# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: John Michael H. Macawili
# Submitted to: Prof. Carlito O. Daarol
# Faculty
# Math Department
# March 28, 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] 0.4178714 3.4125364 0.8232094 0.1467935 2.8936739 1.6916231
## [7] 3.3408214 -0.3457566 -0.3903914 3.1658033 -0.3830377 1.8520203
## [13] 1.8187866 1.2299977 2.3487623 2.4421826 1.0176370 2.7522617
## [19] 2.9017568 3.5595622
data[1:300] # display the first 300 elements
## [1] 0.4178713874 3.4125364052 0.8232093543 0.1467934578 2.8936738939
## [6] 1.6916230575 3.3408213878 -0.3457565823 -0.3903914449 3.1658033336
## [11] -0.3830377446 1.8520202583 1.8187865592 1.2299977256 2.3487622768
## [16] 2.4421825980 1.0176370147 2.7522616772 2.9017567891 3.5595621867
## [21] 0.0091845846 2.3237566137 3.4692742989 1.2621893104 -3.0527714702
## [26] 1.5636457304 0.0332942408 3.6025660674 3.4985824823 1.8476188984
## [31] 2.2983023376 3.2955155141 3.3875039184 4.8604138429 3.1213423701
## [36] 0.4119355616 0.5238355496 2.5008097699 2.9266312353 -0.0122721160
## [41] 2.2300764931 2.3601033676 4.5770014472 1.3128583145 4.3552481379
## [46] 2.5040326418 0.9800223917 1.4582439687 2.5552565453 2.3247803585
## [51] 3.3697840797 0.9278829303 -0.3009021168 -0.1846071005 -1.1780204299
## [56] 5.6304416598 1.8271806727 1.4424607068 2.8825607371 1.2801513912
## [61] 1.0500906290 1.0737749725 3.9185006984 -2.2602770611 0.2686754930
## [66] 0.6424679898 0.6060784313 4.2350146164 1.6958963267 1.7056589144
## [71] -0.3480628005 3.9683465372 3.6620751883 3.8288424434 -1.5646240038
## [76] 0.5729388301 0.8519424679 3.4382488688 0.8793056948 -0.1248791371
## [81] 2.4928543954 1.8370250080 0.9135537562 2.5134335681 4.6629737195
## [86] 3.6754647964 2.5703392826 1.6202232104 4.0532712070 1.4684392006
## [91] 0.9861803047 5.4403261660 -0.0331691149 0.3755060732 1.7837788072
## [96] 4.7082041142 2.1939133602 1.1885343070 2.4390624813 2.6356495639
## [101] 0.7515225505 2.2575071625 4.5867022135 1.0721232962 -2.7534102554
## [106] 1.6708718227 2.3278084910 3.8535236554 0.5038014533 4.0448811316
## [111] 2.3533997569 1.1052460216 -0.9053939770 1.9543198573 0.5548589376
## [116] 2.2474421670 -0.5740664219 1.5475508950 3.9724927233 3.0484955161
## [121] 2.8224775480 2.4214327294 2.1486250327 3.6957749486 1.5590661659
## [126] 2.9061690160 0.4867355971 -0.3826361433 2.1515189339 3.9990090517
## [131] 3.4218845968 1.6602279643 0.8417727218 3.7651277107 1.7737019149
## [136] 0.7820515613 -0.0175514207 1.9368247238 1.1508297662 1.0674413735
## [141] 1.8751536613 3.0334192522 4.1479768392 -0.0751014965 0.0257848109
## [146] 1.3299915867 3.1129728167 2.7331752423 4.3480816543 0.0009823095
## [151] -0.2966957464 3.5317815201 2.6867429247 3.8387515392 2.7363077063
## [156] 1.8994981101 1.6831094446 3.8734852019 2.8125492052 3.6590011640
## [161] 1.6172614719 -0.6811290017 0.5331017857 1.6594815274 2.1879833908
## [166] 1.8782162875 2.1292842141 3.1494864487 -0.3883753005 2.7316977099
## [171] 2.0396837643 1.9679339317 1.4531092447 2.7377442564 2.4566576105
## [176] 0.9716395664 2.5942584821 1.8037962756 2.1933925404 3.1514589889
## [181] 1.2562171406 2.5169577202 2.5980616715 4.6757798458 4.1673875485
## [186] 2.0513454497 -1.1771006504 1.1223195605 3.0791966795 1.4773259615
## [191] 1.0265584756 -0.8644619587 1.6513443391 0.8785428322 1.6405963395
## [196] 4.8874208657 0.6333478369 0.1773707673 1.8996314626 1.3274462403
## [201] 3.4644399566 0.5893416609 -0.2581021448 3.6739842068 0.2920604151
## [206] 4.2080799590 2.5541784131 6.0509337144 5.2533001720 1.9339912345
## [211] 1.7942095211 1.2656598553 3.9022411519 1.3949080661 3.4016309933
## [216] 0.9973245952 2.8850571549 1.9109461076 3.3354162571 -0.3778919783
## [221] -1.0386639299 2.9724084051 4.2404740591 1.0749285500 1.9621109800
## [226] 2.5448814465 1.4451688026 1.3220716329 2.9684961109 4.3048235667
## [231] 2.1916650132 3.4630330899 0.2855501883 3.6910858743 2.5351606611
## [236] 6.6266466467 5.3868341898 2.6345116556 2.5794409295 2.0771113019
## [241] 2.5703507372 2.0776979555 3.7563037813 3.2807786094 3.3073673765
## [246] -0.2053095111 0.8162741665 2.8318250860 1.9251341875 1.1461117418
## [251] 5.1500631599 1.9624973152 4.5432516377 1.4277224305 0.7302375826
## [256] 3.1552605229 0.9470495090 1.4831808875 2.7697964090 0.6585846805
## [261] 2.9594041772 0.8617015866 0.7114341342 2.7945344857 1.3403278457
## [266] 0.0715938726 -0.9777855723 3.6550650528 1.5819493606 2.3694396505
## [271] 2.8732682553 -0.1209759337 4.3172025335 2.0896074008 4.4701994244
## [276] 1.0567968470 5.0764135806 5.5137743394 1.6283844092 0.7981582737
## [281] 1.1588688612 3.3782289523 1.3058103900 4.2461295864 -1.0528641187
## [286] 2.0244870715 1.6001996742 2.6795030657 0.2930124754 2.2298501573
## [291] 1.2211812413 1.1154037170 -0.2580448536 5.9206950506 1.3462188558
## [296] 1.2752306982 1.2380822042 4.3346253395 2.0393354031 3.9260349993
# Exer2: Draw histogram with one main title and different thickness
maintitle <- "Histogram and Density Plot"
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
hist(data, breaks=300,col="gray",main = maintitle)
# Exer3: Draw histogram with one main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
hist(data, breaks=40,col="lightblue",main = maintitle)
hist(data, breaks=100,col="gray",main = maintitle)
# Question: What causes the subtitle to be in the second line?
# Exer4: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# # Add density curve. We define the range of the density curve
x = seq(from=min(data), to=max(data), length.out=100)
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/
20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
# Exer5: Draw histogram with main title and sub title
subtitle <- "This is my second title"
maintitle <- paste0("Histogram and Density Plot \n",subtitle)
hist(data, breaks=20,col="lightblue",main = maintitle)
# Add density curve and the location of the mean value
(x = seq(from=min(data), to=max(data), length.out=100))
## [1] -3.66033636 -3.54655701 -3.43277766 -3.31899832 -3.20521897 -3.09143962
## [7] -2.97766028 -2.86388093 -2.75010158 -2.63632224 -2.52254289 -2.40876354
## [13] -2.29498420 -2.18120485 -2.06742550 -1.95364616 -1.83986681 -1.72608746
## [19] -1.61230812 -1.49852877 -1.38474942 -1.27097008 -1.15719073 -1.04341138
## [25] -0.92963204 -0.81585269 -0.70207334 -0.58829400 -0.47451465 -0.36073531
## [31] -0.24695596 -0.13317661 -0.01939727 0.09438208 0.20816143 0.32194077
## [37] 0.43572012 0.54949947 0.66327881 0.77705816 0.89083751 1.00461685
## [43] 1.11839620 1.23217555 1.34595489 1.45973424 1.57351359 1.68729293
## [49] 1.80107228 1.91485163 2.02863097 2.14241032 2.25618967 2.36996901
## [55] 2.48374836 2.59752770 2.71130705 2.82508640 2.93886574 3.05264509
## [61] 3.16642444 3.28020378 3.39398313 3.50776248 3.62154182 3.73532117
## [67] 3.84910052 3.96287986 4.07665921 4.19043856 4.30421790 4.41799725
## [73] 4.53177660 4.64555594 4.75933529 4.87311464 4.98689398 5.10067333
## [79] 5.21445268 5.32823202 5.44201137 5.55579072 5.66957006 5.78334941
## [85] 5.89712875 6.01090810 6.12468745 6.23846679 6.35224614 6.46602549
## [91] 6.57980483 6.69358418 6.80736353 6.92114287 7.03492222 7.14870157
## [97] 7.26248091 7.37626026 7.49003961 7.60381895
norm_dist = dnorm(x, mean=mean(data), sd=sd(data)) * (max(data)-min(data))/
20*length(data)
lines(x, norm_dist, col='violet',lwd=4)
abline(v = mean(data), col="black", lwd=3, lty=2)
# Add legend to top right position
legend("topright",
legend = c("Histogram", "density curve", "Average"),
col = c("lightblue", "violet", "black"),
lty = 1)
# Compute Quartile values Q1,Q2 and Q3
# These quantities divide the data into 4 equal parts
hist(data, breaks=20,col="lightblue",main = maintitle)
Quantiles = quantile(data)
Quantiles
## 0% 25% 50% 75% 100%
## -3.6603364 0.9099228 1.9576553 2.9915554 7.6038190
# 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] 0.4178713874 3.4125364052 0.8232093543 0.1467934578 2.8936738939
## [6] 1.6916230575 3.3408213878 -0.3457565823 -0.3903914449 3.1658033336
## [11] -0.3830377446 1.8520202583 1.8187865592 1.2299977256 2.3487622768
## [16] 2.4421825980 1.0176370147 2.7522616772 2.9017567891 3.5595621867
## [21] 0.0091845846 2.3237566137 3.4692742989 1.2621893104 -3.0527714702
## [26] 1.5636457304 0.0332942408 3.6025660674 3.4985824823 1.8476188984
## [31] 2.2983023376 3.2955155141 3.3875039184 4.8604138429 3.1213423701
## [36] 0.4119355616 0.5238355496 2.5008097699 2.9266312353 -0.0122721160
## [41] 2.2300764931 2.3601033676 4.5770014472 1.3128583145 4.3552481379
## [46] 2.5040326418 0.9800223917 1.4582439687 2.5552565453 2.3247803585
## [51] 3.3697840797 0.9278829303 -0.3009021168 -0.1846071005 -1.1780204299
## [56] 5.6304416598 1.8271806727 1.4424607068 2.8825607371 1.2801513912
## [61] 1.0500906290 1.0737749725 3.9185006984 -2.2602770611 0.2686754930
## [66] 0.6424679898 0.6060784313 4.2350146164 1.6958963267 1.7056589144
## [71] -0.3480628005 3.9683465372 3.6620751883 3.8288424434 -1.5646240038
## [76] 0.5729388301 0.8519424679 3.4382488688 0.8793056948 -0.1248791371
## [81] 2.4928543954 1.8370250080 0.9135537562 2.5134335681 4.6629737195
## [86] 3.6754647964 2.5703392826 1.6202232104 4.0532712070 1.4684392006
## [91] 0.9861803047 5.4403261660 -0.0331691149 0.3755060732 1.7837788072
## [96] 4.7082041142 2.1939133602 1.1885343070 2.4390624813 2.6356495639
## [101] 0.7515225505 2.2575071625 4.5867022135 1.0721232962 -2.7534102554
## [106] 1.6708718227 2.3278084910 3.8535236554 0.5038014533 4.0448811316
## [111] 2.3533997569 1.1052460216 -0.9053939770 1.9543198573 0.5548589376
## [116] 2.2474421670 -0.5740664219 1.5475508950 3.9724927233 3.0484955161
## [121] 2.8224775480 2.4214327294 2.1486250327 3.6957749486 1.5590661659
## [126] 2.9061690160 0.4867355971 -0.3826361433 2.1515189339 3.9990090517
## [131] 3.4218845968 1.6602279643 0.8417727218 3.7651277107 1.7737019149
## [136] 0.7820515613 -0.0175514207 1.9368247238 1.1508297662 1.0674413735
## [141] 1.8751536613 3.0334192522 4.1479768392 -0.0751014965 0.0257848109
## [146] 1.3299915867 3.1129728167 2.7331752423 4.3480816543 0.0009823095
## [151] -0.2966957464 3.5317815201 2.6867429247 3.8387515392 2.7363077063
## [156] 1.8994981101 1.6831094446 3.8734852019 2.8125492052 3.6590011640
## [161] 1.6172614719 -0.6811290017 0.5331017857 1.6594815274 2.1879833908
## [166] 1.8782162875 2.1292842141 3.1494864487 -0.3883753005 2.7316977099
## [171] 2.0396837643 1.9679339317 1.4531092447 2.7377442564 2.4566576105
## [176] 0.9716395664 2.5942584821 1.8037962756 2.1933925404 3.1514589889
## [181] 1.2562171406 2.5169577202 2.5980616715 4.6757798458 4.1673875485
## [186] 2.0513454497 -1.1771006504 1.1223195605 3.0791966795 1.4773259615
## [191] 1.0265584756 -0.8644619587 1.6513443391 0.8785428322 1.6405963395
## [196] 4.8874208657 0.6333478369 0.1773707673 1.8996314626 1.3274462403
## [201] 3.4644399566 0.5893416609 -0.2581021448 3.6739842068 0.2920604151
## [206] 4.2080799590 2.5541784131 6.0509337144 5.2533001720 1.9339912345
## [211] 1.7942095211 1.2656598553 3.9022411519 1.3949080661 3.4016309933
## [216] 0.9973245952 2.8850571549 1.9109461076 3.3354162571 -0.3778919783
## [221] -1.0386639299 2.9724084051 4.2404740591 1.0749285500 1.9621109800
## [226] 2.5448814465 1.4451688026 1.3220716329 2.9684961109 4.3048235667
## [231] 2.1916650132 3.4630330899 0.2855501883 3.6910858743 2.5351606611
## [236] 6.6266466467 5.3868341898 2.6345116556 2.5794409295 2.0771113019
## [241] 2.5703507372 2.0776979555 3.7563037813 3.2807786094 3.3073673765
## [246] -0.2053095111 0.8162741665 2.8318250860 1.9251341875 1.1461117418
## [251] 5.1500631599 1.9624973152 4.5432516377 1.4277224305 0.7302375826
## [256] 3.1552605229 0.9470495090 1.4831808875 2.7697964090 0.6585846805
## [261] 2.9594041772 0.8617015866 0.7114341342 2.7945344857 1.3403278457
## [266] 0.0715938726 -0.9777855723 3.6550650528 1.5819493606 2.3694396505
## [271] 2.8732682553 -0.1209759337 4.3172025335 2.0896074008 4.4701994244
## [276] 1.0567968470 5.0764135806 5.5137743394 1.6283844092 0.7981582737
## [281] 1.1588688612 3.3782289523 1.3058103900 4.2461295864 -1.0528641187
## [286] 2.0244870715 1.6001996742 2.6795030657 0.2930124754 2.2298501573
## [291] 1.2211812413 1.1154037170 -0.2580448536 5.9206950506 1.3462188558
## [296] 1.2752306982 1.2380822042 4.3346253395 2.0393354031 3.9260349993
## [301] -1.3909942762 2.0448451933 2.5830987900 2.5625239090 2.2084031808
## [306] 4.1921730148 0.3495814089 0.6976900290 1.2683087217 4.2273425847
## [311] 1.2370631748 2.4779446330 3.2158784547 1.4674950116 2.4897861481
## [316] 3.9715021346 3.1815081071 0.8477171864 2.0666930260 -0.0056971070
## [321] 4.5260213415 2.1288013184 1.8848866671 4.2167727963 3.6879406750
## [326] 2.5285262759 1.6236578172 -3.4841053882 2.3039439593 3.0053535249
## [331] 2.0239675566 2.1693195832 3.0045128307 4.9537731950 0.8951255936
## [336] 2.0423057868 1.4620160056 1.3111487929 3.0443917448 0.3669218068
## [341] 3.4561680485 2.3229386317 2.9762696048 -2.1060415248 0.4539085864
## [346] 3.3944460347 0.6049944733 2.4611492766 2.0666642543 1.4253483993
## [351] 2.8240550094 1.4963447539 1.0324405095 0.4653501150 0.2450977892
## [356] 3.1092803747 0.6698855850 -1.6091983407 3.0427624128 -0.2011775126
## [361] 2.2506698387 1.8847617004 0.5310752192 1.6657959341 -1.1034160503
## [366] 0.0883408226 1.2406705249 -0.7013683399 0.6749288406 3.1770792468
## [371] 2.1592632848 1.0734903183 2.6266426332 1.8556427625 0.6844065589
## [376] 0.4185049767 1.8387919322 0.8586201087 2.3095205579 4.8451006622
## [381] 2.1286414534 1.6788510459 1.9719079210 4.8679532275 1.4740787743
## [386] 1.7739410949 2.7141722347 0.6831609866 2.9112625020 1.9091518754
## [391] 1.5064296954 0.0857823260 2.3385170800 2.8029804549 0.6976708508
## [396] 0.8072950211 1.7111427867 1.7521089717 2.8860178567 0.7024494931
## [401] 3.6285793041 3.6913236991 -0.6529396003 1.9609908329 1.1843756186
## [406] 2.3585991220 0.8201502967 1.3474967905 1.1847958704 5.3169486040
## [411] 2.3822777430 -0.4772785959 2.1565194956 6.0999342804 1.1352402078
## [416] 1.4034424166 2.4488774440 1.4882752784 0.3910163000 2.1598729632
## [421] 1.2671448319 -1.6902961400 2.0196530913 0.2233829389 4.4703431645
## [426] 4.0819501006 3.8826838777 4.1087278020 1.3573603477 2.1449823492
## [431] 0.4026943189 2.1043238523 3.1135479935 1.2243211010 3.1763562684
## [436] 0.0232345165 -1.3009293401 3.4636058258 3.6016259802 4.8429268944
## [441] 2.0131047361 0.7605719118 0.8827951888 4.2890266381 2.5851291923
## [446] 2.1920550992 -0.2803017875 2.8816068932 2.9759156064 -1.7004514926
## [451] 1.2889012380 -0.2600736449 2.9904000891 4.8191264814 1.1026094032
## [456] 2.7393183924 -0.1053359423 2.7902967261 2.7295829385 2.1873851737
## [461] 1.1536301823 2.2445901677 1.2661825872 2.7607230569 3.2065868673
## [466] 3.5061365825 0.8141343262 2.2124955552 3.0675412080 -1.7828087513
## [471] 2.3174439898 0.6852862251 0.9988732564 2.9069680843 2.0735315219
## [476] 0.9623806782 1.6648360147 2.0199742230 2.3373832636 2.7411897492
## [481] 0.7286122558 0.4941044006 2.9843058600 3.4669717257 1.8389017251
## [486] -1.0134324835 1.0543931464 3.8806071044 1.1193068228 1.9770474301
## [491] -0.4805968245 2.1389976481 1.9984024924 1.8287909433 1.5995285676
## [496] 0.3547725725 0.6052240185 0.7460008149 3.0980297193 0.9639395397
## [501] -1.6933448000 3.9242209791 1.7669026540 1.5582204651 3.2498753566
## [506] 2.4874043872 3.1723169386 2.8037565142 1.7564924814 -0.7258742703
## [511] 3.4500225868 2.1987015150 3.6511247271 -0.3106294355 0.3527361142
## [516] 1.4828168828 1.4243276305 2.0086863169 2.8581016370 1.4909444684
## [521] 3.0304954682 5.0612152733 2.4927846819 2.8709683607 0.8751823154
## [526] 0.3743916397 2.6930076056 0.4406440571 3.0711542773 -0.7355695036
## [531] -0.4580836097 -0.3735181055 2.3351573848 1.2157225389 4.1082943187
## [536] -1.5861383198 1.2416162961 3.5226870044 4.5667564556 1.5672281862
## [541] 3.6395772926 2.5399663909 6.4634128766 1.2632813648 2.2047859929
## [546] 1.3951956466 3.1752756451 4.7650051681 3.1824333200 0.4011428003
## [551] 2.4511095387 4.0084374752 2.0838066223 -0.1619608647 2.6664919249
## [556] 0.4404140939 0.6045874159 4.2111949701 3.6686101414 1.4057946899
## [561] 5.6597219534 2.9206439096 1.8034025814 1.9901297350 4.2951974891
## [566] 3.7595089825 1.3364125307 1.8160617629 2.7039655926 2.0509789773
## [571] 0.9651028406 3.9836688445 1.1830178692 1.2010860441 2.3324532941
## [576] 2.8452204441 7.6038189529 3.5053918072 1.4273934677 -0.9407798355
## [581] 3.9248811673 1.3798515323 2.8801366107 2.8208701483 2.8532470107
## [586] 0.0425060231 0.6638768981 1.3852042788 2.4093275534 2.9489640269
## [591] 1.4595071029 3.9927183397 1.3240354721 1.6778498291 -0.7812219100
## [596] 1.7849035890 2.4362990954 1.8798306326 3.0115663633 2.9107328100
## [601] 2.4934247835 3.9206589704 2.8539334629 3.5030161113 1.3079884282
## [606] -0.3377140233 -1.2540975762 1.4961953094 0.4161534616 -0.3870903504
## [611] 1.7850070811 -0.0757522066 1.6812921302 3.2718081238 1.2439621118
## [616] 0.4579760533 1.1777421400 6.1318993301 0.1294240650 2.4429581873
## [621] 3.8758876093 1.6997636447 3.3498376907 2.1220707224 3.1967621746
## [626] 2.6905824683 1.8255488135 4.1684427116 2.1702292738 2.1707120772
## [631] 2.0137632333 5.3444482317 0.9926333254 3.8353753784 3.2880204871
## [636] 1.1290590542 3.8682327721 3.6552464241 1.2450426832 1.8638475050
## [641] 0.7819034073 2.5775373241 3.5658250268 0.4454522572 0.2751717967
## [646] 3.1406741149 2.9950214939 0.9892870508 4.4014391038 0.4662975708
## [651] 5.1063107410 2.7328230977 2.2372786688 0.2939222536 2.2785046020
## [656] 2.6994343811 3.1706701833 2.4321721049 0.9893028829 3.4931735442
## [661] -0.7493007579 3.0629945019 1.6690662285 0.9383859692 -1.7829209159
## [666] 3.4755306877 2.6911171131 -0.2273484782 1.2611288450 2.4994095303
## [671] 0.8664953858 0.5649582470 0.0791677204 0.5981985066 1.8064753547
## [676] 0.7890538936 3.7614945326 1.4312488110 1.4442364429 2.6971661249
## [681] 0.6790698148 2.2621065751 3.1953234783 0.5535787290 2.7689474980
## [686] 1.2658648202 3.2452870241 1.1401204020 1.7867495468 2.2008205331
## [691] 0.9329878126 2.6374597354 3.1701755476 1.3981013103 1.1977589959
## [696] 2.3234839838 1.3590552202 0.8966624552 -1.1097570861 1.6776458002
## [701] 0.9498946482 0.5155529015 1.1997042807 1.4114944583 4.6963255728
## [706] 2.0675314124 1.8841840634 4.1537962290 -0.0122609229 -0.3913859501
## [711] -0.3291613799 2.9981696795 2.6313950315 2.0213852684 3.6371917688
## [716] 2.9500582984 4.0664730358 0.4509932520 -0.0737254157 2.3899600881
## [721] 3.5021767620 2.1820060169 2.3181315799 1.5407892800 2.5338152940
## [726] 4.3506910500 2.7755012599 1.9441738062 -0.9283487192 1.4891395133
## [731] 0.8791718698 1.4682715256 2.1334747760 1.5033534274 0.8552243590
## [736] -3.6603363551 4.6062046433 0.7139735683 0.0903671353 3.2996018976
## [741] 0.6627436468 3.0919128378 3.1478608431 4.2746936691 1.1444211051
## [746] 1.6829584042 1.2899328375 0.8710122676 0.0713242266 2.8743522040
## [751] 4.3984074846 3.7679367910 0.2316712853 3.9542723163 3.4823279440
## [756] 4.9994362543 2.3388149865 2.2488961911 3.1769669320 1.0229517724
## [761] 0.1645278219 0.1752545997 1.8947667875 0.9866287848 3.0971686938
## [766] 2.7102535403 2.6237660299 0.5128181638 3.0393277210 4.9689965122
## [771] 3.0546788937 -0.0159395307 3.9136995286 3.4024517436 1.2186065791
## [776] 0.5420060793 3.8965190917 4.5548779320 1.1236109731 1.1392320721
## [781] 1.1308367391 0.7075210022 0.3793246026 2.3291196154 4.7426664260
## [786] 2.6259260039 4.0645704180 3.0427971347 0.8655791339 3.3529861371
## [791] 2.4392113561 2.1783358547 3.3147234815 2.9232012985 1.3216926862
## [796] 2.9817616030 1.8186578892 1.3817023038 2.3118915452 1.9758218858
## [801] -0.0732277313 0.0796623313 4.0194594668 3.6729473331 2.5368000957
## [806] 2.6907484771 3.4227447564 2.1124424864 1.2931507622 0.6373643831
## [811] 2.8486125880 -0.7292311197 0.1795991870 2.6094074071 -0.6895182653
## [816] 1.3775998172 1.9481149269 3.0601638582 1.9120162040 -0.8319772979
## [821] 1.5528902211 2.5291136876 1.3835083186 1.2743313753 4.8248441440
## [826] 2.5384526257 0.8535104374 0.9693792064 3.3002537546 1.0315290196
## [831] 5.0657256868 2.4461473400 0.9992374755 2.3376506467 0.2007569340
## [836] 1.1354658542 2.4477184039 2.7708716631 3.2998226435 3.0674023189
## [841] 5.4539298990 3.3668998815 0.3415644890 3.1941678208 4.1041213217
## [846] 2.0607846061 -1.0160615782 0.6437176202 2.3322452564 1.2026444888
## [851] 1.0583059629 -0.4750889022 3.1916861765 -0.5218072835 2.6539712042
## [856] -0.2747317608 0.7289652780 2.1827239465 3.1833225052 2.3781262319
## [861] 3.2821499572 2.9607861810 1.8264040948 2.7670046734 0.3439987228
## [866] 1.3363154868 0.2770983355 2.3180639289 1.8654376808 0.3775114202
## [871] 2.6294810069 -1.9447149415 0.4045502791 1.8862650328 1.6709603230
## [876] 1.0121541156 1.5272713362 1.3623863754 1.0394988653 0.3949740553
## [881] 0.4783141114 3.3730708312 -0.3681353569 2.4313916421 3.3296541572
## [886] 1.0982904623 1.2391265881 0.4126673417 2.7742872695 0.0593332301
## [891] -0.4790045452 2.6534185172 0.5625213262 1.6864494939 1.4795327586
## [896] 4.1113253140 0.2073343053 1.8451399510 3.5007128441 1.9336147010
## [901] 1.0098555047 1.8258657790 -2.2854831407 1.6285177123 0.7889378206
## [906] 0.2954436337 0.7523460625 1.9032660090 2.0410877167 2.5916859091
## [911] 1.7345725412 1.2318118051 3.5384567124 4.3144054949 0.4622608610
## [916] 2.9270936990 2.9273674320 5.7863549594 -0.3944431180 4.9589725089
## [921] 0.4892404830 2.5368171999 3.5207319869 2.0373695335 3.7781873638
## [926] 2.4035918242 1.9838298183 0.8632462271 2.7221740492 4.1490194723
## [931] 0.8939101994 0.8985197180 -0.4314265136 2.1858060217 2.8033586887
## [936] 3.7075435414 3.2192522378 0.8141339156 0.6829263639 2.4269252954
## [941] 3.2401688962 3.3017601862 -0.2309773999 2.2211432317 2.9711273250
## [946] 2.1537066806 0.3951092771 3.0413604651 1.1979604519 1.5723676692
## [951] 0.8968947728 3.8922221101 1.1261360262 1.9368463392 1.3689692057
## [956] 3.3856238873 0.6545584518 3.2210556110 2.5905522925 0.6936648040
## [961] 1.4839490445 3.1002374276 0.8990298018 -0.5045069064 2.6353999348
## [966] 2.2396548524 3.9704872658 2.3751208637 2.1483206198 2.7951631116
## [971] 3.5026355544 3.1349445439 1.2452192652 -1.2930110864 1.3398565955
## [976] 1.9694776071 0.1250438567 -0.2663985860 3.0094552881 2.4882875392
## [981] 0.1174713531 1.0727148134 0.8388373594 3.6675143868 0.9849710492
## [986] 1.7028655596 0.7817408381 3.3238203350 1.8509268181 -0.4854226391
## [991] 3.1978350269 -0.4208617069 1.8795491055 -0.9991700129 3.9860620141
## [996] 0.2418991703 1.6222345398 3.9158062908 -0.9988344475 4.6961281121
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.6603 0.9099 1.9577 1.9469 2.9916 7.6038
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%
## -0.4790842
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%
## 4.398559
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%
## -0.4790842
# 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] 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE TRUE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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] TRUE FALSE FALSE FALSE TRUE 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 TRUE 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 TRUE 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 FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [817] FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
## [997] FALSE FALSE TRUE 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] -3.0527715 -1.1780204 -2.2602771 -1.5646240 -2.7534103 -0.9053940
## [7] -0.5740664 -0.6811290 -1.1771007 -0.8644620 -1.0386639 -0.9777856
## [13] -1.0528641 -1.3909943 -3.4841054 -2.1060415 -1.6091983 -1.1034161
## [19] -0.7013683 -0.6529396 -1.6902961 -1.3009293 -1.7004515 -1.7828088
## [25] -1.0134325 -0.4805968 -1.6933448 -0.7258743 -0.7355695 -1.5861383
## [31] -0.9407798 -0.7812219 -1.2540976 -0.7493008 -1.7829209 -1.1097571
## [37] -0.9283487 -3.6603364 -0.7292311 -0.6895183 -0.8319773 -1.0160616
## [43] -0.5218073 -1.9447149 -2.2854831 -0.5045069 -1.2930111 -0.4854226
## [49] -0.9991700 -0.9988344
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.398559
(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 TRUE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE TRUE TRUE 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 TRUE TRUE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [253] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [277] TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [541] FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] TRUE 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 FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] TRUE FALSE TRUE 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 TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [769] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [781] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [829] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [841] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [913] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE TRUE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 4.860414 4.577001 5.630442 4.662974 5.440326 4.708204 4.586702 4.675780
## [9] 4.887421 6.050934 5.253300 6.626647 5.386834 5.150063 4.543252 4.470199
## [17] 5.076414 5.513774 5.920695 4.526021 4.953773 4.845101 4.867953 5.316949
## [25] 6.099934 4.470343 4.842927 4.819126 5.061215 4.566756 6.463413 4.765005
## [33] 5.659722 7.603819 6.131899 5.344448 4.401439 5.106311 4.696326 4.606205
## [41] 4.999436 4.968997 4.554878 4.742666 4.824844 5.065726 5.453930 5.786355
## [49] 4.958973 4.696128