# Mindanao State University
# General Santos City
# Submitted by: Roland Fritz C. Adam
# 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] -0.4039912 1.4266027 -0.9013912 1.7963473 2.5602453 4.3794270
## [7] 5.3009881 1.1066330 1.2364662 -0.6262573 2.8060451 0.5767450
## [13] -0.2757780 0.4405118 3.8564487 2.2473057 2.5534552 0.3696604
## [19] 1.4044373 3.4330014
data[1:300] # display the first 300 elements
## [1] -0.40399117 1.42660266 -0.90139116 1.79634727 2.56024528 4.37942704
## [7] 5.30098811 1.10663302 1.23646617 -0.62625731 2.80604506 0.57674501
## [13] -0.27577804 0.44051177 3.85644865 2.24730572 2.55345522 0.36966037
## [19] 1.40443727 3.43300136 1.74364695 2.51728037 1.74065025 3.03417235
## [25] 2.01976186 2.12098345 3.53835497 3.81291902 3.03429451 4.23280102
## [31] 3.82601290 3.94999686 2.68623509 3.45574894 1.96246531 2.82372147
## [37] 3.47765800 1.62728287 1.30718496 -1.78914721 1.61552461 3.62015209
## [43] 4.00606735 1.89359218 3.58236071 1.62167951 5.38416955 0.17241925
## [49] 1.72561688 3.11130606 2.08555090 5.46233573 1.44570514 0.40924558
## [55] -1.08207385 0.52300887 0.54249510 2.78160451 2.75007403 2.75234094
## [61] 1.57387052 0.80129602 2.23006398 0.46606418 0.31402600 3.54621198
## [67] 0.16404095 -0.21638751 2.78357975 2.61252253 4.15592250 4.70486406
## [73] 3.33751988 4.72400865 0.63555615 1.95342380 2.19818155 1.13889328
## [79] 1.38957441 1.66884221 1.29583458 3.12762974 1.95089050 0.71432179
## [85] 1.20629869 2.05536890 3.56938039 2.65415532 2.14583804 -0.45756064
## [91] 0.55261186 3.73615382 2.63836981 -0.44820453 1.02273830 0.21050426
## [97] 3.33810791 3.73197838 2.07169827 2.59590585 3.29734652 0.39765194
## [103] 1.59148879 -1.17111333 2.91109574 2.68126977 1.71730953 3.50434798
## [109] 0.56533429 -0.45565082 1.88553221 1.85166443 3.34907196 2.81108025
## [115] -0.08868357 3.51785846 3.48199119 -0.32550888 2.17126354 4.24854725
## [121] 1.85501276 2.23002350 3.17589038 1.83730396 1.67552336 3.48453941
## [127] 2.49529641 -0.03792833 4.70991836 1.85500226 0.65348891 5.18215162
## [133] 0.27847395 0.92093167 0.50378108 0.82713078 2.63696673 2.09691846
## [139] 3.45870281 2.27929617 1.52450848 2.33894629 1.05313138 1.14977552
## [145] 5.89172024 4.37981630 1.36254042 2.03225365 3.58023750 2.56800464
## [151] 2.44477913 4.20425225 0.42754150 0.48366519 -0.47271402 1.12525596
## [157] 1.26151230 3.40753555 3.27109338 2.96163274 2.01444810 5.38062519
## [163] 0.50896989 3.10689219 1.31821375 -0.27514948 -0.72760708 3.63233825
## [169] -2.48640282 3.42991226 0.47666313 3.31240808 0.61709572 3.16932755
## [175] 2.20995133 3.40435959 3.33188759 3.02441612 2.89252661 -0.04459067
## [181] 5.98254741 2.16526162 3.82314209 2.22473266 1.39808581 2.93236286
## [187] 1.53197404 0.91772096 2.49010128 2.23532799 0.34430010 1.67452388
## [193] 1.52252715 4.81639611 1.03069777 0.98656757 0.22412080 2.73619201
## [199] 2.56588813 4.64362392 0.04167771 0.11355408 1.97219083 0.44953939
## [205] -0.93919907 0.27527885 1.13221642 3.03687916 1.70229745 2.88387674
## [211] 3.68992549 2.29432886 4.35951913 4.32271404 1.41505678 -1.31067690
## [217] 1.96943763 2.43196245 0.37903732 -0.01739904 1.85826990 0.44451672
## [223] 2.93997317 4.81024918 2.23410927 3.31106350 0.78537810 2.92334542
## [229] 4.01673758 3.37665165 2.73630548 1.72482335 0.34449318 1.61320269
## [235] 0.48836715 2.18830257 3.03535973 1.69433284 0.92903199 4.30367661
## [241] 0.27942615 2.30360337 2.05453950 2.08262594 1.03606014 1.13188690
## [247] 3.48573404 1.83803728 3.34943885 1.42177877 2.02008376 2.96908255
## [253] 5.53648720 2.64346606 1.13007729 3.73419078 1.21269087 1.35484588
## [259] 1.25304314 2.38475330 1.31758092 2.95715042 2.17930175 3.31986717
## [265] 4.04929264 1.15201913 1.67457581 2.98787705 2.81842156 3.89884297
## [271] 0.64338472 1.89105492 2.15998853 1.90660788 -0.32179724 -1.90934190
## [277] -1.70203437 -0.06595772 2.50492197 2.53987505 2.73059713 1.54188930
## [283] 1.76367417 0.15977499 0.32014373 0.18984263 2.96660965 1.31146432
## [289] 3.09980675 1.82959404 2.31292841 4.18847807 4.06579320 2.67673717
## [295] 3.11511825 1.71973315 2.95368211 0.63510101 4.96050776 0.61143272
# 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] -2.48640282 -2.39901338 -2.31162394 -2.22423450 -2.13684506 -2.04945562
## [7] -1.96206618 -1.87467674 -1.78728730 -1.69989786 -1.61250842 -1.52511898
## [13] -1.43772954 -1.35034010 -1.26295066 -1.17556122 -1.08817178 -1.00078234
## [19] -0.91339290 -0.82600346 -0.73861402 -0.65122458 -0.56383514 -0.47644570
## [25] -0.38905626 -0.30166682 -0.21427738 -0.12688794 -0.03949850 0.04789094
## [31] 0.13528038 0.22266982 0.31005926 0.39744870 0.48483814 0.57222758
## [37] 0.65961702 0.74700646 0.83439590 0.92178533 1.00917477 1.09656421
## [43] 1.18395365 1.27134309 1.35873253 1.44612197 1.53351141 1.62090085
## [49] 1.70829029 1.79567973 1.88306917 1.97045861 2.05784805 2.14523749
## [55] 2.23262693 2.32001637 2.40740581 2.49479525 2.58218469 2.66957413
## [61] 2.75696357 2.84435301 2.93174245 3.01913189 3.10652133 3.19391077
## [67] 3.28130021 3.36868965 3.45607909 3.54346853 3.63085797 3.71824741
## [73] 3.80563685 3.89302629 3.98041573 4.06780517 4.15519461 4.24258405
## [79] 4.32997349 4.41736293 4.50475237 4.59214181 4.67953125 4.76692069
## [85] 4.85431013 4.94169957 5.02908900 5.11647844 5.20386788 5.29125732
## [91] 5.37864676 5.46603620 5.55342564 5.64081508 5.72820452 5.81559396
## [97] 5.90298340 5.99037284 6.07776228 6.16515172
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%
## -2.486403 1.032561 2.054769 2.984919 6.165152
# 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
summary(data)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.486 1.033 2.055 2.001 2.985 6.165
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",
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%
## -0.4557463
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%
## 4.289416
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%
## -0.4557463
# mark those values that is lower than -.42 as true
# and higher than -.42 as false
(Low5Percent <- (data < Cutoff))
## [1] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [169] TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE 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 TRUE
## [277] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE 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 FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [553] FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] TRUE 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 TRUE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE
## [685] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE
## [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [781] TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [793] FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE TRUE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [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 TRUE FALSE FALSE FALSE
## [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE TRUE TRUE FALSE FALSE FALSE TRUE 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
# count all true values using the sum command
sum(Low5Percent[TRUE])
## [1] 50
# there are 50 of them
# filter those 50 values that are smaller than the cutoff
data[Low5Percent==TRUE]
## [1] -0.9013912 -0.6262573 -1.7891472 -1.0820739 -0.4575606 -1.1711133
## [7] -0.4727140 -0.7276071 -2.4864028 -0.9391991 -1.3106769 -1.9093419
## [13] -1.7020344 -0.8193178 -0.4693856 -1.5069348 -1.4316741 -1.1694187
## [19] -1.4565382 -0.9490689 -1.8178089 -0.5161560 -1.1882866 -1.6949871
## [25] -0.7494735 -1.1715301 -0.6108012 -0.8240508 -1.6086942 -0.6359931
## [31] -0.4766162 -0.5369361 -1.0924377 -0.8039349 -0.6515796 -0.7807452
## [37] -0.5865904 -0.6240106 -0.8985191 -0.7123267 -1.7170952 -1.0473325
## [43] -0.5699327 -1.6416877 -1.5634607 -1.4198363 -0.7618374 -0.6154008
## [49] -1.3500304 -0.7573491
# How to get the top 5%
(Cutoff <- quantile(data,prob = 0.95))
## 95%
## 4.289416
(Top5Percent <- (data >= Cutoff))
## [1] FALSE FALSE FALSE FALSE FALSE TRUE TRUE 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 TRUE FALSE
## [49] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [73] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] TRUE TRUE 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] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 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 FALSE 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 TRUE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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] TRUE TRUE 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 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 TRUE FALSE FALSE
## [445] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE 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 TRUE
## [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 TRUE 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 TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## [673] FALSE FALSE 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 TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE TRUE 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 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 TRUE FALSE FALSE FALSE FALSE FALSE
## [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [853] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [877] TRUE 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 TRUE
## [913] FALSE FALSE FALSE FALSE TRUE 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 TRUE FALSE FALSE
## [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE FALSE FALSE
sum(Top5Percent[TRUE]) # counts all the true values
## [1] 50
data[Top5Percent==TRUE]
## [1] 4.379427 5.300988 5.384170 5.462336 4.704864 4.724009 4.709918 5.182152
## [9] 5.891720 4.379816 5.380625 5.982547 4.816396 4.643624 4.359519 4.322714
## [17] 4.810249 4.303677 5.536487 4.960508 4.873470 5.100670 5.065901 4.599945
## [25] 5.833303 5.029470 4.476711 4.689125 4.327433 5.605478 4.837975 4.381043
## [33] 4.406755 4.547944 5.470323 5.489361 4.617099 4.963088 4.589540 4.541976
## [41] 4.809303 5.090811 6.165152 4.736786 4.919337 4.436285 4.421776 4.447797
## [49] 4.551210 4.444971