Home » date » 2009 » Mar » 23 »

Centrummaten - Aantal Nieuwe Gebouwen - Morre Christophe

*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 23 Mar 2009 10:03:38 -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/Mar/23/t1237824256oaqynlwvdtiqkzw.htm/, Retrieved Mon, 23 Mar 2009 17:04:18 +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/Mar/23/t1237824256oaqynlwvdtiqkzw.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 «
2194 2419 2742 2137 2710 2173 2363 2126 1905 2121 1983 1734 2074 2049 2406 2558 2251 2059 2397 1747 1707 2319 1631 1627 1791 2034 1997 2169 2028 2253 2218 1855 2187 1852 1570 1851 1954 1828 2251 2277 2085 2282 2266 1878 2267 2069 1746 2299 2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2945 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2259 2844 2546 2456 2295 2379 2479 2057 2280 2351 2275 2543 2305 2188 2720 2398 2147 1898 2538 2081 2057 2497 2460 2195 2823 2100 2640 2342 2171 2482
 
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 Mean2287.5333333333332.967705550729669.3870954960257
Geometric Mean2263.14545703274
Harmonic Mean2238.91388342336
Quadratic Mean2312.10795389752
Winsorized Mean ( 1 / 35 )2284.0380952381031.725799590744371.9930821193373
Winsorized Mean ( 2 / 35 )2283.4476190476231.56585934779772.3391558546934
Winsorized Mean ( 3 / 35 )2284.5904761904830.940119098410573.8390976752201
Winsorized Mean ( 4 / 35 )2285.0476190476230.642393785044474.5714461826048
Winsorized Mean ( 5 / 35 )2281.5238095238129.756358311018576.673488928885
Winsorized Mean ( 6 / 35 )2281.4666666666729.725727521439776.7505745661282
Winsorized Mean ( 7 / 35 )2283.2666666666729.028397321206978.656311659294
Winsorized Mean ( 8 / 35 )2285.9333333333328.55364871081980.0574860496618
Winsorized Mean ( 9 / 35 )2285.8476190476227.885725670047181.9719610704955
Winsorized Mean ( 10 / 35 )2280.5142857142926.943442712105984.640790343011
Winsorized Mean ( 11 / 35 )2278.5238095238126.521002442525285.9139398845008
Winsorized Mean ( 12 / 35 )2280.0095238095225.940737953549987.8930093620376
Winsorized Mean ( 13 / 35 )2280.6285714285725.281656097017290.2088281984677
Winsorized Mean ( 14 / 35 )2279.2952380952424.792102325015891.9363436071083
Winsorized Mean ( 15 / 35 )2285.0095238095223.611432070134696.7755584253512
Winsorized Mean ( 16 / 35 )2285.0095238095222.3428352834896102.270347286589
Winsorized Mean ( 17 / 35 )2275.9428571428620.3914432449941111.612642116520
Winsorized Mean ( 18 / 35 )2279.219.4265282539109117.324102907639
Winsorized Mean ( 19 / 35 )2278.1142857142918.9948629757166119.933178176998
Winsorized Mean ( 20 / 35 )2280.418.5695041268334122.803494612695
Winsorized Mean ( 21 / 35 )2281.418.2977390064252124.682071331267
Winsorized Mean ( 22 / 35 )2280.9809523809518.2408790040693125.047754106153
Winsorized Mean ( 23 / 35 )2280.1047619047618.0671008345514126.202027806493
Winsorized Mean ( 24 / 35 )2272.3333333333316.9897225271831133.747524698986
Winsorized Mean ( 25 / 35 )2274.4761904761916.6744254572480136.405071125705
Winsorized Mean ( 26 / 35 )227216.0557122992378141.507269042673
Winsorized Mean ( 27 / 35 )2273.0285714285715.7464250093669144.352039912326
Winsorized Mean ( 28 / 35 )2269.0285714285714.9918198521853151.351109725203
Winsorized Mean ( 29 / 35 )2272.0666666666714.3731362331624158.077306845840
Winsorized Mean ( 30 / 35 )2276.3523809523813.4834451537699168.825723321604
Winsorized Mean ( 31 / 35 )2268.6761904761912.2091097859434185.818313558632
Winsorized Mean ( 32 / 35 )2268.0666666666711.3691332869833199.493365889501
Winsorized Mean ( 33 / 35 )2268.6952380952410.7311733414290211.411666358670
Winsorized Mean ( 34 / 35 )2269.3428571428610.5880386290105214.33080636153
Winsorized Mean ( 35 / 35 )2265.009523809529.7205881659852233.011571433030
Trimmed Mean ( 1 / 35 )2283.3106796116530.888465214230673.9211438242555
Trimmed Mean ( 2 / 35 )2282.5544554455429.944025256532776.2273754410348
Trimmed Mean ( 3 / 35 )2282.0808080808128.972188189191778.7679823553043
Trimmed Mean ( 4 / 35 )2281.1752577319628.139395935036781.0669590419898
Trimmed Mean ( 5 / 35 )2280.1052631578927.294989567178683.5356708067643
Trimmed Mean ( 6 / 35 )2279.7849462365626.590899475021385.7355332555832
Trimmed Mean ( 7 / 35 )2279.4615384615425.795728544820688.3658522960857
Trimmed Mean ( 8 / 35 )2278.820224719125.047307445412290.9806465100303
Trimmed Mean ( 9 / 35 )2277.7471264367824.289069412266093.7766321045845
Trimmed Mean ( 10 / 35 )2276.6352941176523.550855914428996.6688982510746
Trimmed Mean ( 11 / 35 )2276.1445783132522.881115358778999.4769941335032
Trimmed Mean ( 12 / 35 )2275.8641975308622.1835549219977102.592402594323
Trimmed Mean ( 13 / 35 )2275.4050632911421.4762197918758105.949980273153
Trimmed Mean ( 14 / 35 )2274.8571428571420.7661252950461109.546538438725
Trimmed Mean ( 15 / 35 )2274.4133333333320.0190728276031113.612321255822
Trimmed Mean ( 16 / 35 )2273.3972602739719.3393426706753117.552974730686
Trimmed Mean ( 17 / 35 )2272.3239436619718.7485079180739121.200255166514
Trimmed Mean ( 18 / 35 )227218.3654643646689123.710457567892
Trimmed Mean ( 19 / 35 )2271.3731343283618.0531883624516125.815622632761
Trimmed Mean ( 20 / 35 )2270.817.7416041898913127.992935458105
Trimmed Mean ( 21 / 35 )227017.4258137880305130.266513094454
Trimmed Mean ( 22 / 35 )2269.0655737704917.0804088210191132.846092710509
Trimmed Mean ( 23 / 35 )2268.1016949152516.6654553509498136.095993007835
Trimmed Mean ( 24 / 35 )2267.1403508771916.1839643127076140.085599984735
Trimmed Mean ( 25 / 35 )2266.7272727272715.7785912696556143.658406126946
Trimmed Mean ( 26 / 35 )2266.1132075471715.3252275102823147.868160914854
Trimmed Mean ( 27 / 35 )2266.1132075471714.8687809152405152.407465041361
Trimmed Mean ( 28 / 35 )2265.0612244898014.3469641768289157.877387618210
Trimmed Mean ( 29 / 35 )2264.7446808510613.8329022322698163.721585161485
Trimmed Mean ( 30 / 35 )2264.1555555555613.2946771286522170.305418751083
Trimmed Mean ( 31 / 35 )2263.1627906976712.7781968510717177.111279241865
Trimmed Mean ( 32 / 35 )2262.7073170731712.3905079672264182.616186766366
Trimmed Mean ( 33 / 35 )2262.2564102564112.0569229052975187.631324179938
Trimmed Mean ( 34 / 35 )2261.7027027027011.7441356437720192.581452676093
Trimmed Mean ( 35 / 35 )2261.0285714285711.3358571207768199.458104256138
Median2266
Midrange2505
Midmean - Weighted Average at Xnp2261.96153846154
Midmean - Weighted Average at X(n+1)p2266.11320754717
Midmean - Empirical Distribution Function2266.11320754717
Midmean - Empirical Distribution Function - Averaging2266.11320754717
Midmean - Empirical Distribution Function - Interpolation2266.11320754717
Midmean - Closest Observation2262.46296296296
Midmean - True Basic - Statistics Graphics Toolkit2266.11320754717
Midmean - MS Excel (old versions)2266.11320754717
Number of observations105
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/23/t1237824256oaqynlwvdtiqkzw/1kf981237824216.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/23/t1237824256oaqynlwvdtiqkzw/1kf981237824216.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/23/t1237824256oaqynlwvdtiqkzw/2sh2m1237824216.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/23/t1237824256oaqynlwvdtiqkzw/2sh2m1237824216.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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