# Mindanao State University
# General Santos City
# Introduction to R base commands
# Prepared by: Prof. Carlito O. Daarol
# Faculty
# Math Department
# March 16, 2023
# Processing of continuous data
# Using random number generators
# Exer1: generate data with mean 2 and standard deviation 1.5 using rnorm() command
data <- rnorm(1000,2,1.5) # 1 thousand values
length(data) # count number of elements
## [1] 1000
data[1:20]
## [1] 2.9586183 0.7023246 2.9348483 3.1502535 0.4367144 0.7838208 0.8775168
## [8] 1.6023675 3.5981725 3.2775581 3.2580656 3.6692089 2.8254490 2.5590166
## [15] 0.7305049 0.1013654 2.6017912 0.4028442 3.5063000 1.5319480
data[1:300]
## [1] 2.958618291 0.702324645 2.934848262 3.150253472 0.436714366
## [6] 0.783820832 0.877516847 1.602367509 3.598172546 3.277558139
## [11] 3.258065609 3.669208909 2.825448978 2.559016584 0.730504930
## [16] 0.101365437 2.601791231 0.402844227 3.506300023 1.531947950
## [21] 1.770450852 0.560375770 1.249232190 -0.144020997 4.376057886
## [26] 3.938922154 3.397049991 -0.316597539 1.236102899 2.734727045
## [31] 3.148403086 1.562282823 1.704328771 4.126555759 2.016457118
## [36] 3.413904869 -0.268470429 1.638475083 2.959634016 4.467867338
## [41] 1.763267419 1.357624378 3.016203692 1.485485072 2.529935454
## [46] 1.831341596 1.272436391 1.321471619 3.210141837 2.529913884
## [51] 1.705185265 2.128539877 2.159983302 3.414583897 1.322096003
## [56] 0.490928209 3.486235179 1.231450989 1.665785938 1.014717130
## [61] 1.396196854 2.320899501 4.168870420 -0.699333708 1.747916145
## [66] 3.148939362 -1.398415737 -1.275848675 3.144738760 1.423377043
## [71] 2.174538969 4.390995261 5.334768784 -0.005028605 2.105366779
## [76] 2.804325375 4.186041672 0.366592091 1.672329041 7.185521133
## [81] 3.463770712 1.560884122 1.673748087 1.378659138 1.375408990
## [86] 4.784208013 2.974846351 2.615349089 2.609857786 2.485494696
## [91] 1.738924283 2.620152208 1.126861519 2.499965651 0.767325475
## [96] 0.388482095 3.015690657 -0.990292988 3.681221203 1.972873956
## [101] 0.776211657 -0.063914383 1.251252024 -0.104429569 0.285169671
## [106] 2.771036104 4.476771962 2.408859313 4.080467823 0.675405685
## [111] 2.059253984 1.659031532 0.652226079 1.528229670 3.222746522
## [116] -0.032314428 -0.280080038 1.408932613 1.416034868 1.967111759
## [121] 2.956924899 1.730102105 -0.332726796 3.703902526 4.067623990
## [126] 1.692857659 1.714013538 0.284179431 0.981756735 3.328441331
## [131] 4.497231571 3.236512902 3.846895401 2.613862611 0.343431141
## [136] 4.289190385 2.087943830 1.463912500 3.039247209 3.875655512
## [141] 1.200527459 2.179041393 1.503507147 3.823704895 1.974691055
## [146] 3.731727328 1.577796142 5.414360875 4.358571864 2.039735996
## [151] 1.079855459 0.772738009 0.333349467 2.413013700 3.349285481
## [156] 3.032358993 1.972523156 2.160523882 -0.992764076 5.587297080
## [161] 4.553401160 4.544580608 2.079688057 1.014759837 1.824913410
## [166] 3.778906226 5.395218823 1.420480602 -0.354125036 0.864412879
## [171] 2.251834087 0.909440156 3.953179588 3.810967952 -1.040891588
## [176] 2.877007312 2.952580882 0.247553006 3.199930751 3.242705340
## [181] 2.247970568 2.752710483 1.790764853 2.489282882 1.564037840
## [186] 0.577983294 2.653630963 2.225822882 1.424770673 0.954084962
## [191] 2.216526431 3.159771611 0.187449827 3.410415999 2.109446513
## [196] 2.937215128 4.465479424 0.227257637 2.642657747 1.861952637
## [201] 2.547750845 -0.133964517 1.797359423 4.169459297 -0.532815487
## [206] 3.502146625 3.542260466 2.078560882 2.760297008 2.200688412
## [211] 2.217182367 -0.118496898 1.014964204 1.075722380 1.691040490
## [216] 4.138312571 1.665203436 0.577877407 2.654288506 3.728979985
## [221] 1.708115058 2.861428787 -0.498373630 3.508157909 3.480309715
## [226] 3.172564385 0.110831984 1.632071382 1.278204748 2.491191722
## [231] 3.096234073 2.378045210 3.869028144 -0.320053011 2.023865730
## [236] -1.340747061 1.800083559 0.562733737 1.278884826 4.045059860
## [241] 3.886580379 2.745663794 1.701965006 2.550714889 0.199753906
## [246] 1.038035372 0.322942595 0.216197328 1.783850272 2.132751991
## [251] 3.046311928 3.532143361 2.854966138 2.012576927 2.650516116
## [256] 0.507154647 3.954029795 -1.129646739 1.844805190 -0.225546530
## [261] 5.792523770 3.537735628 0.893827667 0.748937049 0.074502568
## [266] 3.494902802 4.055103535 1.069612370 2.694027012 0.770925613
## [271] 2.770957917 3.682432514 4.482093750 -0.424071209 3.316067048
## [276] 5.638222236 3.314284948 2.224962925 1.647363380 1.083164972
## [281] 2.677992399 -0.489169692 -2.339908171 3.269046604 3.203171510
## [286] 3.066623294 -0.138691326 -0.045106277 1.733691871 1.165234739
## [291] 1.799460370 3.174923883 0.158165235 0.876277079 3.753351755
## [296] 3.849640418 0.212396372 1.913198646 2.476630178 -0.707672545
# 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] -2.74949240 -2.64913873 -2.54878505 -2.44843138 -2.34807771 -2.24772404
## [7] -2.14737037 -2.04701669 -1.94666302 -1.84630935 -1.74595568 -1.64560201
## [13] -1.54524833 -1.44489466 -1.34454099 -1.24418732 -1.14383365 -1.04347997
## [19] -0.94312630 -0.84277263 -0.74241896 -0.64206529 -0.54171161 -0.44135794
## [25] -0.34100427 -0.24065060 -0.14029693 -0.03994325 0.06041042 0.16076409
## [31] 0.26111776 0.36147143 0.46182511 0.56217878 0.66253245 0.76288612
## [37] 0.86323979 0.96359347 1.06394714 1.16430081 1.26465448 1.36500816
## [43] 1.46536183 1.56571550 1.66606917 1.76642284 1.86677652 1.96713019
## [49] 2.06748386 2.16783753 2.26819120 2.36854488 2.46889855 2.56925222
## [55] 2.66960589 2.76995956 2.87031324 2.97066691 3.07102058 3.17137425
## [61] 3.27172792 3.37208160 3.47243527 3.57278894 3.67314261 3.77349628
## [67] 3.87384996 3.97420363 4.07455730 4.17491097 4.27526464 4.37561832
## [73] 4.47597199 4.57632566 4.67667933 4.77703300 4.87738668 4.97774035
## [79] 5.07809402 5.17844769 5.27880136 5.37915504 5.47950871 5.57986238
## [85] 5.68021605 5.78056972 5.88092340 5.98127707 6.08163074 6.18198441
## [91] 6.28233809 6.38269176 6.48304543 6.58339910 6.68375277 6.78410645
## [97] 6.88446012 6.98481379 7.08516746 7.18552113
## [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='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%
## -2.749492 1.078822 1.999511 3.093486 7.185521
# 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] 2.9586182909 0.7023246445 2.9348482622 3.1502534721 0.4367143655
## [6] 0.7838208319 0.8775168471 1.6023675087 3.5981725463 3.2775581387
## [11] 3.2580656094 3.6692089092 2.8254489775 2.5590165841 0.7305049302
## [16] 0.1013654371 2.6017912307 0.4028442270 3.5063000230 1.5319479503
## [21] 1.7704508523 0.5603757703 1.2492321900 -0.1440209967 4.3760578863
## [26] 3.9389221543 3.3970499906 -0.3165975392 1.2361028986 2.7347270450
## [31] 3.1484030863 1.5622828234 1.7043287708 4.1265557591 2.0164571184
## [36] 3.4139048693 -0.2684704289 1.6384750832 2.9596340158 4.4678673381
## [41] 1.7632674191 1.3576243782 3.0162036921 1.4854850718 2.5299354538
## [46] 1.8313415956 1.2724363909 1.3214716185 3.2101418374 2.5299138840
## [51] 1.7051852650 2.1285398768 2.1599833024 3.4145838967 1.3220960028
## [56] 0.4909282086 3.4862351788 1.2314509892 1.6657859377 1.0147171301
## [61] 1.3961968538 2.3208995006 4.1688704201 -0.6993337083 1.7479161451
## [66] 3.1489393620 -1.3984157373 -1.2758486754 3.1447387598 1.4233770428
## [71] 2.1745389690 4.3909952614 5.3347687845 -0.0050286054 2.1053667787
## [76] 2.8043253755 4.1860416722 0.3665920905 1.6723290407 7.1855211334
## [81] 3.4637707117 1.5608841223 1.6737480867 1.3786591384 1.3754089898
## [86] 4.7842080127 2.9748463514 2.6153490892 2.6098577860 2.4854946957
## [91] 1.7389242831 2.6201522081 1.1268615193 2.4999656508 0.7673254752
## [96] 0.3884820953 3.0156906572 -0.9902929879 3.6812212033 1.9728739560
## [101] 0.7762116570 -0.0639143827 1.2512520243 -0.1044295685 0.2851696712
## [106] 2.7710361038 4.4767719616 2.4088593133 4.0804678231 0.6754056851
## [111] 2.0592539845 1.6590315320 0.6522260788 1.5282296701 3.2227465217
## [116] -0.0323144283 -0.2800800380 1.4089326132 1.4160348684 1.9671117588
## [121] 2.9569248986 1.7301021046 -0.3327267958 3.7039025260 4.0676239898
## [126] 1.6928576587 1.7140135378 0.2841794305 0.9817567346 3.3284413305
## [131] 4.4972315706 3.2365129016 3.8468954008 2.6138626115 0.3434311410
## [136] 4.2891903854 2.0879438302 1.4639125002 3.0392472087 3.8756555117
## [141] 1.2005274588 2.1790413927 1.5035071472 3.8237048951 1.9746910546
## [146] 3.7317273284 1.5777961417 5.4143608753 4.3585718638 2.0397359958
## [151] 1.0798554586 0.7727380094 0.3333494670 2.4130136995 3.3492854807
## [156] 3.0323589926 1.9725231559 2.1605238824 -0.9927640759 5.5872970800
## [161] 4.5534011597 4.5445806079 2.0796880567 1.0147598371 1.8249134103
## [166] 3.7789062255 5.3952188235 1.4204806020 -0.3541250358 0.8644128795
## [171] 2.2518340868 0.9094401565 3.9531795884 3.8109679517 -1.0408915876
## [176] 2.8770073117 2.9525808820 0.2475530058 3.1999307512 3.2427053403
## [181] 2.2479705677 2.7527104831 1.7907648534 2.4892828821 1.5640378401
## [186] 0.5779832941 2.6536309627 2.2258228819 1.4247706731 0.9540849618
## [191] 2.2165264313 3.1597716108 0.1874498269 3.4104159995 2.1094465126
## [196] 2.9372151278 4.4654794235 0.2272576370 2.6426577471 1.8619526373
## [201] 2.5477508452 -0.1339645170 1.7973594226 4.1694592971 -0.5328154866
## [206] 3.5021466253 3.5422604663 2.0785608821 2.7602970079 2.2006884118
## [211] 2.2171823668 -0.1184968977 1.0149642040 1.0757223799 1.6910404898
## [216] 4.1383125713 1.6652034362 0.5778774075 2.6542885055 3.7289799848
## [221] 1.7081150583 2.8614287866 -0.4983736298 3.5081579090 3.4803097153
## [226] 3.1725643846 0.1108319843 1.6320713822 1.2782047480 2.4911917216
## [231] 3.0962340734 2.3780452102 3.8690281440 -0.3200530115 2.0238657296
## [236] -1.3407470615 1.8000835589 0.5627337373 1.2788848258 4.0450598605
## [241] 3.8865803785 2.7456637936 1.7019650055 2.5507148889 0.1997539063
## [246] 1.0380353717 0.3229425947 0.2161973280 1.7838502721 2.1327519907
## [251] 3.0463119279 3.5321433609 2.8549661383 2.0125769274 2.6505161157
## [256] 0.5071546471 3.9540297951 -1.1296467389 1.8448051901 -0.2255465299
## [261] 5.7925237698 3.5377356275 0.8938276668 0.7489370492 0.0745025683
## [266] 3.4949028021 4.0551035351 1.0696123695 2.6940270123 0.7709256133
## [271] 2.7709579174 3.6824325140 4.4820937496 -0.4240712093 3.3160670475
## [276] 5.6382222361 3.3142849480 2.2249629254 1.6473633796 1.0831649718
## [281] 2.6779923989 -0.4891696921 -2.3399081707 3.2690466037 3.2031715103
## [286] 3.0666232938 -0.1386913257 -0.0451062774 1.7336918715 1.1652347386
## [291] 1.7994603697 3.1749238830 0.1581652352 0.8762770785 3.7533517547
## [296] 3.8496404176 0.2123963722 1.9131986465 2.4766301781 -0.7076725452
## [301] 2.6362706015 0.1379536385 0.5628338462 1.3069367258 3.1205538835
## [306] 2.1778399943 1.9385404561 3.0155968354 4.4091756534 2.1919397312
## [311] 3.3523409294 1.1083633051 1.5892517701 1.7164657298 1.9501713503
## [316] 1.2247546285 2.7511615982 3.7864672110 3.5068547474 -0.0026791715
## [321] 0.8932860114 6.2677825112 2.2274450919 1.2524838088 2.3898592252
## [326] 2.6170538461 2.9744148890 4.0454034797 5.3435300316 0.2013002404
## [331] 2.3504869179 1.8263538142 4.2748899152 4.0108194900 1.2770964065
## [336] -1.0385782545 5.6060638708 2.4438871306 -0.0704964069 2.8445218413
## [341] 4.6370980690 4.2093387066 1.6042666715 1.6609493542 4.0016295504
## [346] 1.9248640319 4.9764499105 0.3523052658 2.6228395307 3.2988500988
## [351] 0.4728501296 1.2112950115 2.5714353374 2.8362317063 0.6541219534
## [356] -0.1399578756 -1.4988755235 2.2204150601 2.1563644719 3.2668160881
## [361] 3.1210529126 3.0541633385 2.7786836248 3.6906529190 0.9328170734
## [366] 4.7136032298 4.3070021978 1.2738437338 2.5496567153 0.9472884470
## [371] 1.1936038739 2.6836004118 0.8230868622 1.8259321601 0.6618778453
## [376] 1.3528206752 1.9223424676 2.3829267279 1.0042281852 5.1117747490
## [381] 2.7576809635 2.9867906298 1.0606637868 2.1851857307 -0.5350099559
## [386] 3.3132603166 1.2926182207 4.6149240065 0.9004830662 3.3836352179
## [391] 3.0810671086 0.9817699113 1.5282840375 2.8463366094 2.1974274438
## [396] 1.9812799164 0.4342202886 2.7606971676 1.7336363659 0.6304897866
## [401] 3.4264943473 3.7661460997 2.0922571972 -0.8887359702 4.0959306173
## [406] 1.2186054181 5.5439897072 2.6855533944 1.9547622688 1.7441836782
## [411] 0.8664700423 1.8656264242 2.7958975508 -0.3183715350 0.0318592632
## [416] 7.1278604194 1.9113431963 5.9895205873 1.1721113014 2.9673077896
## [421] 1.9784868011 2.8670507472 1.7154894980 4.0279575493 2.0506461475
## [426] -1.3904212344 3.0671978325 1.2855614105 -0.2520089264 2.7607084156
## [431] 3.6794281993 -0.5078979338 -0.5748662886 3.0914438618 2.1573033269
## [436] 1.3858548042 1.1148570490 2.2856798985 2.7143317640 0.0157750292
## [441] 3.9048970050 1.3506079274 0.9281744472 0.2367334023 3.4569631661
## [446] 2.5463113515 0.9875946464 2.9732866561 -0.0587482837 1.0209844367
## [451] 2.4264914609 0.5491943662 3.3998513286 1.1574929203 1.4375581072
## [456] 1.7168643224 0.4908228542 4.6802989880 1.0749470004 2.2905924776
## [461] 4.5123325449 1.5655551598 1.5399354585 0.8837370594 4.9804987620
## [466] 4.9404358503 1.1031191154 3.8075286344 1.4462593295 3.0160735648
## [471] -0.8663025021 0.1966062536 3.1280542745 4.7555964965 1.2241491530
## [476] 2.9766234602 1.6494154731 2.6703547871 1.1604434242 1.6513664426
## [481] 1.5865015939 2.4677688482 2.4269884704 -0.5060422161 3.8524950711
## [486] 1.0890758954 0.1284032615 2.2462915096 1.4291121631 2.9453272495
## [491] 2.3005964021 2.9124514696 0.7425825286 1.8282848587 3.6290360528
## [496] 0.3022696712 1.7696390525 2.4354072673 0.6843477437 -0.3768327663
## [501] -0.8664053963 1.8127081871 3.0231681694 -0.1523781663 1.1483808375
## [506] 0.1447109630 2.9739415654 1.3150580469 4.0864934371 0.3123531961
## [511] 0.0738201969 0.9605857327 1.5225027992 2.4828233164 3.4056266156
## [516] -0.3897409905 1.7721668657 4.1589433151 2.0175976160 0.0340369199
## [521] -0.4482421455 3.2862944234 1.6156029746 4.4127410754 3.9405346832
## [526] 1.0805439809 2.1738343681 4.3184023683 3.4400659169 0.7217471944
## [531] 5.4515632147 0.5843869992 4.9174777174 1.3200516092 2.4984788874
## [536] 0.9296043050 0.5040218097 2.8781117384 2.3528421016 3.5226561003
## [541] -1.2836747143 0.7515020963 1.4123282454 2.5739970563 3.3298879035
## [546] -0.8364378638 2.2032700315 1.8035770149 2.3105855912 3.9179509695
## [551] 3.2588536596 1.5519036564 1.5494843230 2.4757572091 3.0013738365
## [556] 0.4096792041 2.8286494524 1.1870360609 -0.0890256189 2.5050964681
## [561] 3.5707388680 2.1751792915 4.3913627513 1.9743856721 3.6416603048
## [566] 2.9901738634 2.2349325607 1.4240650547 2.5220659844 1.6703268837
## [571] 1.2114373056 4.7876355425 2.4499789481 0.4348906254 6.2861043448
## [576] 3.1178763888 3.5697849706 2.4100670079 4.2280064122 0.8566919805
## [581] 0.4011161890 1.6750704606 2.2051019554 1.9247776770 1.2185157079
## [586] 4.0016758153 4.2918054231 4.7670790540 2.3248727672 1.8781336142
## [591] 2.9837419357 1.2305662762 1.8925480988 2.0124398503 1.3413939917
## [596] -0.2473559329 3.4984196445 1.6954210120 0.3495812770 4.0096160473
## [601] 3.8611475113 5.3894072268 3.0796414431 2.2649716049 5.5601025605
## [606] 2.9066967081 1.5961402958 1.3973255727 2.6549272342 -0.1156836095
## [611] 4.4508380155 0.9235410613 0.3431995268 1.9535879620 1.3580077324
## [616] 5.0206798624 -0.9569559191 2.7058008877 2.1202460209 1.8804858694
## [621] 2.1144846719 0.1543764202 3.7910402832 -0.5164708391 -0.1741003164
## [626] 2.4529272889 3.2420520328 1.5163787013 5.2510472770 2.6887432621
## [631] 2.5067249199 0.2594007761 4.0478511993 2.7642847246 1.6648705080
## [636] 2.5032880527 2.1506081103 1.1726318755 2.8506317384 4.8523531140
## [641] 2.5717037855 2.4874086574 1.7005295917 0.3397845889 4.2792955661
## [646] 1.7975006732 2.3414686716 -0.0759065190 2.0873158539 4.0904591058
## [651] 1.8728791236 2.3498215582 -0.8637713349 4.7594716998 0.5464008878
## [656] 2.5807937288 0.0176284796 4.3530713881 2.9143734962 1.3821688821
## [661] -1.2263283044 3.3689177670 0.4990158949 2.1289553977 0.7145822197
## [666] 4.1918763308 2.6999127447 1.5422138053 1.6380816923 4.7320138438
## [671] 2.7424725600 4.1377101689 3.3521906703 1.2087439691 1.5425080778
## [676] 3.2284699769 4.2139969706 2.0490342410 0.2703236682 2.7872201028
## [681] 1.9841715948 3.6240799008 2.0883146356 4.0105086385 1.8875041532
## [686] 2.4691705684 3.1530237040 0.6433967043 0.9836773199 1.5897257814
## [691] 0.7804210851 0.7698624113 1.5896640877 1.5778363474 -0.8750735241
## [696] 3.2955521160 0.6962072458 5.1066419423 3.0672024681 0.4189929196
## [701] 1.6937684352 1.7213150489 2.0009303700 2.0008568840 4.2301937076
## [706] 1.4650534247 1.0966970048 3.5751225509 1.7783000520 1.4216062766
## [711] 4.1158839508 3.2760366448 0.4296833835 1.9184112005 2.2664630324
## [716] -0.7971861505 2.7174697980 0.7730044642 4.0792302193 1.7536562838
## [721] 2.6476610093 2.7283243502 6.2059706304 0.4276443970 0.8445320520
## [726] 2.6639660356 2.2242532778 -1.8441376650 1.0224420168 1.5060811050
## [731] 1.6751170065 0.9095302861 2.4803598653 0.0715149275 1.0561032016
## [736] 1.4248009895 0.7392830282 -0.0628841190 1.7936063834 0.0311991057
## [741] 1.9193789974 2.6198320956 3.5164743265 1.6931345966 3.3557300586
## [746] 1.0420774595 2.1855784431 3.9107249766 0.3100616868 2.1646560705
## [751] 1.1410565275 1.2644993463 1.2377345439 0.1381258180 0.5780400516
## [756] 1.9006393111 1.2018879540 1.7155320601 1.2282705095 1.3384569977
## [761] 3.9959433305 2.0272682050 1.3256919251 2.2619180499 2.5807455786
## [766] 4.2313819294 5.6640721024 3.1374718413 3.3340031416 1.0511211373
## [771] 3.4837832018 1.8376705428 2.8970215591 -0.7609370829 2.2100209658
## [776] 2.4432635426 0.9998218708 4.5408676419 2.5788652429 -0.2165940995
## [781] 1.5221807575 2.0141453943 4.0438403193 3.3991070933 2.0510468342
## [786] 0.0004246439 1.7981137122 0.8178735706 4.6341367789 2.6656376154
## [791] 2.1970665143 0.9416566708 2.1476519069 2.7072427316 0.4658037616
## [796] 1.7661642078 3.1972138650 1.6461498639 2.5888941862 1.6009994446
## [801] 2.2449174075 1.0496757387 -0.0638206326 -1.2305559264 2.6562230407
## [806] 3.6416780679 -0.5734915897 2.2574035374 1.9532002423 1.0608641956
## [811] 3.6836530255 0.0399968364 0.8047669184 1.9432655374 1.9776747791
## [816] 2.2025980223 4.1372662622 2.4065132275 -0.3601002918 2.7069701628
## [821] 3.3660584590 1.9983183802 2.5340867666 2.1163225300 5.3113199194
## [826] 3.9101523815 5.8203852084 4.1981460969 0.4555228722 2.1887783818
## [831] 2.0325715808 1.5711214320 0.6317774579 0.2682633897 0.9581680340
## [836] 0.3318954535 3.0586919060 0.6933212970 1.6334732007 2.5918311877
## [841] 1.3902865947 1.6701099068 1.6135096630 2.2927429862 0.6711404253
## [846] 2.1828932713 4.8493456652 3.7965209135 3.8648597390 1.4645560190
## [851] 1.3541359868 2.8188770359 4.4493900035 2.4735648165 2.1698280275
## [856] 3.0925699117 1.8173659363 4.3724579677 0.0306542627 0.9374968819
## [861] 2.0207597666 -0.2240882570 1.9859404443 0.5007259133 1.6624396185
## [866] 2.0007032235 2.5055315290 2.4656119193 3.3430747443 0.8755670059
## [871] 0.9816477859 3.1686401036 1.1820014132 0.1534070817 4.5153848536
## [876] 0.3678423958 0.4607830246 2.2984375559 2.1411022594 1.7832746511
## [881] 1.3723506835 3.0091515973 4.1085793035 1.0943778421 5.3687896787
## [886] 0.0801480130 -0.1011923638 -0.8332575223 0.3525053309 0.3223568306
## [891] 1.9345408277 0.5617142808 3.1416159884 2.5375224315 3.1937659062
## [896] 1.3492688626 2.3236703898 0.7281553117 1.7542004151 3.7501098667
## [901] 2.2481481925 5.7259971132 1.2488983056 1.8374185169 2.4499439401
## [906] 1.5687678922 3.4931874898 1.4035691763 2.4302233825 1.7427789504
## [911] 1.8662041381 2.6848750574 2.0803193979 0.6175123183 2.1388385296
## [916] -0.1573091912 4.6865153821 0.7115272281 1.3994525365 1.4098451328
## [921] 1.9599361344 2.3994431269 1.5763687859 3.1574621499 1.0075798278
## [926] 1.8087194378 4.0930613017 4.7808078845 1.7401554544 1.3912735154
## [931] -0.0300881871 -0.3622824267 3.2014087691 -0.1309192015 3.1516436084
## [936] 0.1994585622 1.9822406220 2.6500358402 0.5090287951 2.0694589695
## [941] 1.2653544677 1.8871403824 0.8404483935 3.4009761770 0.8828216676
## [946] 3.7273084741 1.7213583493 1.6537979996 3.1252688730 3.3602046904
## [951] 1.9099708805 1.5442247792 1.7201209048 1.4949009279 1.3671944423
## [956] 1.2458677529 -0.6744004595 1.1203730710 4.6478960674 0.1398417532
## [961] 3.0005450711 2.8975349086 3.3949388840 2.4174680123 -2.7494923984
## [966] 3.3309851316 3.5025186552 2.0023282452 1.6567949528 4.5548934166
## [971] 1.2246024240 4.1805546204 1.3585226248 3.3880296541 2.2810538242
## [976] 3.2597378293 2.2768841349 4.6594269692 3.6756392393 5.8829899433
## [981] 3.3918674292 -0.3866070581 1.5459698358 5.6906828317 1.4922370455
## [986] 0.7445866608 3.5726733650 1.1279315978 3.5012367620 -0.3764357598
## [991] -0.5201370695 1.1691489942 -0.1536423317 3.8673038817 2.9274228660
## [996] 1.1622594499 0.7313016439 1.7035707639 7.1490612003 1.4464237075
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.749 1.079 2.000 2.081 3.093 7.186
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%
## -0.3184556
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
1
## [1] 1
quantile(data,prob = 0.95)
## 95%
## 4.615885
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%
## -0.3184556
# 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE TRUE FALSE FALSE TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] TRUE FALSE FALSE FALSE FALSE FALSE TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [433] TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [517] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] TRUE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] TRUE 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 TRUE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE 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 TRUE
## [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 FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE TRUE TRUE 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] -0.6993337 -1.3984157 -1.2758487 -0.9902930 -0.3327268 -0.9927641
## [7] -0.3541250 -1.0408916 -0.5328155 -0.4983736 -0.3200530 -1.3407471
## [13] -1.1296467 -0.4240712 -0.4891697 -2.3399082 -0.7076725 -1.0385783
## [19] -1.4988755 -0.5350100 -0.8887360 -1.3904212 -0.5078979 -0.5748663
## [25] -0.8663025 -0.5060422 -0.3768328 -0.8664054 -0.3897410 -0.4482421
## [31] -1.2836747 -0.8364379 -0.9569559 -0.5164708 -0.8637713 -1.2263283
## [37] -0.8750735 -0.7971862 -1.8441377 -0.7609371 -1.2305559 -0.5734916
## [43] -0.3601003 -0.8332575 -0.3622824 -0.6744005 -2.7494924 -0.3866071
## [49] -0.3764358 -0.5201371
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.615885
(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 FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [85] FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE 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 TRUE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
## [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE TRUE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE TRUE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 5.334769 7.185521 4.784208 5.414361 5.587297 5.395219 5.792524 5.638222
## [9] 6.267783 5.343530 5.606064 4.637098 4.976450 4.713603 5.111775 5.543990
## [17] 7.127860 5.989521 4.680299 4.980499 4.940436 4.755596 5.451563 4.917478
## [25] 4.787636 6.286104 4.767079 5.389407 5.560103 5.020680 5.251047 4.852353
## [33] 4.759472 4.732014 5.106642 6.205971 5.664072 4.634137 5.311320 5.820385
## [41] 4.849346 5.368790 5.725997 4.686515 4.780808 4.647896 4.659427 5.882990
## [49] 5.690683 7.149061