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Tijdsreeks 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: Fri, 06 Aug 2010 10:06:02 +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/06/t1281089166vjsye9swiwki47u.htm/, Retrieved Fri, 06 Aug 2010 12:06:06 +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/06/t1281089166vjsye9swiwki47u.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:
Gosselin Claudia
 
Dataseries X:
» Textbox « » Textfile « » CSV «
155 154 153 151 171 170 155 145 146 146 147 149 146 155 149 140 155 152 137 127 134 125 132 141 133 143 141 132 144 140 130 122 124 119 128 131 121 123 116 109 116 109 103 98 95 83 92 94 76 75 77 68 80 66 69 67 68 64 72 70 55 55 54 55 67 54 57 53 49 47 64 58 38 41 38 41 60 49 53 55 56 52 68 68 41 46 41 47 62 48 53 61 59 46 69 69 42 42 42 50 64 47 51 66 64 49 71 68 39 30 22 33 46 24 27 45 38 18 36 31
 
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 Mean85.05833333333333.9035159012386721.7901849218399
Geometric Mean74.403696749972
Harmonic Mean64.5469574728297
Quadratic Mean95.1218954815346
Winsorized Mean ( 1 / 40 )85.08333333333333.8973089784588721.8313030359164
Winsorized Mean ( 2 / 40 )84.86666666666673.8507872041315522.0387838038966
Winsorized Mean ( 3 / 40 )84.94166666666673.8410523154238122.1141655180228
Winsorized Mean ( 4 / 40 )85.04166666666673.8286732574393922.2117848529969
Winsorized Mean ( 5 / 40 )85.08333333333333.8236801485765122.2516868637687
Winsorized Mean ( 6 / 40 )85.13333333333333.8043343505279522.3779840280124
Winsorized Mean ( 7 / 40 )85.253.7758307376130722.5778129169772
Winsorized Mean ( 8 / 40 )85.31666666666673.7514513220186222.7423094006078
Winsorized Mean ( 9 / 40 )85.24166666666673.7403095303490322.7900033339519
Winsorized Mean ( 10 / 40 )85.0753.7159502236205722.8945477953977
Winsorized Mean ( 11 / 40 )85.16666666666673.7062732294269922.979057774387
Winsorized Mean ( 12 / 40 )85.16666666666673.656970883269823.2888555542769
Winsorized Mean ( 13 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 14 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 15 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 16 / 40 )85.05833333333333.6095169845578223.5650181720237
Winsorized Mean ( 17 / 40 )84.91666666666673.5898351540481623.6547537763422
Winsorized Mean ( 18 / 40 )84.76666666666673.5691789366714923.749626502536
Winsorized Mean ( 19 / 40 )84.9253.4791931052854124.4093953483025
Winsorized Mean ( 20 / 40 )85.09166666666673.463252382297924.5698716910165
Winsorized Mean ( 21 / 40 )84.91666666666673.4396066670880224.6879003576759
Winsorized Mean ( 22 / 40 )84.91666666666673.4396066670880224.6879003576759
Winsorized Mean ( 23 / 40 )84.53333333333333.3448596235159225.2726101684581
Winsorized Mean ( 24 / 40 )83.93333333333333.2666666666666725.6938775510204
Winsorized Mean ( 25 / 40 )83.7253.2399372875799625.8415495636144
Winsorized Mean ( 26 / 40 )83.7253.1918129359232826.2311738440841
Winsorized Mean ( 27 / 40 )83.953.1708107190821926.4758787065978
Winsorized Mean ( 28 / 40 )83.71666666666673.1411960320348326.6512073149526
Winsorized Mean ( 29 / 40 )83.4753.1107242552429626.8345867877255
Winsorized Mean ( 30 / 40 )83.2253.0250231496671927.512186149437
Winsorized Mean ( 31 / 40 )83.2252.9692509712943128.0289543742144
Winsorized Mean ( 32 / 40 )82.95833333333332.8792796872262328.8121830266693
Winsorized Mean ( 33 / 40 )82.95833333333332.8209002832482229.4084600671557
Winsorized Mean ( 34 / 40 )82.6752.7863503457569229.671430272901
Winsorized Mean ( 35 / 40 )82.38333333333332.7509657925505729.9470584317776
Winsorized Mean ( 36 / 40 )82.38333333333332.6879277611063630.6493851975487
Winsorized Mean ( 37 / 40 )81.76666666666672.6137894759977531.2828050680915
Winsorized Mean ( 38 / 40 )81.13333333333332.4724230659402732.8153116070684
Winsorized Mean ( 39 / 40 )81.13333333333332.4724230659402732.8153116070684
Winsorized Mean ( 40 / 40 )78.82.1993314492202935.8290697966131
Trimmed Mean ( 1 / 40 )84.89830508474583.8600084635052821.994331330468
Trimmed Mean ( 2 / 40 )84.70689655172413.8184240734895322.1837320636608
Trimmed Mean ( 3 / 40 )84.62280701754393.7985564706622422.2776224787283
Trimmed Mean ( 4 / 40 )84.50892857142863.7796446350843122.3589614184836
Trimmed Mean ( 5 / 40 )84.36363636363643.7616369848945222.4273731629109
Trimmed Mean ( 6 / 40 )84.20370370370373.7420449662539922.502055550657
Trimmed Mean ( 7 / 40 )84.02830188679243.7236153573148322.5663216587942
Trimmed Mean ( 8 / 40 )83.82692307692313.7076320149483122.6092888234195
Trimmed Mean ( 9 / 40 )83.6078431372553.6929878109203822.6396206589206
Trimmed Mean ( 10 / 40 )83.393.6773094852765722.6769055837921
Trimmed Mean ( 11 / 40 )83.18367346938783.6623865590580122.7129692969338
Trimmed Mean ( 12 / 40 )82.95833333333333.6457111508348622.7550483022595
Trimmed Mean ( 13 / 40 )82.72340425531923.632462632411822.7733668936312
Trimmed Mean ( 14 / 40 )82.48913043478263.6181674678519522.7985938096323
Trimmed Mean ( 15 / 40 )82.24444444444443.6005031938212322.8424861795937
Trimmed Mean ( 16 / 40 )81.98863636363643.5789897729273222.9083181471559
Trimmed Mean ( 17 / 40 )81.72093023255813.5570646517132722.9742605868007
Trimmed Mean ( 18 / 40 )81.4523809523813.5330748003700623.0542475194268
Trimmed Mean ( 19 / 40 )81.18292682926833.5067418205449923.150528605682
Trimmed Mean ( 20 / 40 )80.88753.4855939394541523.2062315361574
Trimmed Mean ( 21 / 40 )80.56410256410263.461052493606523.2773419972469
Trimmed Mean ( 22 / 40 )80.23684210526323.4338290438115523.3665803048251
Trimmed Mean ( 23 / 40 )79.89189189189193.4002726314223523.495731240372
Trimmed Mean ( 24 / 40 )79.55555555555563.3714306975977723.596971936051
Trimmed Mean ( 25 / 40 )79.24285714285713.3459864845168823.6829579287134
Trimmed Mean ( 26 / 40 )78.92647058823533.3173735986216123.7918546831836
Trimmed Mean ( 27 / 40 )78.59090909090913.2872556959560523.9077566091348
Trimmed Mean ( 28 / 40 )78.218753.251256529838524.0580062760798
Trimmed Mean ( 29 / 40 )77.83870967741943.2100939383059124.2481096109287
Trimmed Mean ( 30 / 40 )77.453.1627622376257524.4880880006146
Trimmed Mean ( 31 / 40 )77.0517241379313.1156788306559124.7303166744276
Trimmed Mean ( 32 / 40 )76.6253.0636709264303425.0108454334814
Trimmed Mean ( 33 / 40 )76.18518518518523.011284863600825.2998931140926
Trimmed Mean ( 34 / 40 )75.71153846153852.9524048201538225.6440234566457
Trimmed Mean ( 35 / 40 )75.222.8822171171173226.0979644986746
Trimmed Mean ( 36 / 40 )74.70833333333332.7976938218897726.7035415915777
Trimmed Mean ( 37 / 40 )74.15217391304352.6983565209778627.4804953817487
Trimmed Mean ( 38 / 40 )73.59090909090912.5847818948186828.4708389665007
Trimmed Mean ( 39 / 40 )73.02380952380952.4673214033362829.5963912221033
Trimmed Mean ( 40 / 40 )72.42.3060122089209131.3961911042437
Median68
Midrange94.5
Midmean - Weighted Average at Xnp76.0952380952381
Midmean - Weighted Average at X(n+1)p77.45
Midmean - Empirical Distribution Function76.0952380952381
Midmean - Empirical Distribution Function - Averaging77.45
Midmean - Empirical Distribution Function - Interpolation77.45
Midmean - Closest Observation76.0952380952381
Midmean - True Basic - Statistics Graphics Toolkit77.45
Midmean - MS Excel (old versions)76.9375
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Aug/06/t1281089166vjsye9swiwki47u/1m6ez1281089158.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/06/t1281089166vjsye9swiwki47u/1m6ez1281089158.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Aug/06/t1281089166vjsye9swiwki47u/2xgd31281089158.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/06/t1281089166vjsye9swiwki47u/2xgd31281089158.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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