# Mindanao State University
# General Santos City
# Introduction to R base commands
# Prepared by: Kathleen I. Pena
# Student
# Math Department
# March 20, 2023
# Processing of continuous data
# Using random number generators
# Exer1: generate data with mean 2 and standard deviation 1.5 using rnorm()command
data <- rnorm(1000,2,1.5) # 1 thousand values
length(data) # count number of elements
## [1] 1000
data[1:20] # display first 20 elements
## [1] 2.2296841 1.1049094 3.9602813 4.2698936 2.1249888 1.8774173
## [7] 1.7619420 3.6914363 0.8972161 1.4192792 2.2767342 3.3721199
## [13] 2.8348667 2.1718366 2.3441778 2.4237953 0.5837338 0.4645595
## [19] -0.6386079 2.1436816
data[1:300] # display the first 300 elements
## [1] 2.2296841228 1.1049094212 3.9602812623 4.2698936156 2.1249887660
## [6] 1.8774173489 1.7619419853 3.6914363152 0.8972160596 1.4192792027
## [11] 2.2767342492 3.3721198732 2.8348666892 2.1718365952 2.3441777656
## [16] 2.4237952841 0.5837337551 0.4645595175 -0.6386079139 2.1436816086
## [21] 2.3668466140 1.0835631294 5.6243891041 4.8946230226 -0.6031665111
## [26] 0.3056013197 2.6586925986 2.3256288505 2.9290246165 0.6478939407
## [31] 0.7428539510 3.7450219264 2.8930284057 6.2956862825 -0.0009758503
## [36] 2.6863401938 1.8683838314 0.3270077263 2.5510711336 4.1164754909
## [41] 3.0854930511 0.6832912468 2.3579212132 0.2058461441 1.5697273266
## [46] 3.2363039433 1.7219018542 -0.0344447107 3.4905615106 3.9570553190
## [51] 2.7415711567 3.6690112887 3.0260060636 1.5355680944 2.8593551907
## [56] 3.1456229262 6.7222687170 2.4027617099 4.4281433004 3.9121025548
## [61] 1.6747855121 3.2535130693 0.3293790617 1.5282044456 0.0330420433
## [66] 1.5386968371 2.1239076628 0.2560797096 0.8453794154 3.2607641518
## [71] 3.2595801134 1.7897695995 1.2203987930 2.4326905467 3.7265381640
## [76] 1.5149614859 1.1495079145 -0.3226731883 1.6706367954 0.5508943330
## [81] 4.2653576956 3.8456504517 -0.6934667806 3.4829456187 3.0222308967
## [86] 0.0112389805 3.3754523482 2.2531577166 3.5677435869 2.7663393969
## [91] 2.0003562839 4.2873121719 -0.1961392893 0.4057293185 2.1399840328
## [96] 2.1626040952 1.5663443577 4.1654685757 2.3728465033 4.7613581114
## [101] 2.2990449803 1.3330739180 2.7325205571 1.3579738394 2.6085653507
## [106] 2.0778879951 0.3336357911 1.5119856936 2.3990289615 5.8644697030
## [111] 1.1862738658 -1.4072425502 0.6809881813 4.1363483591 -0.7374403222
## [116] 2.7958822072 3.8656261740 0.5673135772 1.2771567021 1.1782132720
## [121] 2.8884871098 0.7165691770 -0.7310594623 -0.2138358345 1.7069013464
## [126] 5.0515241745 0.6444732306 0.4516367265 1.6273344068 1.6695318553
## [131] 3.4113128010 1.1787872283 2.4080871515 2.7006654622 1.7281166354
## [136] 0.8996407993 2.4460306538 2.7475318399 2.6458375689 3.3842014404
## [141] 5.9579947915 1.0118800283 3.1274810728 0.8271358219 0.7336033266
## [146] -0.0336861321 1.7022337835 0.9909843978 2.4671802245 -1.2243245490
## [151] 1.4175418774 0.2197672499 1.0869169821 -0.0670433966 3.5632508272
## [156] 3.9559221857 1.7045896065 1.4014695250 2.9658560487 2.4576057605
## [161] 2.7344749757 3.4487250921 2.3651199606 2.9527058848 1.3928273400
## [166] 3.5628522965 0.4623767436 4.2726923114 1.7112476488 2.9488322016
## [171] -0.7379376490 3.9010495056 -0.9293350023 0.3035894102 0.5650932864
## [176] 4.9514050244 4.4863231473 2.2208938273 0.4940212160 2.4266344538
## [181] 1.7430031310 -0.1968066959 1.7888048890 1.3599893607 1.1321227789
## [186] 0.9962462066 2.9918284329 3.2161748813 1.6038608676 1.3150143893
## [191] 2.7680412820 1.9903583867 2.9665966564 1.8566272577 2.9462290414
## [196] 3.1397872125 -0.8032141291 3.6276110185 2.6328981914 -1.1254275680
## [201] 1.1757860840 0.5985511903 3.1230334196 2.2820141225 -0.9299889879
## [206] -0.0897264640 4.3888416622 1.7028243288 2.8754077420 1.8048222618
## [211] 1.2678206331 4.9948082188 4.0031634197 3.1355948991 1.0325621520
## [216] 2.4739557723 4.4411807671 1.7462855400 2.3342918248 3.5269246292
## [221] 0.9334606550 3.2754286406 2.9659950431 3.0502517735 0.4342313046
## [226] -0.1726596258 -0.0242252629 2.4480196109 1.4554949309 0.4103248948
## [231] 0.7666611760 3.2603092982 3.5612465976 4.3276636467 2.8279861376
## [236] 3.0752117694 2.3803006419 -0.7486830160 2.5303383185 2.3249862798
## [241] 2.6878594474 1.7325185402 2.6476676365 1.4910628962 3.5692817430
## [246] 2.9001447265 2.6698266702 -1.0741440739 2.5748088983 2.1196925896
## [251] -0.8484608739 2.3013062994 0.0670319706 0.0718843416 4.2572130269
## [256] 0.1788857092 1.0602013306 2.7853776258 2.1629191207 0.2067633947
## [261] 1.5163326838 3.0422931820 2.4162122330 1.1425554129 3.6363161358
## [266] 3.7731157517 2.9251261471 0.5833767049 3.8330889092 2.7872759418
## [271] -2.4230746287 1.6929893457 2.0448309019 1.8594383338 -1.1917919172
## [276] 0.8437414900 1.5942616598 4.4873766087 4.7073591970 2.2016683444
## [281] 1.1001424073 1.1201842158 0.5939001638 0.9037699428 4.0075069754
## [286] -0.1702852210 -0.1791956881 0.9689944391 4.3090419205 3.3065073330
## [291] 1.9985182660 0.0518591037 -0.2519106756 1.6789416979 1.2097068111
## [296] 1.7882820153 -0.0850449718 4.1647757251 3.4588744314 -0.0925579001
# Exer2: Draw histogram with one main title and different thickness
maintitle <- "Histogram and Density Plot"
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
hist(data, breaks=300,col="gray",main = maintitle)
# Exer3: Draw histogram with one main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
# Question: What causes the subtitle to be in the second line?
# Exer4: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# Add density curve. We define the range of the density curve
x = seq(from=min(data), to=max(data), length.out=100)
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/
20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
# Exer5: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# Add density curve and the location of the mean value
(x = seq(from=min(data), to=max(data), length.out=100))
## [1] -2.423074629 -2.329954034 -2.236833440 -2.143712845 -2.050592251
## [6] -1.957471657 -1.864351062 -1.771230468 -1.678109873 -1.584989279
## [11] -1.491868685 -1.398748090 -1.305627496 -1.212506901 -1.119386307
## [16] -1.026265712 -0.933145118 -0.840024524 -0.746903929 -0.653783335
## [21] -0.560662740 -0.467542146 -0.374421552 -0.281300957 -0.188180363
## [26] -0.095059768 -0.001939174 0.091181421 0.184302015 0.277422609
## [31] 0.370543204 0.463663798 0.556784393 0.649904987 0.743025581
## [36] 0.836146176 0.929266770 1.022387365 1.115507959 1.208628554
## [41] 1.301749148 1.394869742 1.487990337 1.581110931 1.674231526
## [46] 1.767352120 1.860472714 1.953593309 2.046713903 2.139834498
## [51] 2.232955092 2.326075687 2.419196281 2.512316875 2.605437470
## [56] 2.698558064 2.791678659 2.884799253 2.977919847 3.071040442
## [61] 3.164161036 3.257281631 3.350402225 3.443522820 3.536643414
## [66] 3.629764008 3.722884603 3.816005197 3.909125792 4.002246386
## [71] 4.095366980 4.188487575 4.281608169 4.374728764 4.467849358
## [76] 4.560969953 4.654090547 4.747211141 4.840331736 4.933452330
## [81] 5.026572925 5.119693519 5.212814113 5.305934708 5.399055302
## [86] 5.492175897 5.585296491 5.678417086 5.771537680 5.864658274
## [91] 5.957778869 6.050899463 6.144020058 6.237140652 6.330261246
## [96] 6.423381841 6.516502435 6.609623030 6.702743624 6.795864219
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/
20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
abline(v = mean(data), col="black", lwd=3, lty=2)
# Add legend to top right position
legend("topright",
legend = c("Histogram", "density curve", "Average"),
col = c("lightblue", "violet", "black"),
lty = 1)
# Compute Quartile values Q1,Q2 and Q3
# These quantities divide the data into 4 equal parts
hist(data, breaks=20,col="lightblue",main = maintitle)
Quantiles = quantile(data)
Quantiles
## 0% 25% 50% 75% 100%
## -2.423075 1.031582 2.000209 3.057468 6.795864
# locate the quartiles Q1, Q2, Q3
abline(v = Quantiles[2], col="black", lwd=3, lty=3)
abline(v = Quantiles[3], col="red", lwd=3, lty=3)
abline(v = Quantiles[4], col="blue", lwd=3, lty=3)
# Exer6: Locate the lowest 5% and the highest 5% of the distribution
data
## [1] 2.2296841228 1.1049094212 3.9602812623 4.2698936156 2.1249887660
## [6] 1.8774173489 1.7619419853 3.6914363152 0.8972160596 1.4192792027
## [11] 2.2767342492 3.3721198732 2.8348666892 2.1718365952 2.3441777656
## [16] 2.4237952841 0.5837337551 0.4645595175 -0.6386079139 2.1436816086
## [21] 2.3668466140 1.0835631294 5.6243891041 4.8946230226 -0.6031665111
## [26] 0.3056013197 2.6586925986 2.3256288505 2.9290246165 0.6478939407
## [31] 0.7428539510 3.7450219264 2.8930284057 6.2956862825 -0.0009758503
## [36] 2.6863401938 1.8683838314 0.3270077263 2.5510711336 4.1164754909
## [41] 3.0854930511 0.6832912468 2.3579212132 0.2058461441 1.5697273266
## [46] 3.2363039433 1.7219018542 -0.0344447107 3.4905615106 3.9570553190
## [51] 2.7415711567 3.6690112887 3.0260060636 1.5355680944 2.8593551907
## [56] 3.1456229262 6.7222687170 2.4027617099 4.4281433004 3.9121025548
## [61] 1.6747855121 3.2535130693 0.3293790617 1.5282044456 0.0330420433
## [66] 1.5386968371 2.1239076628 0.2560797096 0.8453794154 3.2607641518
## [71] 3.2595801134 1.7897695995 1.2203987930 2.4326905467 3.7265381640
## [76] 1.5149614859 1.1495079145 -0.3226731883 1.6706367954 0.5508943330
## [81] 4.2653576956 3.8456504517 -0.6934667806 3.4829456187 3.0222308967
## [86] 0.0112389805 3.3754523482 2.2531577166 3.5677435869 2.7663393969
## [91] 2.0003562839 4.2873121719 -0.1961392893 0.4057293185 2.1399840328
## [96] 2.1626040952 1.5663443577 4.1654685757 2.3728465033 4.7613581114
## [101] 2.2990449803 1.3330739180 2.7325205571 1.3579738394 2.6085653507
## [106] 2.0778879951 0.3336357911 1.5119856936 2.3990289615 5.8644697030
## [111] 1.1862738658 -1.4072425502 0.6809881813 4.1363483591 -0.7374403222
## [116] 2.7958822072 3.8656261740 0.5673135772 1.2771567021 1.1782132720
## [121] 2.8884871098 0.7165691770 -0.7310594623 -0.2138358345 1.7069013464
## [126] 5.0515241745 0.6444732306 0.4516367265 1.6273344068 1.6695318553
## [131] 3.4113128010 1.1787872283 2.4080871515 2.7006654622 1.7281166354
## [136] 0.8996407993 2.4460306538 2.7475318399 2.6458375689 3.3842014404
## [141] 5.9579947915 1.0118800283 3.1274810728 0.8271358219 0.7336033266
## [146] -0.0336861321 1.7022337835 0.9909843978 2.4671802245 -1.2243245490
## [151] 1.4175418774 0.2197672499 1.0869169821 -0.0670433966 3.5632508272
## [156] 3.9559221857 1.7045896065 1.4014695250 2.9658560487 2.4576057605
## [161] 2.7344749757 3.4487250921 2.3651199606 2.9527058848 1.3928273400
## [166] 3.5628522965 0.4623767436 4.2726923114 1.7112476488 2.9488322016
## [171] -0.7379376490 3.9010495056 -0.9293350023 0.3035894102 0.5650932864
## [176] 4.9514050244 4.4863231473 2.2208938273 0.4940212160 2.4266344538
## [181] 1.7430031310 -0.1968066959 1.7888048890 1.3599893607 1.1321227789
## [186] 0.9962462066 2.9918284329 3.2161748813 1.6038608676 1.3150143893
## [191] 2.7680412820 1.9903583867 2.9665966564 1.8566272577 2.9462290414
## [196] 3.1397872125 -0.8032141291 3.6276110185 2.6328981914 -1.1254275680
## [201] 1.1757860840 0.5985511903 3.1230334196 2.2820141225 -0.9299889879
## [206] -0.0897264640 4.3888416622 1.7028243288 2.8754077420 1.8048222618
## [211] 1.2678206331 4.9948082188 4.0031634197 3.1355948991 1.0325621520
## [216] 2.4739557723 4.4411807671 1.7462855400 2.3342918248 3.5269246292
## [221] 0.9334606550 3.2754286406 2.9659950431 3.0502517735 0.4342313046
## [226] -0.1726596258 -0.0242252629 2.4480196109 1.4554949309 0.4103248948
## [231] 0.7666611760 3.2603092982 3.5612465976 4.3276636467 2.8279861376
## [236] 3.0752117694 2.3803006419 -0.7486830160 2.5303383185 2.3249862798
## [241] 2.6878594474 1.7325185402 2.6476676365 1.4910628962 3.5692817430
## [246] 2.9001447265 2.6698266702 -1.0741440739 2.5748088983 2.1196925896
## [251] -0.8484608739 2.3013062994 0.0670319706 0.0718843416 4.2572130269
## [256] 0.1788857092 1.0602013306 2.7853776258 2.1629191207 0.2067633947
## [261] 1.5163326838 3.0422931820 2.4162122330 1.1425554129 3.6363161358
## [266] 3.7731157517 2.9251261471 0.5833767049 3.8330889092 2.7872759418
## [271] -2.4230746287 1.6929893457 2.0448309019 1.8594383338 -1.1917919172
## [276] 0.8437414900 1.5942616598 4.4873766087 4.7073591970 2.2016683444
## [281] 1.1001424073 1.1201842158 0.5939001638 0.9037699428 4.0075069754
## [286] -0.1702852210 -0.1791956881 0.9689944391 4.3090419205 3.3065073330
## [291] 1.9985182660 0.0518591037 -0.2519106756 1.6789416979 1.2097068111
## [296] 1.7882820153 -0.0850449718 4.1647757251 3.4588744314 -0.0925579001
## [301] 2.2317896274 -1.4393718207 4.1316113911 -1.1503901321 3.8086454355
## [306] 1.6003036876 3.5373371489 4.0306998220 5.6702451917 4.1264653679
## [311] 1.5825161971 1.8333590479 -0.5064863057 2.6587861666 2.1933919416
## [316] 3.8893543091 -0.5670642296 1.9687294797 0.9597955651 3.1475360689
## [321] 2.6002128262 1.2944827537 4.1395011107 3.0014270710 1.7387239382
## [326] -0.4532702107 3.8889758394 2.0647442035 1.5210860594 0.3280151728
## [331] 2.8574140984 1.4325130496 5.3272712050 2.1927974997 2.0189367031
## [336] 1.8850496042 0.3455215713 2.7841614606 1.7643233514 3.1737710760
## [341] 4.9339264409 1.4848861472 3.6890204705 3.5778699755 5.1502454448
## [346] 3.3469389851 1.4106384793 1.7370036155 0.4450999568 3.8628266195
## [351] 1.3668457022 1.9439657511 2.3578448853 1.1377794904 2.3583409052
## [356] 0.1145991625 3.4679573809 0.6451881717 1.1184664873 3.2619533156
## [361] -0.7486929709 1.4993205525 2.8155269722 1.9378962309 -0.2897545721
## [366] 3.1485262713 2.4713904252 0.8768620994 4.2036961888 2.8086519387
## [371] -0.3082504930 3.7905340893 0.0635077914 1.0425542562 0.7624986578
## [376] 2.3978464321 2.0143118987 1.5780586488 2.2786677544 0.0259613307
## [381] 3.8396571834 3.2678398386 0.7631920100 5.0757991994 2.5381442123
## [386] 4.9848802447 0.5329001498 -2.0196147104 1.0485465793 0.8349453865
## [391] 2.0754048940 1.9543781676 2.0831881079 1.8637972417 1.8094700965
## [396] -1.5405600117 0.0099564546 1.5424852345 4.6738166782 3.9089208502
## [401] 0.7373567056 2.7563897525 0.4427015626 0.7244080815 3.4853334971
## [406] 2.2655658716 1.8627360716 3.3517196633 2.6280933880 1.6826745326
## [411] 0.5808777315 2.0260307470 4.0516791147 1.5180322783 2.5043660446
## [416] 2.2755202125 1.3792725409 0.2219927126 2.1078038596 1.1829390131
## [421] 2.8071351716 2.5173285379 0.7893775776 1.6883593207 1.3262252380
## [426] 3.2758478393 1.3236696171 2.0714945620 1.4039697316 3.8021336446
## [431] 2.9925050274 2.8290965410 0.8754030052 1.1391160811 0.5795921558
## [436] 2.0133663616 1.8748149016 3.2203025564 0.8749169737 2.0867709171
## [441] 2.5704376854 0.7802799690 3.5319021852 4.3381264464 1.0219106826
## [446] 5.4696431693 -0.3623021715 0.1773470264 4.7812701994 1.1845620500
## [451] 3.1823442604 4.1857007165 3.7402606046 2.3048735531 2.1392960461
## [456] 1.1080368573 0.4968726724 -0.1900850020 1.5195634200 4.1868148220
## [461] 2.8916646647 1.6197612882 -0.4855458295 4.1224301232 -1.4950596193
## [466] 2.9806637512 4.3475178117 1.1325142674 2.8393280346 4.8507239070
## [471] 2.6926143321 0.2205810877 1.2858597910 1.0236049508 2.6636708326
## [476] 1.9070362360 -0.8081152672 2.0941641622 2.2555407754 3.6295425717
## [481] 2.4757547689 1.0779830949 4.0637097431 2.4783278973 3.0869555851
## [486] 2.3857945295 4.7746525757 1.9950704293 1.3645991908 1.6633699674
## [491] 4.5197828988 -0.9656402648 0.1649335877 3.1506744007 6.2170829529
## [496] 0.5930827817 2.9858433317 3.1871909451 4.2168151272 0.8608168491
## [501] 1.0518286976 -0.7313412349 0.0183623500 4.9775896197 3.5177539076
## [506] 3.4909662360 1.4948704109 1.1156469149 2.9459221957 0.7020657510
## [511] 3.3938588315 3.0686344725 1.6865073766 2.5513770597 3.5241067717
## [516] 3.1081531301 3.7257534660 0.6029896934 1.1497152948 2.0395593563
## [521] 3.2261941847 2.3963173714 4.0781251762 3.6822285610 3.0881737038
## [526] 2.0753846633 1.8768899563 -1.4083447786 2.7734692588 0.5137769817
## [531] 2.4086404766 6.7958642185 1.9840333777 1.2387295046 3.9907841735
## [536] 2.2210738038 1.0468999313 -1.5935532918 2.4478514007 1.5468452872
## [541] 3.2893890180 2.1050026456 2.7097032695 2.6164204998 1.6897075460
## [546] 0.0496634939 3.9034851261 2.9708402245 0.7215490151 3.9937111217
## [551] 4.2551986638 3.6609454506 1.6408070901 2.7506392713 1.0992673406
## [556] 1.5331418614 4.4189992720 1.8907146682 2.4001685456 -0.1327159340
## [561] 2.8784433429 1.6957414449 -0.3182859929 3.2367066267 2.3528626209
## [566] 1.1895909220 4.1943037242 0.0247306939 3.1411177209 1.8757868011
## [571] 1.3412963782 2.4867365596 1.8581294531 2.7215160187 0.0728573836
## [576] 0.1029933931 0.6713134362 -0.1772778528 1.8088098440 0.3133342103
## [581] -0.4461156513 1.4883157668 2.7606389415 1.6183218349 2.7024515211
## [586] 2.2952861903 3.2000746526 2.0251810055 3.2018787263 3.8604836957
## [591] 3.4862813904 1.1385617865 1.2613625300 -0.9199000429 2.3357546398
## [596] 1.0971416460 4.2194415617 3.1636718426 4.3493200630 2.8887182462
## [601] 0.9267637224 5.2411014774 0.3303361114 0.6456837984 2.4681297140
## [606] 2.9389652878 2.5040449675 3.5327339664 -0.3416239094 3.3897693506
## [611] 3.1741210187 3.8243925869 0.9134166252 3.1711423073 1.0823607260
## [616] 1.3768720417 -0.4267334047 1.8282180753 -0.1595934835 3.0640584973
## [621] 2.2970523109 1.3735749639 2.5326870573 0.3838782049 5.4546312407
## [626] 0.8308686898 0.5140131981 2.2951193519 1.6413954028 5.1476119613
## [631] 0.6769391644 4.4489488172 4.1858377946 5.2424016761 3.5248218917
## [636] 1.6759824197 1.7460832142 0.0042136373 2.0000618315 1.9843537460
## [641] 0.7064411731 2.4572064859 2.0247778083 3.4208626586 0.6754624575
## [646] 0.3717181879 1.1347609617 -0.9131501378 1.0351195616 3.8821072079
## [651] 1.5508965357 -0.1514472416 1.7126354301 1.3985663229 0.1895628835
## [656] 0.8459472379 0.5149987828 2.3126257928 -0.3967053658 3.7814247763
## [661] 4.0496927800 0.3151391551 3.6611560359 2.8206308419 2.4859021504
## [666] 3.6271549529 2.1519618327 2.9738278302 1.5420149278 -0.1784294296
## [671] 3.0214905211 -0.0930015100 -0.3357678002 6.0276141653 1.3384921165
## [676] 0.4186491186 -0.9953619651 -1.3468841168 -0.2236983304 2.0215213057
## [681] 3.7902739798 0.8820594389 2.7448726501 2.6926234244 1.7728914476
## [686] 2.0199279187 2.0634678143 4.1662017125 1.8102509080 1.3245876915
## [691] 3.3289659052 1.7368819613 4.5823335759 1.6863808964 1.3741174419
## [696] 4.0203853506 2.2391175100 1.6666593900 3.1128390239 1.0875889144
## [701] 2.8768439207 -0.4733724510 3.4731946777 3.1890454357 3.9949626959
## [706] 1.9306316191 1.0238092399 3.7964920669 1.0286417842 4.0596066263
## [711] -0.7095963870 2.7283819618 3.1930815042 1.2557784400 1.1935243428
## [716] 3.6175109509 3.1941577417 0.4377262865 3.5390381688 2.1650408399
## [721] 2.2525438036 3.5324886372 1.9255134822 1.1786250616 1.9951670444
## [726] 1.3231378541 -0.8978182887 3.4242923173 2.6595562958 2.7898955968
## [731] 1.4025868886 1.9172645170 1.4699154262 2.1722456810 2.1790147617
## [736] 1.3142584928 2.7253305204 3.5432365631 1.7230819363 0.5079216971
## [741] 3.0217487815 2.6754997412 2.5707217380 1.7274266505 3.3839463458
## [746] 0.7754089460 2.0347760381 1.5136653833 2.5579897670 -0.6814978311
## [751] 1.6288551101 2.8610714608 1.1837562132 3.7881668530 3.6332898614
## [756] 3.3312976154 3.3842424578 0.0506066916 3.2698099423 1.1872869549
## [761] 3.3402092300 1.8462030776 1.0542063143 0.6270310523 0.3570174467
## [766] 1.9860056214 3.1605404818 3.6463715927 1.1823985132 1.6557774757
## [771] 4.0389516068 1.1915350377 0.9298805218 2.2670530608 5.5053421948
## [776] 4.0561249466 1.0076292341 2.1903360347 3.7656748075 2.9285239927
## [781] 0.8792218126 3.1873214031 2.0361387530 0.2587487039 3.3815683234
## [786] 2.8276493072 3.6458462456 1.9842513953 2.5549823390 3.5732085863
## [791] 1.4198723272 -0.4768005398 2.6953815037 1.9235308086 1.2103254553
## [796] 1.8312510400 1.5052511502 3.0078910356 3.6360666665 -0.2754462919
## [801] 1.6818888912 5.9338890872 -0.1108470411 2.1013262676 4.2355055744
## [806] 1.2093720348 2.8372425414 1.5409275857 2.2024913862 0.3025440622
## [811] 2.8181465694 6.2741710687 1.0443230446 2.9631652040 2.2419430194
## [816] 2.8208360732 0.8669925041 2.3916936426 1.8669669807 4.5880478083
## [821] 0.8551230621 4.8310754324 0.6468055404 -0.1204805651 3.2346195563
## [826] 3.2307814867 2.3308172643 0.1814721032 0.7604643037 1.3556441096
## [831] 0.4871443121 1.0599018375 3.4450348312 1.3914015714 0.1037019063
## [836] -0.1115636294 -0.0330945971 1.9956078074 2.9920898024 1.3410376265
## [841] 2.8634279495 -0.2976156081 1.9411260305 0.9825607529 3.3124675755
## [846] 2.6068723596 1.3453783227 2.8989169234 1.5760403551 0.9197974615
## [851] 2.0294918342 2.4813115101 4.6215943199 2.0107106213 4.6587237289
## [856] 0.6620919824 4.3850498884 3.2326453542 1.7362587640 0.5096438302
## [861] 1.0923250166 2.4448588445 2.1351309639 1.8205498975 3.8152502755
## [866] -1.9340493358 2.6787903472 2.0568862959 2.9972541331 3.9914470871
## [871] -0.7350731115 0.5604214842 1.6773237359 -0.5006270865 2.6526177015
## [876] 4.5825423977 -0.4590418263 1.2672175306 1.7204415215 0.4478439393
## [881] 4.2844128581 1.3082174314 0.5392161804 2.4738152561 2.4721629047
## [886] 1.0899467236 2.0883805404 1.5889676457 0.4583302351 2.5982632700
## [891] -0.9770069709 1.1963201124 2.1779362327 4.3253194809 0.0426538602
## [896] 0.6720466927 3.0489583300 1.8167987998 1.8605393767 1.2964458149
## [901] 2.3616963018 1.8670303433 0.3220559884 -0.1782437696 2.5138206007
## [906] 0.2634799210 1.3223920569 3.0044382607 1.4253568897 0.7866674241
## [911] 1.6643027390 0.7653411251 1.9671228449 0.3875406432 3.1837581875
## [916] 1.7364572278 1.6434768567 0.0577386783 2.2223107592 1.6462795474
## [921] 1.6772960073 3.7349883897 1.1140190265 0.2939840683 0.9877493819
## [926] 2.6606391322 4.7243659961 1.5210020386 1.6557410699 1.5647576729
## [931] 2.7429592666 0.9640142265 3.7632082214 3.9975439037 -0.5673372426
## [936] 2.4461776984 3.0236456061 2.2534994632 -0.0781527933 0.7488947763
## [941] 2.1550084197 4.2777904571 -1.7527702233 3.3989700867 1.2707684486
## [946] 3.0013431675 2.6928604444 1.2535613095 1.5691289550 1.9793128995
## [951] 1.0341503602 4.6417543374 2.1883625980 1.0364712455 1.2966772252
## [956] -0.9382002795 3.7007864999 -1.0014958572 2.0617112707 2.2554093756
## [961] 1.9439778824 1.1700348768 0.0865136400 0.7757354728 2.5265012441
## [966] 2.1456524209 0.9689409403 5.8818489726 -0.5301653126 0.1670521853
## [971] -0.2320367050 2.6982355484 4.1381404550 2.4708149974 3.0485671080
## [976] 1.8811608168 1.6126276599 1.9255955573 2.0056494165 1.9693503315
## [981] 0.6531086172 0.0333014365 3.5926604710 1.7777405212 3.0552708144
## [986] 3.3131289484 1.7018709928 0.5200366534 4.2768663429 3.5039536194
## [991] 1.3296657869 2.4661423295 1.2662335731 4.8124858588 4.3458220957
## [996] 1.3869261461 4.0227400254 2.5030564069 1.8917570319 0.4478081571
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.423 1.032 2.000 2.025 3.057 6.796
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%
## -0.4535588
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%
## 4.39035
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%
## -0.4535588
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [25] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [205] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] TRUE FALSE FALSE FALSE TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 FALSE FALSE FALSE FALSE TRUE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
## [877] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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
# count all true values using the sum command
sum(Low5Percent[TRUE]) # there are 50 of them
## [1] 50
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -0.6386079 -0.6031665 -0.6934668 -1.4072426 -0.7374403 -0.7310595
## [7] -1.2243245 -0.7379376 -0.9293350 -0.8032141 -1.1254276 -0.9299890
## [13] -0.7486830 -1.0741441 -0.8484609 -2.4230746 -1.1917919 -1.4393718
## [19] -1.1503901 -0.5064863 -0.5670642 -0.7486930 -2.0196147 -1.5405600
## [25] -0.4855458 -1.4950596 -0.8081153 -0.9656403 -0.7313412 -1.4083448
## [31] -1.5935533 -0.9199000 -0.9131501 -0.9953620 -1.3468841 -0.4733725
## [37] -0.7095964 -0.8978183 -0.6814978 -0.4768005 -1.9340493 -0.7350731
## [43] -0.5006271 -0.4590418 -0.9770070 -0.5673372 -1.7527702 -0.9382003
## [49] -1.0014959 -0.5301653
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.39035
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## [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 TRUE FALSE TRUE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE TRUE 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 FALSE TRUE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE
## [217] TRUE 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] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE 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 FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [385] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
## [493] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.624389 4.894623 6.295686 6.722269 4.428143 4.761358 5.864470 5.051524
## [9] 5.957995 4.951405 4.486323 4.994808 4.441181 4.487377 4.707359 5.670245
## [17] 5.327271 4.933926 5.150245 5.075799 4.984880 4.673817 5.469643 4.781270
## [25] 4.850724 4.774653 4.519783 6.217083 4.977590 6.795864 4.418999 5.241101
## [33] 5.454631 5.147612 4.448949 5.242402 6.027614 4.582334 5.505342 5.933889
## [41] 6.274171 4.588048 4.831075 4.621594 4.658724 4.582542 4.724366 4.641754
## [49] 5.881849 4.812486