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TIJDREEKS A - STAP 14

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 03 Aug 2010 12:15:37 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/03/t1280837832zjhzccssoh9wze1.htm/, Retrieved Tue, 03 Aug 2010 14:17:14 +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/2010/Aug/03/t1280837832zjhzccssoh9wze1.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:
Lisa Bruggeman
 
Dataseries X:
» Textbox « » Textfile « » CSV «
95 94 93 91 111 110 95 85 86 86 87 89 93 96 99 92 109 110 97 88 93 93 89 89 91 97 99 85 101 105 88 80 87 84 87 87 85 96 102 93 111 117 101 88 98 89 93 93 95 105 109 94 113 125 106 95 109 100 94 94 94 103 103 80 106 117 99 95 116 118 100 100 105 121 131 108 136 149 131 137 164 169 154 160 166 186 197 166 191 207 187 191 222 230 210 224 234 251 258 227 254 281 261 264 286 293 276 292 299 319 329 293 318 346 327 329 353 355 332 346
 
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'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean151.357.4741538778965620.2497837845686
Geometric Mean134.353962885916
Harmonic Mean122.454194052220
Quadratic Mean171.914271271081
Winsorized Mean ( 1 / 40 )151.3333333333337.4703553563620320.2578493410561
Winsorized Mean ( 2 / 40 )151.2833333333337.4390820430563920.3362904801595
Winsorized Mean ( 3 / 40 )151.3083333333337.4371954503786920.3448106672562
Winsorized Mean ( 4 / 40 )150.8416666666677.3374351512300320.5578193957026
Winsorized Mean ( 5 / 40 )150.7166666666677.3116612218151720.613190640861
Winsorized Mean ( 6 / 40 )150.7666666666677.3079111169077420.6306103419690
Winsorized Mean ( 7 / 40 )150.657.2840877379167720.6820682864379
Winsorized Mean ( 8 / 40 )150.1833333333337.1721233542117720.9398703725779
Winsorized Mean ( 9 / 40 )150.1083333333337.1573139007295320.9727190137676
Winsorized Mean ( 10 / 40 )148.5256.8550106650892521.6666329574655
Winsorized Mean ( 11 / 40 )147.9756.754658756441121.9071022438986
Winsorized Mean ( 12 / 40 )148.0756.7471247377598421.9463854241953
Winsorized Mean ( 13 / 40 )147.9666666666676.7276024645214421.9939670108305
Winsorized Mean ( 14 / 40 )147.2666666666676.6028252731161722.3035837804572
Winsorized Mean ( 15 / 40 )146.7666666666676.4838814728716622.6356183839469
Winsorized Mean ( 16 / 40 )146.16.3687503006622.9401363066251
Winsorized Mean ( 17 / 40 )144.46.0824908284247423.7402741858958
Winsorized Mean ( 18 / 40 )143.956.0084773212427123.9578169815289
Winsorized Mean ( 19 / 40 )143.7916666666675.9069452526287824.3428135046071
Winsorized Mean ( 20 / 40 )143.1255.7992267728090324.6800143548574
Winsorized Mean ( 21 / 40 )142.7755.702025077636425.0393497145374
Winsorized Mean ( 22 / 40 )139.8416666666675.2021326675107826.8816032970533
Winsorized Mean ( 23 / 40 )139.0755.0862334451205927.343416597093
Winsorized Mean ( 24 / 40 )138.4754.9964968470216127.7144175688901
Winsorized Mean ( 25 / 40 )137.854.9038321777984228.110668351193
Winsorized Mean ( 26 / 40 )137.4166666666674.8400260337594928.3917205626946
Winsorized Mean ( 27 / 40 )134.7166666666674.4495645985549430.2763705712730
Winsorized Mean ( 28 / 40 )134.0166666666674.3504560972348930.8051991955157
Winsorized Mean ( 29 / 40 )131.8416666666673.9951124873000933.000739550081
Winsorized Mean ( 30 / 40 )130.3416666666673.7914376450672734.3779006457468
Winsorized Mean ( 31 / 40 )130.3416666666673.7914376450672734.3779006457468
Winsorized Mean ( 32 / 40 )129.2753.6488162867041835.4292981181491
Winsorized Mean ( 33 / 40 )1293.6123039041307635.7112810615091
Winsorized Mean ( 34 / 40 )124.4666666666672.9640453594072641.9921598944616
Winsorized Mean ( 35 / 40 )123.5916666666672.8541702702956243.3021351083814
Winsorized Mean ( 36 / 40 )123.5916666666672.8541702702956243.3021351083814
Winsorized Mean ( 37 / 40 )122.9752.7773963206803744.277080330356
Winsorized Mean ( 38 / 40 )121.7083333333332.6210042506603246.4357634302466
Winsorized Mean ( 39 / 40 )120.0833333333332.3553557580470650.9830979558265
Winsorized Mean ( 40 / 40 )118.4166666666672.1550729459643954.9478693463322
Trimmed Mean ( 1 / 40 )150.2288135593227.3754608674269420.3687357657600
Trimmed Mean ( 2 / 40 )149.0862068965527.2687287840281820.5106300326054
Trimmed Mean ( 3 / 40 )147.9298245614047.1667403508404620.6411586466999
Trimmed Mean ( 4 / 40 )146.7232142857147.0522298770650220.8052228647398
Trimmed Mean ( 5 / 40 )145.66.9552147709776320.9339329976628
Trimmed Mean ( 6 / 40 )144.4629629629636.8520995249596721.0830216982018
Trimmed Mean ( 7 / 40 )143.2735849056606.7355853610603721.2711408475276
Trimmed Mean ( 8 / 40 )142.0576923076926.608078131164921.4975806108772
Trimmed Mean ( 9 / 40 )140.8627450980396.4851433221697521.7208376284443
Trimmed Mean ( 10 / 40 )139.636.3472041884676321.9986620650548
Trimmed Mean ( 11 / 40 )138.5408163265316.2435014541205222.1896026363697
Trimmed Mean ( 12 / 40 )137.468756.1409959962255222.3854159951404
Trimmed Mean ( 13 / 40 )136.3404255319156.0234338609590722.6350000147933
Trimmed Mean ( 14 / 40 )135.1739130434785.8904152692210922.9481126313447
Trimmed Mean ( 15 / 40 )134.0222222222225.7560688871097623.2836376441487
Trimmed Mean ( 16 / 40 )132.8636363636365.6180496783721823.6494235490871
Trimmed Mean ( 17 / 40 )131.7093023255815.4749239643682924.056827671538
Trimmed Mean ( 18 / 40 )130.6428571428575.3518658270275924.4107123319674
Trimmed Mean ( 19 / 40 )129.5609756097565.2183892282005524.8277715486609
Trimmed Mean ( 20 / 40 )128.43755.0751892073602925.3069382740911
Trimmed Mean ( 21 / 40 )127.3076923076924.9223172074486625.8633661632056
Trimmed Mean ( 22 / 40 )126.1447368421054.7548942079610126.5294518290026
Trimmed Mean ( 23 / 40 )125.1351351351354.6352449625012626.9964448799293
Trimmed Mean ( 24 / 40 )124.1254.5096374585796527.5243855276770
Trimmed Mean ( 25 / 40 )123.14.3723273409949128.1543421613966
Trimmed Mean ( 26 / 40 )122.0588235294124.2210581641332728.9166409898251
Trimmed Mean ( 27 / 40 )120.9848484848484.0471286793765729.8939959832177
Trimmed Mean ( 28 / 40 )120.031253.9055674006769130.7333705159451
Trimmed Mean ( 29 / 40 )119.0645161290323.7487788223332431.7608804818543
Trimmed Mean ( 30 / 40 )118.1833333333333.6204450569710532.6433163529923
Trimmed Mean ( 31 / 40 )117.3448275862073.4989024053881133.5376109392199
Trimmed Mean ( 32 / 40 )116.4464285714293.3447885071704434.8142874569782
Trimmed Mean ( 33 / 40 )115.5555555555563.1795409338035136.3434715769873
Trimmed Mean ( 34 / 40 )114.6153846153852.9742679551268238.5356619997264
Trimmed Mean ( 35 / 40 )113.922.8638264683490039.7789465454850
Trimmed Mean ( 36 / 40 )113.2291666666672.7451181011898041.247466408673
Trimmed Mean ( 37 / 40 )112.4782608695652.587360419896943.4722043379048
Trimmed Mean ( 38 / 40 )111.7045454545452.3970514713485946.6008122018757
Trimmed Mean ( 39 / 40 )110.9523809523812.1869511605370150.7338174507455
Trimmed Mean ( 40 / 40 )110.251.9838288542807655.5743504597684
Median107
Midrange217.5
Midmean - Weighted Average at Xnp117.786885245902
Midmean - Weighted Average at X(n+1)p117.786885245902
Midmean - Empirical Distribution Function117.786885245902
Midmean - Empirical Distribution Function - Averaging117.786885245902
Midmean - Empirical Distribution Function - Interpolation117.786885245902
Midmean - Closest Observation117.786885245902
Midmean - True Basic - Statistics Graphics Toolkit117.786885245902
Midmean - MS Excel (old versions)119.064516129032
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Aug/03/t1280837832zjhzccssoh9wze1/146kx1280837735.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/03/t1280837832zjhzccssoh9wze1/146kx1280837735.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Aug/03/t1280837832zjhzccssoh9wze1/246kx1280837735.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/03/t1280837832zjhzccssoh9wze1/246kx1280837735.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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