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*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 02 Nov 2009 09:51:33 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/02/t1257180847j58fugong5v70u8.htm/, Retrieved Mon, 02 Nov 2009 17:54:08 +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/2009/Nov/02/t1257180847j58fugong5v70u8.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:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
100,7 100,9 101,8 102,9 103,2 104 105,3 105,9 105,9 106,3 106,4 106,5 106,9 107,7 109,4 109,6 110,7 110,9 110,9 111,9 112,2 112,8 113,2 113,4 113,5 113,5 113,9 114 114,1 114,8 114,9 115,1 115,2 115,3 115,3 115,4 115,4 115,5 115,8 115,8 116,2 116,3 116,8 116,9 117,3 118,2 118,7 118,9 119 119,4 119,5 119,6 119,7 119,8 120,1 120,2 120,2 120,5 120,6 120,9 121,3 121,3 121,5 121,6 121,7 121,8 121,9 122 122,5 122,6 123,1 124,2 124,3 124,3 124,3 124,4 124,8 124,8 125,1 125,2 125,6 125,8 126 126 126,5 126,5 127 128 129,1 129,7 130,7 131,3 131,5 131,9 135,2 137 137 137,1 138,8 141,1 143 143,3 143,3 144,2 146,5 148,6 151,7 157,8
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.9129629629631.09511809835598110.410889149290
Geometric Mean120.401632685974
Harmonic Mean119.907755408857
Quadratic Mean121.442447121931
Winsorized Mean ( 1 / 36 )120.8583333333331.07834912621388112.077183905802
Winsorized Mean ( 2 / 36 )120.8175925925931.06080769261891113.892078114855
Winsorized Mean ( 3 / 36 )120.7898148148151.04192650118815115.929304684230
Winsorized Mean ( 4 / 36 )120.7157407407411.02116081236130118.214231568093
Winsorized Mean ( 5 / 36 )120.7111111111111.00646949625436119.935190843185
Winsorized Mean ( 6 / 36 )120.7833333333330.995615604877538121.315227223854
Winsorized Mean ( 7 / 36 )120.8027777777780.985941731464081122.525270939075
Winsorized Mean ( 8 / 36 )120.6620370370370.95707971876952126.073131287504
Winsorized Mean ( 9 / 36 )120.5037037037040.91520172371727131.669008679589
Winsorized Mean ( 10 / 36 )120.3555555555560.88521697450851135.961644457145
Winsorized Mean ( 11 / 36 )120.3555555555560.881920374402736136.469866270029
Winsorized Mean ( 12 / 36 )120.40.87545468579944137.528534546656
Winsorized Mean ( 13 / 36 )120.2796296296300.824089708588043145.954534289369
Winsorized Mean ( 14 / 36 )120.0722222222220.724084785760698165.826191329346
Winsorized Mean ( 15 / 36 )120.0444444444440.711848170722409168.637708688103
Winsorized Mean ( 16 / 36 )120.1777777777780.68566306667788175.272351127287
Winsorized Mean ( 17 / 36 )120.1148148148150.667438305785481179.963921419608
Winsorized Mean ( 18 / 36 )119.9481481481480.64326997772805186.466261913528
Winsorized Mean ( 19 / 36 )120.0185185185190.60579889003541198.116108320211
Winsorized Mean ( 20 / 36 )119.8703703703700.570989041999817209.934624928247
Winsorized Mean ( 21 / 36 )119.7925925925930.531196562810297225.514622984060
Winsorized Mean ( 22 / 36 )119.7722222222220.508503041540588235.538851172559
Winsorized Mean ( 23 / 36 )119.8148148148150.503394181874186238.013904667576
Winsorized Mean ( 24 / 36 )119.7259259259260.487158335634109245.763886540266
Winsorized Mean ( 25 / 36 )119.7259259259260.487158335634109245.763886540266
Winsorized Mean ( 26 / 36 )119.7740740740740.469998803917912254.83910400545
Winsorized Mean ( 27 / 36 )119.7490740740740.461121736738482259.690802955983
Winsorized Mean ( 28 / 36 )119.6712962962960.445938656974118268.358202243144
Winsorized Mean ( 29 / 36 )119.8324074074070.421336918303737284.409939413431
Winsorized Mean ( 30 / 36 )119.7768518518520.408580109552052293.153898223703
Winsorized Mean ( 31 / 36 )119.8342592592590.402220304659657297.931899188079
Winsorized Mean ( 32 / 36 )119.7453703703700.385429018514452310.680733982878
Winsorized Mean ( 33 / 36 )119.7453703703700.378626766366525316.262295768208
Winsorized Mean ( 34 / 36 )119.7453703703700.378626766366525316.262295768208
Winsorized Mean ( 35 / 36 )119.7777777777780.37508123807562319.338227612519
Winsorized Mean ( 36 / 36 )119.7444444444440.371334242494877322.470784379915
Trimmed Mean ( 1 / 36 )120.7556603773581.04210899591583115.876228734822
Trimmed Mean ( 2 / 36 )120.6490384615381.00103101741147120.524775319670
Trimmed Mean ( 3 / 36 )120.5598039215690.96516421019336124.911183660049
Trimmed Mean ( 4 / 36 )120.4770.932645693658095129.177672527984
Trimmed Mean ( 5 / 36 )120.4112244897960.902902119753974133.360219070707
Trimmed Mean ( 6 / 36 )120.343750.873334018640082137.798078892420
Trimmed Mean ( 7 / 36 )120.2595744680850.842285458318196142.777692859864
Trimmed Mean ( 8 / 36 )120.1684782608700.80889395761148.559001004193
Trimmed Mean ( 9 / 36 )120.0944444444440.776983766279226154.564933858973
Trimmed Mean ( 10 / 36 )120.0386363636360.749016128991561160.261751005617
Trimmed Mean ( 11 / 36 )119.9988372093020.722699177901988166.042581586521
Trimmed Mean ( 12 / 36 )119.9571428571430.692820914526222173.143073977745
Trimmed Mean ( 13 / 36 )119.9085365853660.659106183566072181.925977293378
Trimmed Mean ( 14 / 36 )119.870.629248597510042190.497047548981
Trimmed Mean ( 15 / 36 )119.850.611801872996096195.896752347413
Trimmed Mean ( 16 / 36 )119.8315789473680.593420683082314201.933606905890
Trimmed Mean ( 17 / 36 )119.80.576000971861453207.985760185168
Trimmed Mean ( 18 / 36 )119.7722222222220.558436582921324214.477750715512
Trimmed Mean ( 19 / 36 )119.7571428571430.541620035305368221.109144881657
Trimmed Mean ( 20 / 36 )119.7352941176470.527520766772389226.977403847514
Trimmed Mean ( 21 / 36 )119.7242424242420.516113594975658231.972657937618
Trimmed Mean ( 22 / 36 )119.718750.508327844427821235.514838135134
Trimmed Mean ( 23 / 36 )119.7145161290320.50207842354106238.437882442168
Trimmed Mean ( 24 / 36 )119.7066666666670.49501964046333241.822054887809
Trimmed Mean ( 25 / 36 )119.7051724137930.488626991110376244.982726275047
Trimmed Mean ( 26 / 36 )119.7035714285710.480529769107123249.107504101138
Trimmed Mean ( 27 / 36 )119.6981481481480.473013819734649253.054230456303
Trimmed Mean ( 28 / 36 )119.6942307692310.464845726541289257.492376362847
Trimmed Mean ( 29 / 36 )119.6960.456892431407603261.978513479066
Trimmed Mean ( 30 / 36 )119.6854166666670.450698724513147265.555259327510
Trimmed Mean ( 31 / 36 )119.6782608695650.444612549598703269.174275394574
Trimmed Mean ( 32 / 36 )119.6659090909090.437414361075438273.575629288201
Trimmed Mean ( 33 / 36 )119.6595238095240.430838788681872277.736190317533
Trimmed Mean ( 34 / 36 )119.65250.422977654437969282.881373861199
Trimmed Mean ( 35 / 36 )119.6447368421050.411908394994065290.464429218125
Trimmed Mean ( 36 / 36 )119.6333333333330.39727244659729301.136749749484
Median119.95
Midrange129.25
Midmean - Weighted Average at Xnp119.592727272727
Midmean - Weighted Average at X(n+1)p119.698148148148
Midmean - Empirical Distribution Function119.592727272727
Midmean - Empirical Distribution Function - Averaging119.698148148148
Midmean - Empirical Distribution Function - Interpolation119.698148148148
Midmean - Closest Observation119.592727272727
Midmean - True Basic - Statistics Graphics Toolkit119.698148148148
Midmean - MS Excel (old versions)119.703571428571
Number of observations108
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/02/t1257180847j58fugong5v70u8/10ejh1257180687.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/02/t1257180847j58fugong5v70u8/10ejh1257180687.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/02/t1257180847j58fugong5v70u8/2rajm1257180687.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/02/t1257180847j58fugong5v70u8/2rajm1257180687.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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