -0.62571171 -0.53192731 -0.43814291 -0.34435852 -0.25057412 -0.15678973
## [25] -0.06300533 0.03077907 0.12456346 0.21834786 0.31213225 0.40591665
## [31] 0.49970105 0.59348544 0.68726984 0.78105423 0.87483863 0.96862303
## [37] 1.06240742 1.15619182 1.24997621 1.34376061 1.43754501 1.53132940
## [43] 1.62511380 1.71889819 1.81268259 1.90646699 2.00025138 2.09403578
## [49] 2.18782017 2.28160457 2.37538896 2.46917336 2.56295776 2.65674215
## [55] 2.75052655 2.84431094 2.93809534 3.03187974 3.12566413 3.21944853
## [61] 3.31323292 3.40701732 3.50080172 3.59458611 3.68837051 3.78215490
## [67] 3.87593930 3.96972370 4.06350809 4.15729249 4.25107688 4.34486128
## [73] 4.43864568 4.53243007 4.62621447 4.71999886 4.81378326 4.90756766
## [79] 5.00135205 5.09513645 5.18892084 5.28270524 5.37648964 5.47027403
## [85] 5.56405843 5.65784282 5.75162722 5.84541162 5.93919601 6.03298041
## [91] 6.12676480 6.22054920 6.31433360 6.40811799 6.50190239 6.59568678
## [97] 6.68947118 6.78325558 6.87703997 6.97082437
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/ 20*length(data)
lines(x, norm_dist, col='green',lwd=4)
abline(v = mean(data), col="red", lwd=3, lty=2)
# Add legend to top right position
legend("topright",
legend = c("Histogram", "density curve", "Average"),
col = c("lightblue", "green", "red"),
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%
## -4.048817 1.006447 2.136249 3.228084 6.572345
## 0% 25% 50% 75% 100%
## -2.3138308 0.9883237 1.9792709 3.0830225 6.9708244
# locate the quartiles Q1, Q2, Q3
abline(v = Quantiles[2], col="violet", lwd=3, lty=3)
abline(v = Quantiles[3], col="blue", lwd=3, lty=3)
abline(v = Quantiles[4], col="red", lwd=3, lty=3)
# Exer6: Locate the lowest 5% and the highest 5% of the distribution
data
## [1] 0.821229172 3.837377527 2.393332222 1.599594424 1.166672068
## [6] 4.053530752 0.593225820 3.285132191 3.677014501 2.924939195
## [11] 3.262725480 5.005790149 -0.657632004 3.933699165 2.859036588
## [16] 0.569278862 2.099210139 -0.416898398 2.114783386 2.362481680
## [21] 2.756634873 3.124686812 -0.002088106 0.782613625 1.833376961
## [26] 2.646547918 -2.206918118 3.367529997 2.094360435 4.447022686
## [31] 3.218956683 1.558977029 1.788248084 5.219907260 3.636560868
## [36] 3.313760326 1.425370117 2.641995232 0.339195347 4.654836653
## [41] 2.502123992 3.594602396 2.851749520 2.797659167 1.067314311
## [46] 3.276952638 -0.803047452 3.915062080 1.739429059 -0.081190896
## [51] 3.012392842 1.819204022 -0.619395120 3.488878158 2.283913653
## [56] 3.307519575 -0.367422047 -1.745441588 -0.442531620 0.531535119
## [61] 1.417800807 -1.974664175 3.628294391 3.978784643 2.647974839
## [66] 1.262603879 1.534395202 1.188757193 2.294355433 3.580550863
## [71] -0.403678432 -0.726070370 2.641968470 5.327918540 2.414307190
## [76] 2.995458197 1.855873836 1.275345487 1.496817009 1.273108882
## [81] 2.469768752 3.059223355 0.556097244 2.677023323 0.238609570
## [86] 1.314147238 3.621290350 -0.084699111 0.170200358 2.358064798
## [91] 0.856090755 -2.116907652 0.712541217 1.701862056 1.682213056
## [96] 2.240958667 1.371168246 2.620158363 -0.285188293 2.790153982
## [101] 2.687072775 -1.980080019 0.204291978 2.720255854 3.447957871
## [106] 1.060286615 0.946419659 0.993391576 4.955671438 4.654328774
## [111] 1.606253102 4.718575884 0.531694703 3.855480734 3.049354532
## [116] 2.254468061 4.156862001 2.621037017 1.733721782 2.430890446
## [121] 0.234922208 1.805676173 2.601917124 1.883286733 0.374434707
## [126] 2.216380723 5.549166311 4.023406774 3.662294390 2.697344308
## [131] 4.342555137 -1.139645590 3.630250517 4.143436955 2.175813430
## [136] 1.444428667 -0.316573211 2.155898463 3.241868394 1.333997731
## [141] 3.427736860 2.785605543 1.052682623 2.210117079 2.903835498
## [146] 2.521468452 0.079563228 2.190689247 1.369082479 3.368724266
## [151] 3.212812698 1.094765684 1.396173395 2.039918311 3.691632391
## [156] 0.373745747 2.706188161 2.334990758 -1.190578157 0.056721379
## [161] 2.955582575 0.189104557 1.763113960 2.678547035 -0.509829496
## [166] 3.253045023 1.634019783 1.582134177 1.026194857 3.923583996
## [171] 4.804582269 3.951372875 2.026965567 3.363294724 2.135214757
## [176] 0.237686762 5.423394530 2.867888446 6.099057668 0.665062234
## [181] 4.975725484 2.059326456 3.498997715 3.110910844 3.057571971
## [186] 3.537403565 1.924119452 3.818760854 5.228674355 1.439267255
## [191] 2.589687592 2.518985630 0.227321006 2.514675882 2.731027216
## [196] 3.875905822 3.302706452 -0.518637578 1.217286212 -0.431147824
## [201] 0.619033241 5.307734404 1.442496782 3.752997254 0.631264694
## [206] 0.050544262 5.452915684 -0.581581268 3.804120775 2.114346082
## [211] 3.089953593 0.494220239 3.000950809 0.281694081 3.750178062
## [216] 5.052645303 3.959705101 3.599971308 2.988651350 3.884106603
## [221] 3.018222756 -1.020517332 1.660169793 3.248641645 0.853775358
## [226] 3.431870088 1.552940813 2.656618348 2.573240892 2.770242764
## [231] 5.101064696 2.951055529 2.395515840 2.261005793 3.799198385
## [236] -1.693287506 2.041695485 2.396292810 2.590017285 1.003923408
## [241] 3.503347136 1.041710815 1.850892212 -4.048816523 2.686322408
## [246] 3.613285170 0.721114698 3.523996740 1.331075522 1.138947667
## [251] 1.542041543 1.455160721 2.257322561 1.305537300 3.150189150
## [256] 5.014890015 0.796422030 4.209090580 3.287697457 2.935797890
## [261] 3.151953667 1.873029548 2.241232985 4.261498174 2.996296076
## [266] -0.094307909 1.242206949 0.620982100 2.822070417 -1.135914235
## [271] 1.446925603 2.700423031 2.311281441 3.246191774 1.778366181
## [276] 3.354676670 3.966433758 1.798351827 3.507876567 1.786710854
## [281] 2.234861601 2.619632686 1.285543033 3.659130576 3.320445372
## [286] 1.903271614 -0.168679144 5.005573038 3.409899544 4.423734470
## [291] 2.135520034 1.500676149 1.319288759 0.541255941 3.274995088
## [296] 2.232171677 0.708355272 0.197206895 -1.124595635 3.818604132
## [301] 0.113502509 0.863542726 4.514669874 -1.782424129 1.008119447
## [306] 3.797562582 1.558383901 4.676074244 1.545908202 3.646356694
## [311] 0.630358127 4.521565929 1.790782806 2.735505126 3.048258918
## [316] 3.390187764 2.120341588 4.189878424 4.134147782 3.078116598
## [321] 2.955956019 1.812092759 2.245845572 3.349471751 5.562172253
## [326] 2.719797297 0.335784743 3.550023240 -0.377739564 -0.196931440
## [331] 1.216780612 3.896290714 1.046118364 2.201321864 0.443926486
## [336] 2.853653346 1.440866898 1.458444548 1.002454337 1.242140030
## [341] 2.728621057 -0.210860465 1.986893535 2.038115669 3.739716121
## [346] 1.698567124 1.937946142 0.344911435 3.352325470 2.117253050
## [351] 2.409408190 2.808434974 -0.530089204 2.207742128 0.717960861
## [356] 2.708230029 0.367944748 2.166745394 1.367486110 4.292469574
## [361] 3.062731946 1.682060145 2.588698299 4.223222833 5.923050838
## [366] 2.365688217 4.011290977 1.633523139 2.771040648 1.594327111
## [371] 4.066447537 0.669633192 2.478283037 2.937287205 0.444896878
## [376] 0.784359541 0.185404880 3.769201314 -0.620075077 2.691630509
## [381] 3.400042763 0.390228795 2.983286572 3.874388094 3.450753108
## [386] 4.397456080 2.665394663 0.740571207 0.995950439 3.458493499
## [391] 2.537304622 -1.352480021 5.330434672 0.537171902 3.049730837
## [396] 2.545128005 0.235951328 3.305247716 1.664471100 -0.555109209
## [401] 0.404267920 -0.493676153 1.336981850 3.420855374 3.213705751
## [406] 4.968449621 2.865175086 2.477611252 1.827183891 2.575930506
## [411] 4.660288810 1.902903176 3.227932252 2.136977704 4.895422505
## [416] 0.791639824 1.865176289 -0.578868251 3.162341145 1.286953367
## [421] 2.508602722 2.138965302 3.397457873 0.707480849 2.887197623
## [426] 3.684438453 2.603970220 2.393501757 3.007582261 2.985976111
## [431] 4.451636093 0.475619261 1.471848712 0.891731700 1.439656532
## [436] 2.171476341 3.500679615 2.247092411 -0.375120054 2.670979006
## [441] 3.261137455 0.150691309 0.331520943 4.679101134 3.774405088
## [446] 2.596084294 1.909168819 5.609403977 0.178590339 2.321607690
## [451] 3.122376156 2.432072851 1.837925446 1.506310543 1.170033081
## [456] 1.565734663 1.747138958 3.044962619 3.442690035 -0.086575603
## [461] 1.639286380 3.680374973 3.454924527 3.218532668 2.869687172
## [466] 1.312926371 1.896896807 2.805279332 4.246501002 1.980511333
## [471] 2.636931822 2.635370926 1.942197314 1.250722140 5.743821537
## [476] 2.157263380 0.113593681 3.734232309 2.619078122 3.248016212
## [481] 2.381858775 0.543379922 3.826581738 3.154737098 3.268455949
## [486] 3.389822026 2.714020399 3.113244050 2.030869240 2.342519085
## [491] 2.841751452 3.212325765 0.216694797 0.867062601 3.271861311
## [496] 2.024992765 1.027093660 2.340973504 2.731859275 2.091850178
## [501] 4.671715530 1.306899939 3.347713604 -0.151808147 3.370626598
## [506] 1.329529836 0.510425577 0.685776823 0.575658332 -0.897110917
## [511] -1.015297927 -0.587073262 0.338982781 1.843176367 -0.086311122
## [516] 1.117643655 2.992770540 -0.894649625 1.121214820 2.273730131
## [521] -0.364255029 3.338860656 1.381874059 2.438508740 1.608517086
## [526] -3.453383408 3.315687286 -0.427812569 1.381871116 3.534261892
## [531] -1.796141968 0.970801886 -0.345772384 0.904028534 2.391740521
## [536] 2.608903761 2.196234480 -1.295827857 2.703888834 2.886243549
## [541] 3.744768722 4.952947999 0.886060655 2.577894384 2.837253095
## [546] 2.801302938 1.500419081 5.197270132 -0.668397040 4.335687955
## [551] 1.860060275 3.287603577 -0.163602285 1.500684091 -0.560989067
## [556] 2.476220138 3.922280434 0.113270048 0.957955236 2.615239358
## [561] 3.037034333 1.691658174 5.407110701 1.462812630 3.615511065
## [566] 1.358392709 2.110391150 1.714593604 0.940592590 5.449709970
## [571] -0.771964434 0.377884991 1.794683397 1.905771024 4.095061307
## [576] 0.562466070 -0.519147868 1.557749294 3.457388236 -0.236672440
## [581] 2.931693005 4.817354589 4.027646794 2.083262578 0.316215523
## [586] 3.297158613 3.188946271 5.322201180 1.507460764 3.408209940
## [591] 2.287864823 5.227293471 3.941577149 1.142262863 1.822906946
## [596] 0.282466124 2.869004763 0.900994086 1.347189715 2.956249351
## [601] 4.738465370 3.377291141 1.544962965 0.449083353 0.918333913
## [606] 1.357039511 3.762047568 3.849861447 1.683741935 -0.573708937
## [611] 1.907879715 5.357643567 -2.842318266 2.909810674 3.596962228
## [616] 0.535010056 1.623925813 1.806196405 4.155954401 2.421142579
## [621] 0.976797055 -1.474529214 4.384573784 -1.073040527 0.645286001
## [626] 2.324671650 4.360359294 0.589984047 2.323185319 1.525097583
## [631] 4.377181377 0.361992291 0.686758582 2.155560608 -0.119008858
## [636] 0.871717202 3.446251390 2.494691668 2.364501565 3.215253396
## [641] 0.204448228 2.563630547 1.558376726 2.264028723 4.364915086
## [646] -0.160874507 2.176166652 1.445884925 2.506951999 1.394862401
## [651] 4.111284787 1.521010765 2.505995974 4.032932830 4.631315991
## [656] 4.394996612 0.872581108 0.841752986 1.959909931 2.609873147
## [661] 1.072819742 1.069301750 2.610870660 0.678860568 1.108947142
## [666] 0.805991594 3.340395275 3.039716794 2.662724142 1.174128298
## [671] -0.083592561 2.332425223 -1.445845425 2.972602685 1.589460536
## [676] 1.759238405 -0.482712543 0.797382313 1.082916254 1.658249912
## [681] 3.353401423 0.270184313 0.652409661 -1.826127956 2.830918058
## [686] 2.423091202 3.539976146 3.238188802 3.481034448 -0.091598674
## [691] 1.217774384 1.124290003 3.589904492 1.230983883 1.504501984
## [696] 0.636609340 0.891169944 2.216547778 1.543714372 1.227534793
## [701] 0.353001199 4.498274025 -0.485511166 3.108905057 2.022881223
## [706] 0.787080262 4.268957353 2.542488087 0.443231883 1.500713509
## [711] 3.671849193 3.717497563 4.020020580 1.787743003 3.784645354
## [716] 0.523191047 3.815737934 1.528491779 2.272036687 5.562215485
## [721] 3.207999930 1.029383409 0.130855196 4.209865150 2.707681577
## [726] 2.270850791 0.042597923 2.169169858 -1.193313651 1.693586525
## [731] 5.494186056 1.131460495 2.916419950 -0.140452524 2.788957300
## [736] 2.061768996 0.990722338 -3.369788355 -1.412824267 1.578237856
## [741] 1.190450413 0.611913747 2.082301596 2.974801431 2.736006418
## [746] -0.149491335 4.649623184 5.099263090 1.200325517 0.375263709
## [751] 0.783210014 1.023444956 0.096386115 2.888010703 2.514412320
## [756] 0.690045327 -0.076948381 -1.746524304 2.996471350 1.007288161
## [761] 1.712200219 1.963046826 0.193687456 4.264189871 1.968467517
## [766] 1.693109162 2.063799159 -1.313037159 2.221751721 1.846086714
## [771] 1.345478395 1.641272795 3.875485328 5.323516656 -1.214151424
## [776] 3.228538412 3.891812977 4.041207066 1.472064223 2.389706111
## [781] 1.258081638 1.498693765 0.501103656 0.868328542 4.180414440
## [786] 0.747762576 4.335575695 2.503060303 2.686365169 4.081352530
## [791] 3.963756298 2.752641208 3.637856339 3.860374853 2.716194574
## [796] 3.487793216 1.962184615 -0.059098919 2.259020624 2.275531128
## [801] 3.278430561 1.396193072 1.031218578 5.074902455 1.653979314
## [806] 1.859946851 1.995574411 2.564537957 1.200629140 0.683558692
## [811] 2.700470981 -3.597115135 2.947885175 -1.195893883 0.735949308
## [816] 1.912398892 2.050307469 3.393033304 1.444523288 1.187529615
## [821] 2.808144588 3.434201002 3.505892513 0.780978236 3.340418387
## [826] 1.328393893 3.549885619 1.552589526 -0.970563267 2.050335058
## [831] 6.572344991 0.391663208 3.579157221 2.253371847 0.942110990
## [836] -0.471121338 2.545032862 1.177068242 2.552550463 3.772306546
## [841] 3.685970590 4.417383204 4.103417695 3.106714411 -0.739444344
## [846] 1.740737773 2.023378834 3.258267139 0.165454808 2.021612705
## [851] 5.338693796 1.821566574 1.523816609 3.329721809 2.206487678
## [856] 3.057689454 1.377759094 1.892258602 2.290167214 2.958968933
## [861] 1.992014510 5.248384507 -0.209220921 4.723675263 2.794831291
## [866] 2.980129024 1.872860019 -0.099251244 3.264786140 3.611471943
## [871] 2.298030555 -0.627558674 2.872968917 2.794863115 4.646036824
## [876] 2.910528893 -0.207718851 0.223129582 -2.628202007 -0.826171537
## [881] 2.290834934 0.419054058 -1.358499855 0.939842049 2.060529244
## [886] 0.359497144 3.303663399 1.706547070 4.906608897 0.150566834
## [891] 2.875086504 1.593282024 0.173754953 3.399651277 0.982088868
## [896] 3.173492438 1.504077219 2.976825213 1.841652146 2.158963826
## [901] 2.294963101 1.555336971 2.113958487 2.001469172 1.318477902
## [906] 1.473852069 -1.071563300 1.150616891 -0.316193841 -1.159017104
## [911] 2.481011436 1.988627359 1.195625645 1.910462311 -0.200671423
## [916] 4.092273369 3.299621029 1.265179266 2.911308488 2.388576456
## [921] 2.174049022 1.574866004 0.141476669 1.409880150 -0.380906638
## [926] 2.010385464 1.579105932 4.405505632 2.856350854 1.812059054
## [931] -0.144218679 2.031185459 4.624570973 3.149920604 3.031947852
## [936] -0.734539464 1.709979235 5.173935949 1.633287718 0.736385139
## [941] -0.600908140 4.520711803 4.465173838 0.966000431 0.500436334
## [946] 3.988023399 3.062981268 1.340544137 2.232746314 1.068666277
## [951] 2.146884094 2.885083372 2.603627573 1.541750847 -0.762945213
## [956] 3.516617444 0.620178247 -0.185762415 2.791928823 0.795575131
## [961] 1.320561892 -0.513274270 1.562332611 4.195137020 2.646975482
## [966] 0.799830772 2.183676096 -1.054089781 4.470274452 3.194105966
## [971] 3.304821761 1.946560879 1.941523760 1.901542474 2.634410178
## [976] 3.460014180 3.044501809 5.218272334 1.055482192 -1.043825681
## [981] 1.490282110 5.112009627 3.777069287 4.661879196 1.673506356
## [986] -0.867613088 2.060579282 2.667610954 1.123657470 4.136973746
## [991] 3.676783149 3.436749985 -0.147798784 0.816086186 1.948450516
## [996] 3.547672396 0.543291707 0.605950356 2.738584900 1.360471914
## [1] 2.530177288 2.143332874 2.746199168 0.719113711 3.232395769
## [6] 3.598421558 0.127198038 -1.503509401 1.050541220 1.151609537
## [11] -0.572450468 3.038265558 0.197863242 4.860585483 1.710900274
## [16] 1.485092047 0.895875984 0.923357331 1.910365810 3.153440230
## [21] 5.010958756 0.755184887 1.158725547 1.823975814 1.506325857
## [26] 1.704515986 1.713639650 3.160925415 1.414242457 2.707675194
## [31] 2.341946038 1.129226259 4.182953723 3.417128179 3.255165889
## [36] 3.050537428 2.475892922 0.471431642 -0.353586459 0.942395991
## [41] 2.195329920 -0.347077145 0.728226538 2.307199605 4.608967711
## [46] -0.385539696 1.518083355 1.753246217 3.545468955 2.544699326
## [51] 3.687908090 1.620374109 1.809311743 3.212057677 3.642046331
## [56] 3.876534306 1.596265342 0.032585972 4.061138520 0.085849664
## [61] 2.404834534 3.087918676 5.872727541 2.283672648 1.196295504
## [66] 1.233684308 2.262108864 4.452514598 3.949865359 -0.050176936
## [71] 3.637212882 2.147307277 1.228652779 -1.424132221 4.937082631
## [76] 4.192570668 4.034292375 1.807741853 2.156662917 2.765336126
## [81] 1.885006343 2.427363882 0.316559238 3.227560324 1.674700750
## [86] 1.687935833 3.238086919 2.480804793 4.636530544 0.989985656
## [91] 2.535757969 2.363786877 -0.735467884 1.478721561 0.520861394
## [96] 2.713386952 1.642647259 -0.037914271 3.959072365 3.314178223
## [101] 0.826894935 3.328842004 2.539816450 2.061748170 1.023174000
## [106] 3.123598409 1.888814555 2.729755999 1.389092323 1.974727131
## [111] -0.341875633 3.708689969 1.474457846 3.305266794 1.993896485
## [116] 2.832705608 3.515096871 1.279004326 -0.272400201 3.139851774
## [121] 2.601644120 3.665667964 0.271425626 3.618607885 2.144880645
## [126] 4.445766383 2.523612002 -0.020189260 -0.257353206 -0.145147876
## [131] -0.047247099 2.050614013 1.236013310 2.363416859 2.517244585
## [136] 1.304038810 1.917367420 -1.211608141 0.428109438 4.346467012
## [141] 3.788015986 2.093734014 -1.588739174 3.909932624 6.463161197
## [146] 3.468100432 2.779234339 1.676909458 1.675912605 0.690178805
## [151] 3.250445641 2.144752442 0.617494189 3.585437557 0.206888255
## [156] 3.203807411 4.440939895 1.280856587 1.935435715 4.178268818
## [161] 1.262791599 0.272436452 2.928181335 -0.492347346 2.018337993
## [166] -0.730428992 0.997378204 1.572415724 -1.457216895 3.518809718
## [171] 1.663995567 1.068353486 0.300325269 1.030573957 0.308612800
## [176] 0.699477267 -0.153392950 4.030240483 -0.194282410 1.165441111
## [181] 1.641423348 2.488442296 0.741316155 0.856488470 0.983337798
## [186] 2.083313483 1.570658083 1.905182556 0.461582624 3.497110274
## [191] 0.659806586 1.354965996 3.476212143 2.173673922 2.386844337
## [196] 2.532199310 1.236225597 1.106821765 1.036577506 -0.923559008
## [201] -0.053306284 0.619580407 1.339366374 0.474729949 4.055617949
## [206] 0.171897568 1.798803505 2.640163492 1.102006198 2.213618030
## [211] 2.904938322 2.105417090 2.671740080 2.892075649 2.396420297
## [216] 0.931163012 -0.105280531 4.169012377 1.416835465 2.743818708
## [221] 1.022452138 3.196422030 4.057218674 0.418284821 4.070606396
## [226] 1.566327480 1.971362382 2.212321251 1.325151358 0.817347620
## [231] 0.702017185 0.575768065 3.359805982 2.448653822 2.628997705
## [236] 1.033070397 0.502434249 1.309088383 0.147361924 1.553261239
## [241] 1.543415280 1.841584929 0.545868640 2.684525553 0.671906639
## [246] 3.370868886 3.766572555 1.458995962 -1.192609842 3.133190955
## [251] -0.253741954 3.731545695 3.156001676 2.019016098 3.081962525
## [256] 0.100097260 2.065700847 -1.344194409 1.107828410 1.292434102
## [261] -0.249759471 1.671808251 0.870730135 2.751599332 4.565996911
## [266] 2.555980169 1.374525175 3.437746432 0.512168458 3.349913109
## [271] 2.077407561 2.323326595 1.681436741 0.405728801 2.850494583
## [276] 2.917843674 -0.640816317 3.744387143 0.882666789 2.784893779
## [281] 1.293912914 2.871666767 -1.931946562 2.576898384 2.182307034
## [286] 0.409494306 2.941600253 1.969838494 1.505428559 1.984665864
## [291] 0.779161449 1.151433270 4.417826017 3.019182127 4.821058864
## [296] 0.903414285 0.775890111 2.548923544 2.023319588 -1.283316974
## [301] 2.843334388 3.791127537 2.727501758 0.084800737 3.762286605
## [306] 1.906066477 3.647685143 3.318479599 3.363670088 0.112869548
## [311] 3.696904778 2.670190665 1.806064861 2.465276520 2.808989959
## [316] 0.468075074 4.215663510 4.242839821 3.156593306 2.928239489
## [321] 1.356616528 3.156794451 0.423533038 2.242986577 3.661551815
## [326] 2.629650327 3.165818882 2.452213535 1.232440687 -1.133389292
## [331] 0.894224538 2.823904596 1.935928037 3.483511182 3.832543702
## [336] -0.861916168 4.984598540 1.952361582 0.286865821 0.055158082
## [341] 2.379040529 -0.173660490 3.225836552 2.208381300 3.188691651
## [346] 1.048714756 2.161081977 3.130581308 2.267401776 2.576000817
## [351] 1.061350289 2.562822617 1.779872724 2.581195842 3.305822463
## [356] 1.054408858 3.532968681 3.293229925 0.893107325 2.122795738
## [361] 5.362675129 1.431438747 2.335042709 0.688480279 2.162196027
## [366] 3.354258502 3.123758426 1.564255673 3.604707524 1.207751502
## [371] 2.834967156 2.818033594 2.372260733 0.855656311 1.970700172
## [376] 3.464764762 3.996491909 -1.006815847 6.077779644 1.171913635
## [381] 2.183911892 -0.409136348 0.540803440 2.892210365 -2.313830834
## [386] 3.287515102 1.228894555 2.416861505 3.218405279 0.442600495
## [391] 1.152121761 1.918816634 5.085136509 2.340981436 0.225363416
## [396] 2.650111441 1.546065239 3.416400116 3.728335967 -0.075835543
## [401] 2.662689019 3.348521888 0.656007574 1.851563159 4.367323559
## [406] 4.260037384 2.485114422 4.649729924 3.455070252 4.500497842
## [411] 2.737772064 0.839881779 0.411234736 1.403309507 2.016034317
## [416] 3.089654806 2.740801133 0.718235196 1.689392058 -1.138564402
## [421] 2.162500079 -1.396105805 3.841785089 0.321492204 1.744290455
## [426] 1.121264753 2.007073041 3.553109837 1.145926270 2.717221687
## [431] 1.731559338 1.864233634 1.088270411 2.904283375 3.460662548
## [436] 2.882144395 0.712056808 2.015545388 1.925089917 0.951316625
## [441] 2.073535970 0.918360691 3.034638140 1.800058214 4.711403469
## [446] 4.406282623 2.523212245 0.256268959 -0.377925330 1.721799075
## [451] -1.267460795 0.765756189 -1.844186864 1.501848507 2.604277963
## [456] 1.470494218 0.280247815 2.598111005 0.993362799 0.173576505
## [461] 1.978208313 2.759458714 4.540381778 3.806814572 0.205926391
## [466] 0.293934955 3.381173766 1.808457183 -0.962907672 3.846865721
## [471] -0.255110394 3.274892071 0.024715089 2.629875730 1.929529854
## [476] 1.861949536 3.271939473 4.778326882 2.916302346 1.928689723
## [481] -0.738310412 1.940751337 3.349450242 3.947046256 1.474226154
## [486] 1.232188009 2.076782926 2.930108487 1.132746521 4.002752759
## [491] 0.321609212 3.446949147 0.327071081 2.832617373 2.116345770
## [496] 1.506431092 2.945092837 1.784839602 1.804973631 0.678844833
## [501] 2.878389541 1.957052172 0.495954231 1.463548172 2.997808291
## [506] 4.599522815 1.593848958 0.734987043 1.088179772 4.276039815
## [511] 2.706992830 0.419563916 -0.190828394 4.646634545 3.867677116
## [516] 1.091423082 2.565232361 -0.235310586 2.088105950 3.838892117
## [521] 0.780392103 3.497348544 1.761181256 5.664401532 3.086202407
## [526] 0.237233981 1.260898700 2.359870674 3.155885377 1.948759564
## [531] 0.058906615 2.625769585 3.771159289 2.937258998 2.608707807
## [536] 2.182464355 0.995502397 0.135115007 3.389874103 2.650406508
## [541] -0.102808221 -0.709460990 -0.000895197 3.327990687 1.307480922
## [546] -0.365220801 1.840558866 0.764029148 1.525026772 1.861289791
## [551] 1.700814355 1.501580131 2.544489507 0.070328639 1.337052387
## [556] 1.747570131 -1.961627736 2.543923457 0.688791416 0.590444108
## [561] 0.991633753 -0.712132747 3.447999136 1.882484164 1.811347425
## [566] 1.525523472 1.229467285 2.499544151 5.048437995 -0.411702768
## [571] 0.186052120 -0.011130375 2.838464256 1.976884315 4.100665838
## [576] 0.382058766 0.714654180 2.715702938 1.532748053 2.610324391
## [581] 0.048376161 1.557858427 4.829675682 1.797138555 1.872398867
## [586] 2.524812567 2.217701927 4.182107597 3.323807812 0.522046580
## [591] 3.535104646 3.141316692 2.764213808 2.629983972 1.501340855
## [596] 0.836505885 2.994686360 2.046504073 2.335098988 -1.068560461
## [601] 2.705439912 1.217405755 2.515929565 1.927540380 0.041056053
## [606] 1.831137493 1.346638256 1.419562581 1.661246639 1.686114906
## [611] 2.641105090 0.674673905 3.800677471 -0.341894144 3.229826960
## [616] 0.203270730 1.489295518 1.944794185 2.426837501 3.667799911
## [621] 0.994648176 0.953452542 5.038023383 3.045969100 2.018308240
## [626] 2.366316862 1.259191369 2.974882685 0.829283681 0.909215385
## [631] -1.588698039 0.369177288 0.959466944 4.233636130 2.588661533
## [636] 2.628723817 2.531673808 5.008195310 1.715487272 1.561939861
## [641] 2.262866501 -0.628305334 4.966383293 0.201094803 -0.097409016
## [646] 1.980623907 3.463161811 2.827707279 1.632127096 1.689881266
## [651] 2.938860775 3.169826417 2.545262334 2.167451102 0.786746408
## [656] 1.174433777 1.808151768 2.256765490 1.664318428 3.682083871
## [661] 2.389032358 2.349755998 -0.316002973 3.890885197 0.917535810
## [666] 2.600264759 2.111546785 1.802785877 1.066589924 3.110543119
## [671] 3.249189635 3.119623030 0.064578764 1.829429137 2.848358930
## [676] 0.787331179 1.560382276 0.262667467 3.995782210 1.226899920
## [681] 0.954651938 3.281487925 4.820415336 1.317514774 3.846599592
## [686] 0.862624931 0.455424282 1.372588601 4.194724673 -0.101345479
## [691] 1.776637517 0.699565481 4.004800586 1.141184270 1.015499072
## [696] 3.517647772 2.067272037 3.621754447 1.009258632 3.389087903
## [701] 1.654625426 -0.417774552 1.330332661 2.009449879 3.260185754
## [706] 3.132367066 5.699472625 3.102995560 2.392441905 1.976636615
## [711] 0.022718604 2.330169903 3.657076702 0.335034298 0.760166814
## [716] -0.892107845 -0.302705447 1.022199649 3.052578522 2.837881222
## [721] 3.811639561 0.851294720 1.560873560 0.925834282 1.339061536
## [726] 3.036356649 1.303416732 2.233078576 1.114745665 1.687871325
## [731] 1.621385816 1.407710551 3.118722979 1.796508610 2.027289620
## [736] -1.809367161 0.051189795 4.480775023 4.566314411 3.424903022
## [741] 2.499482605 0.824793547 0.642472669 1.599328476 4.835008001
## [746] 2.030676848 2.794320392 0.868820988 1.710283919 0.691529042
## [751] 0.242669611 3.454259522 0.900568465 2.153030232 3.154458308
## [756] 2.618647669 -0.128283894 3.858113671 4.305470978 0.150789955
## [761] 0.149280943 3.231025452 2.490085283 2.364096756 1.025135514
## [766] -1.349241952 -0.888870583 2.400487766 4.010400404 1.431773539
## [771] 1.717793346 -0.140235195 2.001632755 2.569915583 2.312406889
## [776] -0.625889938 0.515663447 1.344223977 2.582920357 5.672484519
## [781] -0.361624579 3.445994720 2.892019826 1.367538088 2.723323294
## [786] 2.768136212 1.150169930 2.209184760 0.819797175 3.945740488
## [791] 1.718827671 0.795124310 0.958613619 2.674885325 0.417610814
## [796] 1.174482868 1.438898803 5.886622714 2.926234357 0.087958317
## [801] 1.623470599 1.533653330 3.476138694 3.169000434 4.771219860
## [806] 0.778234687 3.889638582 1.414590238 0.117138741 2.181539213
## [811] -0.661019573 0.751673110 1.808823976 0.374194549 2.569979866
## [816] -0.174426580 1.191995778 3.305484321 2.376210440 2.451157066
## [821] 0.980142935 3.207755831 3.695241347 -0.383217533 1.476030197
## [826] 0.114510144 1.432213397 4.528917088 2.117178451 5.436893940
## [831] 1.765185751 0.650668795 1.150474106 1.603678349 2.257212133
## [836] 3.289144223 0.646940511 2.632740355 2.251310403 3.309551358
## [841] 1.422059392 3.854038267 3.872250175 2.094830423 1.146041018
## [846] 3.358589013 2.094312586 3.111984773 3.488821377 4.019374806
## [851] 1.567745303 2.772197966 -1.013556737 2.153606827 2.950993778
## [856] 3.917008184 3.627466561 1.865695279 1.780475376 1.781725953
## [861] 1.821037581 1.039892447 3.114531811 0.176677749 0.798862070
## [866] 2.861147184 4.561355659 3.731107757 -0.365523288 1.346407789
## [871] 1.165260384 1.618972903 0.189977420 1.282540302 4.104951561
## [876] 2.575291324 2.205068718 3.248253596 2.786400610 3.195006755
## [881] 3.116829636 0.053566156 2.472377938 2.175234647 1.928495765
## [886] 2.090010895 2.555103661 3.151785408 0.927427743 3.279757393
## [891] 1.723281943 1.106739803 0.924129074 2.106332642 0.486134510
## [896] 4.415798461 1.902221146 4.081812035 3.566409293 2.550826797
## [901] 1.300978814 1.482402924 3.686837507 3.519402761 0.254214540
## [906] 1.632264519 1.980333499 1.032125969 3.876461701 2.592056554
## [911] 1.975759087 3.774132624 2.096028789 2.310212253 3.256699084
## [916] 3.219783287 2.279374775 3.844981400 1.903301043 -1.268651118
## [921] 6.970824368 3.306811878 1.551328966 0.477019187 3.466386799
## [926] 2.539686910 2.149895310 1.440751350 4.791105288 0.859221992
## [931] -0.301622557 2.878786464 0.271319347 3.078591379 1.864334536
## [936] 3.323954774 2.379379256 2.042749414 2.662382839 2.837101919
## [941] 2.810634533 -0.493273204 3.218320455 0.293255144 3.317604916
## [946] 0.097899605 2.304556468 1.172094090 3.527187917 4.100455219
## [951] 3.239234413 4.156748333 1.097566170 4.048763858 2.389237594
## [956] -0.460610156 2.767930096 5.921997961 2.445210337 0.761204027
## [961] 3.536785948 0.948118280 0.968642769 3.483214865 2.107232174
## [966] 1.078639321 -1.460499136 1.522383881 2.951275503 -1.402121121
## [971] 1.929560683 3.203583387 3.554220046 2.739899372 4.078741644
## [976] 2.402984864 1.456365335 4.432085104 1.970794771 3.726039895
## [981] 2.289259145 4.197047367 2.961089323 1.589875594 1.074357706
## [986] -0.128333360 4.190446670 0.249575920 0.337000090 2.713827964
## [991] 2.050379684 -1.687441594 1.922818558 1.697657346 2.016235719
## [996] 4.993716801 2.720917316 -0.430803163 1.681529728 -0.384191759
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -4.049 1.006 2.136 2.059 3.228 6.572
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.3138 0.9883 1.9793 1.9859 3.0830 6.9708
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightgreen",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='red',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("lightgreen", "red", "black"),
lty = 1)
# Locate lowest 5% and highest 5% of the data
quantile(data,prob = 0.05)
## 5%
## -0.6290623
## 5%
## -0.3832662
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%
## 4.660368
## 95%
## 4.307521
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%
## -0.6290623
## 5%
## -0.3832662
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [997] FALSE TRUE FALSE TRUE
# count all true values using the sum command
sum(Low5Percent[TRUE]) # there are 50 of them
## [1] 50
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -0.6576320 -2.2069181 -0.8030475 -1.7454416 -1.9746642 -0.7260704
## [7] -2.1169077 -1.9800800 -1.1396456 -1.1905782 -1.0205173 -1.6932875
## [13] -4.0488165 -1.1359142 -1.1245956 -1.7824241 -1.3524800 -0.8971109
## [19] -1.0152979 -0.8946496 -3.4533834 -1.7961420 -1.2958279 -0.6683970
## [25] -0.7719644 -2.8423183 -1.4745292 -1.0730405 -1.4458454 -1.8261280
## [31] -1.1933137 -3.3697884 -1.4128243 -1.7465243 -1.3130372 -1.2141514
## [37] -3.5971151 -1.1958939 -0.9705633 -0.7394443 -2.6282020 -0.8261715
## [43] -1.3584999 -1.0715633 -1.1590171 -0.7345395 -0.7629452 -1.0540898
## [49] -1.0438257 -0.8676131
## [1] -1.5035094 -0.5724505 -0.3855397 -1.4241322 -0.7354679 -1.2116081
## [7] -1.5887392 -0.4923473 -0.7304290 -1.4572169 -0.9235590 -1.1926098
## [13] -1.3441944 -0.6408163 -1.9319466 -1.2833170 -1.1333893 -0.8619162
## [19] -1.0068158 -0.4091363 -2.3138308 -1.1385644 -1.3961058 -1.2674608
## [25] -1.8441869 -0.9629077 -0.7383104 -0.7094610 -1.9616277 -0.7121327
## [31] -0.4117028 -1.0685605 -1.5886980 -0.6283053 -0.4177746 -0.8921078
## [37] -1.8093672 -1.3492420 -0.8888706 -0.6258899 -0.6610196 -1.0135567
## [43] -1.2686511 -0.4932732 -0.4606102 -1.4604991 -1.4021211 -1.6874416
## [49] -0.4308032 -0.3841918
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.660368
## 95%
## 4.307521
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
## [181] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [205] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE TRUE 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 TRUE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [445] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [589] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 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 TRUE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE
## [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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE
## [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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [145] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] TRUE 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 TRUE FALSE TRUE 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] TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## [409] FALSE TRUE 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] TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE TRUE 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 TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [745] TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [829] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.005790 5.219907 5.327919 4.955671 4.718576 5.549166 4.804582 5.423395
## [9] 6.099058 4.975725 5.228674 5.307734 5.452916 5.052645 5.101065 5.014890
## [17] 5.005573 4.676074 5.562172 5.923051 5.330435 4.968450 4.895423 4.679101
## [25] 5.609404 5.743822 4.671716 4.952948 5.197270 5.407111 5.449710 4.817355
## [33] 5.322201 5.227293 4.738465 5.357644 5.562215 5.494186 5.099263 5.323517
## [41] 5.074902 6.572345 5.338694 5.248385 4.723675 4.906609 5.173936 5.218272
## [49] 5.112010 4.661879
## [1] 4.860585 5.010959 4.608968 5.872728 4.452515 4.937083 4.636531 4.445766
## [9] 4.346467 6.463161 4.440940 4.565997 4.417826 4.821059 4.984599 5.362675
## [17] 6.077780 5.085137 4.367324 4.649730 4.500498 4.711403 4.406283 4.540382
## [25] 4.778327 4.599523 4.646635 5.664402 5.048438 4.829676 5.038023 5.008195
## [33] 4.966383 4.820415 5.699473 4.480775 4.566314 4.835008 5.672485 5.886623
## [41] 4.771220 4.528917 5.436894 4.561356 4.415798 6.970824 4.791105 5.921998
## [49] 4.432085 4.993717