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Central tendency: prijs ruwe olie per barrel

*The author of this computation has been verified*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Fri, 12 Dec 2008 06:03:33 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229087120cwx6cjc2u3esi5g.htm/, Retrieved Fri, 12 Dec 2008 14:05:22 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229087120cwx6cjc2u3esi5g.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
32.68 31.54 32.43 26.54 25.85 27.6 25.71 25.38 28.57 27.64 25.36 25.9 26.29 21.74 19.2 19.32 19.82 20.36 24.31 25.97 25.61 24.67 25.59 26.09 28.37 27.34 24.46 27.46 30.23 32.33 29.87 24.87 25.48 27.28 28.24 29.58 26.95 29.08 28.76 29.59 30.7 30.52 32.67 33.19 37.13 35.54 37.75 41.84 42.94 49.14 44.61 40.22 44.23 45.85 53.38 53.26 51.8 55.3 57.81 63.96 63.77 59.15 56.12 57.42 63.52 61.71 63.01 68.18 72.03 69.75 74.41 74.33 64.24 60.03 59.44 62.5 55.04 58.34 61.92 67.65 67.68 70.3 75.26 71.44 76.36 81.71 92.6 90.6 92.23 94.09 102.79 109.65 124.05 132.69 135.81 116.07 101.42 75.73 55.48
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean50.34767676767682.7538104326842618.2829130756836
Geometric Mean44.0438528677522
Harmonic Mean39.0194688395435
Quadratic Mean57.2544216809514
Winsorized Mean ( 1 / 33 )50.31737373737372.7438531951137618.3382164275329
Winsorized Mean ( 2 / 33 )50.15292929292932.6914829984284218.6339387327411
Winsorized Mean ( 3 / 33 )49.92747474747472.6246002663846219.0228871752153
Winsorized Mean ( 4 / 33 )49.72383838383842.5538391022366319.4702314410844
Winsorized Mean ( 5 / 33 )49.50717171717172.4599641762663520.1251596241991
Winsorized Mean ( 6 / 33 )49.43323232323232.4408154925288820.2527526044238
Winsorized Mean ( 7 / 33 )48.9297979797982.3315979984866720.9855206650357
Winsorized Mean ( 8 / 33 )48.82555555555562.3063242585764621.1702909397885
Winsorized Mean ( 9 / 33 )48.83646464646462.2951368298381421.2782366661375
Winsorized Mean ( 10 / 33 )48.67383838383842.2634809942290821.5039748546315
Winsorized Mean ( 11 / 33 )47.69717171717172.0863291758053522.8617671028639
Winsorized Mean ( 12 / 33 )47.06202020202021.9818893834774223.7460377932119
Winsorized Mean ( 13 / 33 )46.98191919191921.9691971586236323.858413052331
Winsorized Mean ( 14 / 33 )46.9295959595961.9577743102382223.9708916978718
Winsorized Mean ( 15 / 33 )46.82202020202021.9365593325910824.1779425055742
Winsorized Mean ( 16 / 33 )46.81717171717171.9337886250865724.2100771045108
Winsorized Mean ( 17 / 33 )46.43424242424241.8762809111464824.7480226166504
Winsorized Mean ( 18 / 33 )46.34878787878791.8589999332598124.9321084146108
Winsorized Mean ( 19 / 33 )46.16838383838381.8249023926427125.2990976528480
Winsorized Mean ( 20 / 33 )46.10777777777781.804376488307125.553302249597
Winsorized Mean ( 21 / 33 )45.86171717171721.7508397728318726.1941257466060
Winsorized Mean ( 22 / 33 )45.82393939393941.7283887231157826.5125193083487
Winsorized Mean ( 23 / 33 )45.83090909090911.7259645536044826.5537950910965
Winsorized Mean ( 24 / 33 )45.03333333333331.6193148238888627.8101161484977
Winsorized Mean ( 25 / 33 )44.99797979797981.6068683362129228.0035263524025
Winsorized Mean ( 26 / 33 )44.95858585858591.5997097243007228.1042148932605
Winsorized Mean ( 27 / 33 )45.05404040404041.5735764536485228.6316183109994
Winsorized Mean ( 28 / 33 )44.94656565656571.5523688826557628.9535342783167
Winsorized Mean ( 29 / 33 )44.85575757575761.5283225383736729.3496670038575
Winsorized Mean ( 30 / 33 )44.73757575757581.5014510063698929.7962274944551
Winsorized Mean ( 31 / 33 )44.77202020202021.4829292910336930.1916082396696
Winsorized Mean ( 32 / 33 )44.39060606060611.4029471572366531.6409679663497
Winsorized Mean ( 33 / 33 )44.19727272727271.3803209021799532.0195634634465
Trimmed Mean ( 1 / 33 )49.78773195876292.6475050804264618.8055283923169
Trimmed Mean ( 2 / 33 )49.23578947368422.5361978560510619.4132288836273
Trimmed Mean ( 3 / 33 )48.74763440860222.4404027442098419.9752415966020
Trimmed Mean ( 4 / 33 )48.31978021978022.3596372363418920.4776308305296
Trimmed Mean ( 5 / 33 )47.92932584269662.2913311105926120.9176777730306
Trimmed Mean ( 6 / 33 )47.57022988505752.2399726960724921.2369686329060
Trimmed Mean ( 7 / 33 )47.20858823529412.18525011005621.6032883458289
Trimmed Mean ( 8 / 33 )46.91530120481932.1473345445264621.8481565084519
Trimmed Mean ( 9 / 33 )46.62345679012352.1082872426560222.1143759952687
Trimmed Mean ( 10 / 33 )46.31531645569622.0644908306856622.4342563150614
Trimmed Mean ( 11 / 33 )46.01207792207792.0190775468126922.7886630678017
Trimmed Mean ( 12 / 33 )45.80986666666671.9980947005065122.9267745192728
Trimmed Mean ( 13 / 33 )45.66835616438361.9899914623706722.9490211530752
Trimmed Mean ( 14 / 33 )45.52746478873241.9811311903792122.9805401125495
Trimmed Mean ( 15 / 33 )45.3837681159421.9710434280572523.0252502151483
Trimmed Mean ( 16 / 33 )45.24208955223881.9608932251638823.0721841310140
Trimmed Mean ( 17 / 33 )45.09215384615381.9477154947960523.1513041646134
Trimmed Mean ( 18 / 33 )44.96809523809521.9392385562485923.1885319592062
Trimmed Mean ( 19 / 33 )44.8436065573771.9298485462926123.2368527797299
Trimmed Mean ( 20 / 33 )44.72661016949151.9217542123002723.2738452624258
Trimmed Mean ( 21 / 33 )44.60666666666671.9129046385598823.3188135819717
Trimmed Mean ( 22 / 33 )44.49909090909091.9079916331675923.3224769624460
Trimmed Mean ( 23 / 33 )44.38660377358491.9027099485436823.3280978046906
Trimmed Mean ( 24 / 33 )44.26470588235291.8937493540373723.3741100890585
Trimmed Mean ( 25 / 33 )44.21.8969424915707223.3006536552414
Trimmed Mean ( 26 / 33 )44.13276595744681.8990704601443223.2391408763701
Trimmed Mean ( 27 / 33 )44.13276595744681.8988743508259023.241540936214
Trimmed Mean ( 28 / 33 )43.97837209302331.8986039905632223.1635308424571
Trimmed Mean ( 29 / 33 )43.89487804878051.8973622615245323.134684893285
Trimmed Mean ( 30 / 33 )43.81076923076921.8951416464929423.1174114672871
Trimmed Mean ( 31 / 33 )43.72810810810811.8919721282856923.1124483571172
Trimmed Mean ( 32 / 33 )43.63285714285711.8853122948147323.1435700402860
Trimmed Mean ( 33 / 33 )43.56181818181821.8877654566766223.0758635972225
Median42.94
Midrange77.505
Midmean - Weighted Average at Xnp43.8652
Midmean - Weighted Average at X(n+1)p44.2647058823529
Midmean - Empirical Distribution Function44.2647058823529
Midmean - Empirical Distribution Function - Averaging44.2647058823529
Midmean - Empirical Distribution Function - Interpolation44.2
Midmean - Closest Observation43.8652
Midmean - True Basic - Statistics Graphics Toolkit44.2647058823529
Midmean - MS Excel (old versions)44.2647058823529
Number of observations99
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087120cwx6cjc2u3esi5g/1ybhp1229087010.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087120cwx6cjc2u3esi5g/1ybhp1229087010.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087120cwx6cjc2u3esi5g/29yue1229087010.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087120cwx6cjc2u3esi5g/29yue1229087010.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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