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tijdreeks 1 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: Sun, 15 Aug 2010 13:10:19 +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/15/t1281877859zzu6k1hc7abbms9.htm/, Retrieved Sun, 15 Aug 2010 15:11:02 +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/15/t1281877859zzu6k1hc7abbms9.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:
Magali De Reu
 
Dataseries X:
» Textbox « » Textfile « » CSV «
333 332 331 329 349 348 333 323 324 324 325 327 329 333 329 333 355 358 338 326 320 322 322 324 326 330 331 333 364 363 341 327 313 321 312 312 312 314 312 319 356 351 329 313 298 303 278 275 276 276 273 287 320 313 281 266 258 259 237 231 237 236 229 243 271 262 227 208 212 222 200 193 204 203 190 209 240 234 210 195 202 204 180 169 178 181 163 174 194 187 160 143 151 154 141 127 134 138 120 129 151 152 124 99 104 109 96 87 94 89 63 76 100 104 80 55 60 71 62 61
 
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 Mean237.2333333333338.3930304330799928.2655156829064
Geometric Mean214.169787983089
Harmonic Mean185.668751880872
Quadratic Mean254.287960129194
Winsorized Mean ( 1 / 40 )237.2666666666678.3844738909270728.2983368728019
Winsorized Mean ( 2 / 40 )237.28.3712158556544728.3351909794298
Winsorized Mean ( 3 / 40 )237.1758.3607866765957328.367545922912
Winsorized Mean ( 4 / 40 )237.1758.3509645067667128.4009110334285
Winsorized Mean ( 5 / 40 )237.3416666666678.2740905026549728.6849251395678
Winsorized Mean ( 6 / 40 )237.4916666666678.2208656764147728.8888878634786
Winsorized Mean ( 7 / 40 )237.6666666666678.176067875270329.068577987901
Winsorized Mean ( 8 / 40 )237.6666666666678.0499085136104329.5241450588948
Winsorized Mean ( 9 / 40 )237.5916666666678.0024111897981729.6900098022405
Winsorized Mean ( 10 / 40 )237.5916666666677.894928839275130.0942125639833
Winsorized Mean ( 11 / 40 )237.7757.8670363450502630.2242152662231
Winsorized Mean ( 12 / 40 )238.0757.8219074172645230.4369493653838
Winsorized Mean ( 13 / 40 )238.1833333333337.8057561836446130.5138064435575
Winsorized Mean ( 14 / 40 )238.657.736917665193530.8456171213542
Winsorized Mean ( 15 / 40 )238.5257.7241568983233330.8803929205239
Winsorized Mean ( 16 / 40 )239.0583333333337.6139733682780831.3973167189311
Winsorized Mean ( 17 / 40 )240.6166666666677.3952648122514232.5365856092195
Winsorized Mean ( 18 / 40 )241.0666666666677.2983223325785533.0304220177538
Winsorized Mean ( 19 / 40 )241.3833333333337.2185004236346133.4395399552797
Winsorized Mean ( 20 / 40 )241.7166666666677.1743023293022433.6920101177525
Winsorized Mean ( 21 / 40 )242.5916666666677.0599820648050434.3615131653122
Winsorized Mean ( 22 / 40 )243.3256.965995462754434.9303988641686
Winsorized Mean ( 23 / 40 )243.5166666666676.8538972876662435.5296638461275
Winsorized Mean ( 24 / 40 )243.9166666666676.8038296940817935.8499077187123
Winsorized Mean ( 25 / 40 )245.3756.5780177011582137.3022711624501
Winsorized Mean ( 26 / 40 )245.3756.5780177011582137.3022711624501
Winsorized Mean ( 27 / 40 )245.3756.5278123198720637.5891627970103
Winsorized Mean ( 28 / 40 )245.6083333333336.4480285549588638.0904537316988
Winsorized Mean ( 29 / 40 )247.0583333333336.2769452310212239.3596445787593
Winsorized Mean ( 30 / 40 )247.8083333333336.1900604323325540.0332655944610
Winsorized Mean ( 31 / 40 )249.15.9869068158180441.6074623613402
Winsorized Mean ( 32 / 40 )250.1666666666675.8108168878246543.0518929603234
Winsorized Mean ( 33 / 40 )251.2666666666675.6907184412179144.1537688539888
Winsorized Mean ( 34 / 40 )251.555.6000806566820644.9189958897911
Winsorized Mean ( 35 / 40 )251.555.5384680961020845.4186962234266
Winsorized Mean ( 36 / 40 )253.355.3482588333979947.3705570152885
Winsorized Mean ( 37 / 40 )253.9666666666675.2201255301847948.6514481688482
Winsorized Mean ( 38 / 40 )253.3333333333334.9583183273082251.0925916026983
Winsorized Mean ( 39 / 40 )253.3333333333334.8917745706488451.787614019125
Winsorized Mean ( 40 / 40 )253.6666666666674.8578726040481552.2176449121539
Trimmed Mean ( 1 / 40 )237.7033898305088.3240740329925728.5561359603925
Trimmed Mean ( 2 / 40 )238.1551724137938.2562011899055228.8456115513482
Trimmed Mean ( 3 / 40 )238.6578947368428.187484711867229.1491102744807
Trimmed Mean ( 4 / 40 )239.18758.1142454936256229.4774788596057
Trimmed Mean ( 5 / 40 )239.7363636363648.0347834029548229.8373150355490
Trimmed Mean ( 6 / 40 )240.2685185185197.9652086858007730.164748721127
Trimmed Mean ( 7 / 40 )240.7924528301897.898328743588930.4865067848234
Trimmed Mean ( 8 / 40 )241.3076923076927.8312709379726630.8133499937574
Trimmed Mean ( 9 / 40 )241.8431372549027.7775786080049531.0949139113797
Trimmed Mean ( 10 / 40 )242.417.723349027592931.3866431691681
Trimmed Mean ( 11 / 40 )2437.67714563602731.6523889894259
Trimmed Mean ( 12 / 40 )243.593757.6270464341128831.9381495975293
Trimmed Mean ( 13 / 40 )244.1808510638307.5747923714509832.2359794288402
Trimmed Mean ( 14 / 40 )244.7826086956527.5155806642100332.5700194878264
Trimmed Mean ( 15 / 40 )245.3666666666677.4556608628191632.9101163775156
Trimmed Mean ( 16 / 40 )245.9886363636367.3866123059178333.3019557783696
Trimmed Mean ( 17 / 40 )246.5930232558147.3201440094633633.6869087461972
Trimmed Mean ( 18 / 40 )247.0952380952387.2704026536966133.9864585037259
Trimmed Mean ( 19 / 40 )247.5853658536597.2225964301535834.2792745306959
Trimmed Mean ( 20 / 40 )248.0757.174338389643634.5781013560922
Trimmed Mean ( 21 / 40 )248.5641025641037.1209425002900834.9060679192364
Trimmed Mean ( 22 / 40 )249.0131578947377.0703356931905635.2194250316235
Trimmed Mean ( 23 / 40 )249.4324324324327.0199135241902335.5321232338407
Trimmed Mean ( 24 / 40 )249.8611111111116.9710250298619835.8428079142987
Trimmed Mean ( 25 / 40 )250.2857142857146.9161838846843336.1884123468672
Trimmed Mean ( 26 / 40 )250.6323529411766.8765262305192136.4475237262714
Trimmed Mean ( 27 / 40 )2516.8248483337400836.7773740493438
Trimmed Mean ( 28 / 40 )251.3906256.7651805042958337.1594852259107
Trimmed Mean ( 29 / 40 )251.7903225806456.6998874114147737.5812766870774
Trimmed Mean ( 30 / 40 )252.1166666666676.6409571355402437.9639051300934
Trimmed Mean ( 31 / 40 )252.4137931034486.5770152157855238.3781677283685
Trimmed Mean ( 32 / 40 )252.6428571428576.5233062971458138.7292648290021
Trimmed Mean ( 33 / 40 )252.8148148148156.4770774695477239.0322357580923
Trimmed Mean ( 34 / 40 )252.9230769230776.431085315577339.328210482677
Trimmed Mean ( 35 / 40 )253.026.3801663339586739.6572732991759
Trimmed Mean ( 36 / 40 )253.1256.318147971860640.063164257525
Trimmed Mean ( 37 / 40 )253.1086956521746.2636307987818740.4092616220926
Trimmed Mean ( 38 / 40 )253.0454545454556.2067918321145240.7691221793800
Trimmed Mean ( 39 / 40 )253.0238095238106.170580240585441.0048649654712
Trimmed Mean ( 40 / 40 )2536.122991559770941.3196715249868
Median250.5
Midrange209.5
Midmean - Weighted Average at Xnp252.936507936508
Midmean - Weighted Average at X(n+1)p254.435483870968
Midmean - Empirical Distribution Function252.936507936508
Midmean - Empirical Distribution Function - Averaging254.435483870968
Midmean - Empirical Distribution Function - Interpolation254.435483870968
Midmean - Closest Observation252.936507936508
Midmean - True Basic - Statistics Graphics Toolkit254.435483870968
Midmean - MS Excel (old versions)252.936507936508
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Aug/15/t1281877859zzu6k1hc7abbms9/1wh4s1281877817.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/15/t1281877859zzu6k1hc7abbms9/1wh4s1281877817.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Aug/15/t1281877859zzu6k1hc7abbms9/2793d1281877817.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/15/t1281877859zzu6k1hc7abbms9/2793d1281877817.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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