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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: Fri, 12 Mar 2010 05:36:52 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/12/t12683975645le67jqh933klx7.htm/, Retrieved Fri, 12 Mar 2010 13:39:26 +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/2010/Mar/12/t12683975645le67jqh933klx7.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
6550 8728 12026 14395 14587 13791 9498 8251 7049 9545 9364 8456 7237 9374 11837 13784 15926 13821 11143 7975 7610 10015 12759 8816 10677 10947 15200 17010 20900 16205 12143 8997 5568 11474 12256 10583 10862 10965 14405 20379 20128 17816 12268 8642 7962 13932 15936 12628 12267 12470 18944 21259 22015 18581 15175 10306 10792 14752 13754 11738 12181 12965 19990 23125 23541 21247 15189 14767 10895 17130 17697 16611 12674 12760 20249 22135 20677 19933 15388 15113 13401 16135 17562 14720 12225 11608 20985 19692 24081 22114 14220 13434 13598 17187 16119 13713 13210 14251 20139 21725 26099 21084 18024 16722 14385 21342 17180 14577
 
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'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14595.1111111111435.43891181348433.5181599878763
Geometric Mean13882.0735137741
Harmonic Mean13151.8638592249
Quadratic Mean15274.3321379123
Winsorized Mean ( 1 / 36 )14585.5185185185429.52302658952633.9574775171651
Winsorized Mean ( 2 / 36 )14584.7592592593425.93520948315734.2417319219908
Winsorized Mean ( 3 / 36 )14578.4259259259422.85278552754234.4763625187858
Winsorized Mean ( 4 / 36 )14555.5740740741414.04569078891435.1545116828536
Winsorized Mean ( 5 / 36 )14570.8981481481411.37824071005735.4197103935253
Winsorized Mean ( 6 / 36 )14566.1203703704410.33199285572935.4983784447238
Winsorized Mean ( 7 / 36 )14565.2129629630404.5349232915536.0048345009406
Winsorized Mean ( 8 / 36 )14552.0277777778397.72928266309536.5877706573201
Winsorized Mean ( 9 / 36 )14560.6111111111394.43153113140436.9154338887281
Winsorized Mean ( 10 / 36 )14567.4629629630393.14408946640537.0537504016267
Winsorized Mean ( 11 / 36 )14559.8240740741389.28567189418737.4013870154246
Winsorized Mean ( 12 / 36 )14568.9351851852384.81967660419437.8591222614899
Winsorized Mean ( 13 / 36 )14602.8796296296377.36876980566938.6965769243427
Winsorized Mean ( 14 / 36 )14575.2685185185372.73448962877539.103621811426
Winsorized Mean ( 15 / 36 )14551.1018518519364.23341357883739.9499367970597
Winsorized Mean ( 16 / 36 )14538.8055555556360.46554079713240.3334130730069
Winsorized Mean ( 17 / 36 )14595.4722222222348.56063287510941.8735532519298
Winsorized Mean ( 18 / 36 )14642.1388888889342.43816410727942.7584902140224
Winsorized Mean ( 19 / 36 )14666.5925925926333.13164148242344.0264170864311
Winsorized Mean ( 20 / 36 )14673.4444444444329.57271033453944.522631833048
Winsorized Mean ( 21 / 36 )14648.9444444444320.10135710735245.7634562278087
Winsorized Mean ( 22 / 36 )14510.8333333333296.59783831181748.9242720578358
Winsorized Mean ( 23 / 36 )14440.5555555556285.13763485168950.6441584362115
Winsorized Mean ( 24 / 36 )14328.3333333333267.37720401729653.5884627337433
Winsorized Mean ( 25 / 36 )14284.3518518519260.72489819024354.7870646455444
Winsorized Mean ( 26 / 36 )14298.5555555556252.04942159525556.7291742431228
Winsorized Mean ( 27 / 36 )14347.5555555556238.28631809157460.2114115089132
Winsorized Mean ( 28 / 36 )14285.0740740741222.30776470266064.258097746521
Winsorized Mean ( 29 / 36 )14318.1018518519218.18433396888365.6238767990274
Winsorized Mean ( 30 / 36 )14331.7129629630213.4605852023167.1398560506141
Winsorized Mean ( 31 / 36 )14351.5185185185203.38369372839970.563761801296
Winsorized Mean ( 32 / 36 )14300.8518518519189.37087038809075.517696161739
Winsorized Mean ( 33 / 36 )14278.5462962963184.09987412412877.5586966815039
Winsorized Mean ( 34 / 36 )14164.5833333333167.76948952023584.4288396766262
Winsorized Mean ( 35 / 36 )14151.9444444444164.11417019037386.2323127127179
Winsorized Mean ( 36 / 36 )14150.2777777778163.11646591511486.7495362800567
Trimmed Mean ( 1 / 36 )14571.7452830189421.48210622642134.572630884574
Trimmed Mean ( 2 / 36 )14557.4423076923412.46646022628235.2936389051027
Trimmed Mean ( 3 / 36 )14542.9803921569404.46390598961735.9561883688336
Trimmed Mean ( 4 / 36 )14530.22396.73800188206536.6242203445872
Trimmed Mean ( 5 / 36 )14523.2346938776390.89998650958337.153326157819
Trimmed Mean ( 6 / 36 )14512.5104166667385.00724132936937.6941232755968
Trimmed Mean ( 7 / 36 )14502.2446808511378.56466411383338.3085006488886
Trimmed Mean ( 8 / 36 )14491.6847826087372.48440195695438.9054808912063
Trimmed Mean ( 9 / 36 )14482.6333333333366.88899573782339.4741556753655
Trimmed Mean ( 10 / 36 )14472361.07718357352340.0800733426935
Trimmed Mean ( 11 / 36 )14460.0116279070354.61733349229240.7763813615763
Trimmed Mean ( 12 / 36 )14448.3452380952347.83038319217441.5384794896213
Trimmed Mean ( 13 / 36 )14435.1097560976340.71652451431642.3669200567084
Trimmed Mean ( 14 / 36 )14417.6875333.6411115662143.2131622878222
Trimmed Mean ( 15 / 36 )14402.1025641026326.15043220190444.1578521508348
Trimmed Mean ( 16 / 36 )14387.9868421053318.74044959530645.1401347408940
Trimmed Mean ( 17 / 36 )14374.2297297297310.63889004776346.2731170830528
Trimmed Mean ( 18 / 36 )14354.7083333333302.89787879010947.3912474747977
Trimmed Mean ( 19 / 36 )14330.0714285714294.61905734859148.6393227835774
Trimmed Mean ( 20 / 36 )14301.9411764706286.17421868967949.9763439276802
Trimmed Mean ( 21 / 36 )14271.5454545455276.59549216361151.5971729796074
Trimmed Mean ( 22 / 36 )14241.21875266.63844202264053.4102233795335
Trimmed Mean ( 23 / 36 )14219.8709677419258.69122197261654.9685097905919
Trimmed Mean ( 24 / 36 )14202.6250.98881983788856.5865842517343
Trimmed Mean ( 25 / 36 )14192.8448275862244.60056924819758.0245780752238
Trimmed Mean ( 26 / 36 )14185.7857142857237.85233429872959.6411456549725
Trimmed Mean ( 27 / 36 )14177.1111111111230.95210775685861.3855021666939
Trimmed Mean ( 28 / 36 )14164224.68567117100063.0391779154458
Trimmed Mean ( 29 / 36 )14154.66219.65335883837464.4408994010208
Trimmed Mean ( 30 / 36 )14141.9791666667213.88624704539266.1191608250781
Trimmed Mean ( 31 / 36 )14127.1304347826207.29990552254968.1482724228543
Trimmed Mean ( 32 / 36 )14109.3636363636200.70575027474970.2987513663615
Trimmed Mean ( 33 / 36 )14093.9761904762195.05003226068972.2582612631372
Trimmed Mean ( 34 / 36 )14078.875188.63315091732974.6362711513536
Trimmed Mean ( 35 / 36 )14071.7105263158183.89927784647176.518574140697
Trimmed Mean ( 36 / 36 )14064.8333333333178.16027428507678.9448343059244
Median14076
Midrange15833.5
Midmean - Weighted Average at Xnp14121.9454545455
Midmean - Weighted Average at X(n+1)p14177.1111111111
Midmean - Empirical Distribution Function14121.9454545455
Midmean - Empirical Distribution Function - Averaging14177.1111111111
Midmean - Empirical Distribution Function - Interpolation14177.1111111111
Midmean - Closest Observation14121.9454545455
Midmean - True Basic - Statistics Graphics Toolkit14177.1111111111
Midmean - MS Excel (old versions)14185.7857142857
Number of observations108
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Mar/12/t12683975645le67jqh933klx7/18o4l1268397411.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/12/t12683975645le67jqh933klx7/18o4l1268397411.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Mar/12/t12683975645le67jqh933klx7/2zkju1268397411.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/12/t12683975645le67jqh933klx7/2zkju1268397411.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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