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Central Tendency - Verkoopcijfers Vrouwenkleding 2000-2008 - Amelie Barratt

*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 05 May 2009 13:02:59 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/May/05/t1241550270unh7vgikoxj03nv.htm/, Retrieved Tue, 05 May 2009 21:04:32 +0200
 
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/2009/May/05/t1241550270unh7vgikoxj03nv.htm/},
    year = {2009},
}
@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 = {2009},
    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 «
461683 731993 522673 572709 382812 942567 802385 272643 992660 672651 122826 493878 801948 742156 612673 662804 572750 202510 652313 492663 292397 382618 872790 913865 221989 842162 142783 112683 862759 392482 602262 542540 982375 112533 622742 883970 562056 322091 832619 82723 872811 562534 112447 342593 422622 682787 602944 84298 942258 722391 662901 3007 452988 12759 942577 52626 882755 22968 433067 904437 812315 32428 53073 403145 243133 313018 32720 922852 192947 693108 33335 944749 962536 292541 953227 193417 73378 433219 962953 632986 333186 733212 463421 495024 752596 22640 123421 243440 623653 413304 852981 613232 493203 253344 803665 574904 132570 132785 393406 333452 583642 893230 272991 373159 133072 653091 373307
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean497780.5327102828774.461865117617.2993863462560
Geometric Mean351683.878229291
Harmonic Mean117268.984432551
Quadratic Mean579266.987011865
Winsorized Mean ( 1 / 35 )497775.55140186928744.373734473617.3173211564835
Winsorized Mean ( 2 / 35 )497597.21495327128658.55873393217.3629532305863
Winsorized Mean ( 3 / 35 )497594.71962616828655.331014732417.3648219024356
Winsorized Mean ( 4 / 35 )497600.36448598128547.685162028117.4304978376268
Winsorized Mean ( 5 / 35 )497217.84112149528486.403102214317.4545673364724
Winsorized Mean ( 6 / 35 )497130.5327102828463.083400264017.4658003744482
Winsorized Mean ( 7 / 35 )498391.90654205628272.114458548117.6283916532945
Winsorized Mean ( 8 / 35 )498402.22429906528263.72156817517.6339914436557
Winsorized Mean ( 9 / 35 )498477.84112149527774.874180220117.9470782797096
Winsorized Mean ( 10 / 35 )498511.2990654227529.286399701918.1083988821017
Winsorized Mean ( 11 / 35 )497703.98130841127369.290873611418.1847598319868
Winsorized Mean ( 12 / 35 )499604.01869158926753.423804290618.6743955594747
Winsorized Mean ( 13 / 35 )498489.42056074826596.998234192918.7423188200198
Winsorized Mean ( 14 / 35 )498350.07476635526572.595326905118.7542868370772
Winsorized Mean ( 15 / 35 )498377.97196261726189.922343096219.0293795236850
Winsorized Mean ( 16 / 35 )498463.80373831826177.468039475419.0417118640595
Winsorized Mean ( 17 / 35 )498323.67289719625768.081018139319.3387964181890
Winsorized Mean ( 18 / 35 )496714.94392523425545.278500096219.4444912363498
Winsorized Mean ( 19 / 35 )494844.77570093525287.560077952419.5687039071981
Winsorized Mean ( 20 / 35 )494876.17757009324813.473782538619.9438491324154
Winsorized Mean ( 21 / 35 )500736.55140186923021.912485669821.750432407106
Winsorized Mean ( 22 / 35 )499054.68224299122783.998588960321.9037356544080
Winsorized Mean ( 23 / 35 )500734.11214953322503.380394923222.2515063675722
Winsorized Mean ( 24 / 35 )505005.21495327121952.015147827223.0049592965617
Winsorized Mean ( 25 / 35 )498414.56074766419921.123997987225.0193995478379
Winsorized Mean ( 26 / 35 )495952.33644859819609.142215758225.2918934949660
Winsorized Mean ( 27 / 35 )496194.57943925219040.76929690426.0595867583949
Winsorized Mean ( 28 / 35 )500925.79439252318403.691151192827.2187677068280
Winsorized Mean ( 29 / 35 )498417.70093457918086.470632124027.5574881950337
Winsorized Mean ( 30 / 35 )495648.44859813116506.80599201630.0269142823794
Winsorized Mean ( 31 / 35 )492699.97196261716167.356409015130.4749867262086
Winsorized Mean ( 32 / 35 )495792.60747663515125.025894673432.7796204072114
Winsorized Mean ( 33 / 35 )495583.81308411214477.499547540234.2313126280370
Winsorized Mean ( 34 / 35 )499078.50467289714078.846717359835.44882011234
Winsorized Mean ( 35 / 35 )495988.36448598113723.269286833836.1421432545842
Trimmed Mean ( 1 / 35 )497780.5327102828550.330371189217.4351934369419
Trimmed Mean ( 2 / 35 )497779.52380952428328.401737168817.5717475496121
Trimmed Mean ( 3 / 35 )497882.40594059428124.374783007817.7028790784499
Trimmed Mean ( 4 / 35 )497882.40594059427891.355939605017.8507781055425
Trimmed Mean ( 5 / 35 )498092.41237113427658.216331832618.0088407146438
Trimmed Mean ( 6 / 35 )498289.42105263227406.336271402318.1815407983803
Trimmed Mean ( 7 / 35 )498289.42105263227121.980537015918.3721620319198
Trimmed Mean ( 8 / 35 )498511.6451612926835.113673732318.5768411947985
Trimmed Mean ( 9 / 35 )498551.22471910126505.929344004618.8090452611075
Trimmed Mean ( 10 / 35 )498561.25287356326214.626487802719.0184381648748
Trimmed Mean ( 11 / 35 )498567.54117647125918.103717894319.2362661482927
Trimmed Mean ( 12 / 35 )498668.74698795225598.711914881619.4802280929634
Trimmed Mean ( 13 / 35 )498565.79012345725322.258291389419.6888359792535
Trimmed Mean ( 14 / 35 )498565.79012345725020.364675417919.9263998183563
Trimmed Mean ( 15 / 35 )498573.74683544324668.062828209220.2113052130424
Trimmed Mean ( 16 / 35 )498595.94805194824309.490895133920.5103410105455
Trimmed Mean ( 17 / 35 )498630.68493150723886.951904398720.8746049695727
Trimmed Mean ( 18 / 35 )498657.90140845123447.413596022021.2670749106865
Trimmed Mean ( 19 / 35 )498825.28985507222957.960459156721.7277702321383
Trimmed Mean ( 20 / 35 )499159.86567164222412.90368468322.2710931476839
Trimmed Mean ( 21 / 35 )499512.44615384621833.791974628722.8779520632188
Trimmed Mean ( 22 / 35 )499413.44444444421415.020829678723.3207078534481
Trimmed Mean ( 23 / 35 )499442.04918032820941.636909136623.8492363967225
Trimmed Mean ( 24 / 35 )499340.16949152520407.574192391724.4683745742641
Trimmed Mean ( 25 / 35 )498897.07017543919841.562645045925.1440412784224
Trimmed Mean ( 26 / 35 )498934.61818181819478.662773578625.6144184013796
Trimmed Mean ( 27 / 35 )498934.61818181819071.663973015226.1610428375714
Trimmed Mean ( 28 / 35 )499166.18867924518652.936152247126.7607300322588
Trimmed Mean ( 29 / 35 )499397.09803921618230.708026830827.3931817296528
Trimmed Mean ( 30 / 35 )499277.8775510217744.229005188828.1374793689272
Trimmed Mean ( 31 / 35 )499345.40425531917412.795976571528.6769227025445
Trimmed Mean ( 32 / 35 )499638.42222222217031.999328442229.33527723829
Trimmed Mean ( 33 / 35 )500554.4390243916731.727159219029.9164834724543
Trimmed Mean ( 34 / 35 )500967.69230769216447.414927102830.4587495681267
Trimmed Mean ( 35 / 35 )501128.37837837816130.200126072031.0677099144220
Median493878
Midrange497833.5
Midmean - Weighted Average at Xnp494430.518518519
Midmean - Weighted Average at X(n+1)p498934.618181818
Midmean - Empirical Distribution Function498934.618181818
Midmean - Empirical Distribution Function - Averaging498934.618181818
Midmean - Empirical Distribution Function - Interpolation499166.188679245
Midmean - Closest Observation494430.518518519
Midmean - True Basic - Statistics Graphics Toolkit498934.618181818
Midmean - MS Excel (old versions)498934.618181818
Number of observations107
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/05/t1241550270unh7vgikoxj03nv/18iw41241550178.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/05/t1241550270unh7vgikoxj03nv/18iw41241550178.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/05/t1241550270unh7vgikoxj03nv/2klmw1241550178.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/05/t1241550270unh7vgikoxj03nv/2klmw1241550178.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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