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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: Sat, 24 Jul 2010 13:49:30 +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/Jul/24/t12799794017zzpaki9ccwy4tz.htm/, Retrieved Sat, 24 Jul 2010 15:50:03 +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/Jul/24/t12799794017zzpaki9ccwy4tz.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:
Habimana Christelle
 
Dataseries X:
» Textbox « » Textfile « » CSV «
900 899 898 896 916 915 900 890 891 891 892 894 896 889 878 883 901 897 881 866 867 866 862 871 865 856 847 859 870 872 856 839 829 825 822 827 822 812 810 816 820 823 810 793 777 772 765 765 753 742 736 740 742 742 728 707 699 696 689 692 673 653 642 648 654 653 630 609 598 601 592 591 568 538 523 530 529 534 513 491 480 478 462 461 437 411 400 405 395 407 385 366 349 343 332 327 306 276 269 268 260 274 247 226 212 199 188 179 155 124 117 116 105 112 86 64 53 42 32 24
 
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 Mean599.15833333333324.948644720024624.0156665845832
Geometric Mean491.768184236028
Harmonic Mean306.561078944024
Quadratic Mean658.073292523966
Winsorized Mean ( 1 / 40 )599.21666666666724.934927028187324.0312179774695
Winsorized Mean ( 2 / 40 )599.1524.879003133541524.0825565551795
Winsorized Mean ( 3 / 40 )599.424.825148765002024.1448704164473
Winsorized Mean ( 4 / 40 )599.76666666666724.757899832342624.2252642884983
Winsorized Mean ( 5 / 40 )600.64166666666724.589685489441624.426569706415
Winsorized Mean ( 6 / 40 )601.54166666666724.419873822599324.6332831625842
Winsorized Mean ( 7 / 40 )601.89166666666724.344515472485824.723912346784
Winsorized Mean ( 8 / 40 )602.09166666666724.292763835483524.7848153772942
Winsorized Mean ( 9 / 40 )602.16666666666724.280161390763724.8007687006452
Winsorized Mean ( 10 / 40 )602.58333333333324.165725616759424.9354537450939
Winsorized Mean ( 11 / 40 )605.24166666666723.683572873751425.5553361772310
Winsorized Mean ( 12 / 40 )607.54166666666723.296117467343926.0790952620456
Winsorized Mean ( 13 / 40 )608.51666666666723.146328405907826.289986731172
Winsorized Mean ( 14 / 40 )609.68333333333322.939852492978826.5774740059876
Winsorized Mean ( 15 / 40 )611.18333333333322.684608311548326.9426443225027
Winsorized Mean ( 16 / 40 )612.2522.328974186811527.4195310038749
Winsorized Mean ( 17 / 40 )614.94166666666721.87350409717828.1135415676724
Winsorized Mean ( 18 / 40 )616.44166666666721.554230335477328.5995675592291
Winsorized Mean ( 19 / 40 )616.75833333333321.282687812794728.9793440921757
Winsorized Mean ( 20 / 40 )616.75833333333321.242968834572829.0335281351806
Winsorized Mean ( 21 / 40 )617.45833333333321.105354292420429.2560041768681
Winsorized Mean ( 22 / 40 )617.27521.000113253329429.3938890973427
Winsorized Mean ( 23 / 40 )622.83333333333320.209194226370830.8193056267728
Winsorized Mean ( 24 / 40 )627.03333333333319.663157594173331.8887406730208
Winsorized Mean ( 25 / 40 )627.86666666666719.508717197328532.1839032426307
Winsorized Mean ( 26 / 40 )629.619.140525590692532.893558592046
Winsorized Mean ( 27 / 40 )630.27518.902428824788433.3435986370951
Winsorized Mean ( 28 / 40 )633.54166666666718.339953843438634.5443435722345
Winsorized Mean ( 29 / 40 )638.13333333333317.783797008543635.8828507223045
Winsorized Mean ( 30 / 40 )638.38333333333317.255974418383936.9949165347176
Winsorized Mean ( 31 / 40 )637.60833333333316.894591214397237.740382424286
Winsorized Mean ( 32 / 40 )636.27516.472457967729038.6265972720354
Winsorized Mean ( 33 / 40 )636.27516.353624404469638.9072773266150
Winsorized Mean ( 34 / 40 )636.84166666666716.164850149902939.3966947272007
Winsorized Mean ( 35 / 40 )643.84166666666715.229210450875342.2767594382847
Winsorized Mean ( 36 / 40 )650.74166666666714.389249098285645.2241574401684
Winsorized Mean ( 37 / 40 )651.0514.355104548927745.3532050415218
Winsorized Mean ( 38 / 40 )655.48333333333313.736001192420247.7200987500671
Winsorized Mean ( 39 / 40 )654.83333333333313.534970440920948.3808469469241
Winsorized Mean ( 40 / 40 )657.16666666666713.005683595604750.5291907061891
Trimmed Mean ( 1 / 40 )601.34745762711924.749372068934524.2974834251222
Trimmed Mean ( 2 / 40 )603.55172413793124.540012135822724.5945976227488
Trimmed Mean ( 3 / 40 )605.86842105263224.335738120015424.8962418178853
Trimmed Mean ( 4 / 40 )608.17857142857124.126150569337725.2082722306108
Trimmed Mean ( 5 / 40 )610.47272727272723.909824018290925.5322969673771
Trimmed Mean ( 6 / 40 )612.65740740740723.70860573324925.8411403142199
Trimmed Mean ( 7 / 40 )614.75471698113223.518075521779326.1396693114549
Trimmed Mean ( 8 / 40 )616.87523.315363553915126.4578760941695
Trimmed Mean ( 9 / 40 )619.04901960784323.092835430789926.8069731611416
Trimmed Mean ( 10 / 40 )621.322.840198039085527.2020408464407
Trimmed Mean ( 11 / 40 )623.59183673469422.569973652027327.6292673774868
Trimmed Mean ( 12 / 40 )625.67708333333322.337014432777328.0107749053166
Trimmed Mean ( 13 / 40 )627.60638297872322.126915062576628.3639351081614
Trimmed Mean ( 14 / 40 )629.52173913043521.904973714885028.738758024743
Trimmed Mean ( 15 / 40 )631.41111111111121.67631530736929.1290794656626
Trimmed Mean ( 16 / 40 )633.2521.445431771991629.5284332221767
Trimmed Mean ( 17 / 40 )635.08139534883721.222966002458929.9242525891648
Trimmed Mean ( 18 / 40 )636.7738095238121.022365703679830.2903021714795
Trimmed Mean ( 19 / 40 )638.42682926829320.82617604598930.6550193304090
Trimmed Mean ( 20 / 40 )640.137520.626368337808831.0349107276731
Trimmed Mean ( 21 / 40 )641.93589743589720.392145717756731.4795660211924
Trimmed Mean ( 22 / 40 )643.77631578947420.130648699984331.9799091119193
Trimmed Mean ( 23 / 40 )645.7297297297319.831363247896232.5610358530561
Trimmed Mean ( 24 / 40 )647.38888888888919.582801966175933.0590530408816
Trimmed Mean ( 25 / 40 )648.84285714285719.357127883074333.5195831252528
Trimmed Mean ( 26 / 40 )650.32352941176519.102622920635034.0436772538328
Trimmed Mean ( 27 / 40 )651.77272727272718.842604052641934.5903743161945
Trimmed Mean ( 28 / 40 )653.26562518.556411234677535.2043084591271
Trimmed Mean ( 29 / 40 )654.62903225806518.286185396259135.7991028786126
Trimmed Mean ( 30 / 40 )655.76666666666718.034138478428536.3625169813941
Trimmed Mean ( 31 / 40 )656.96551724137917.793106965488836.9224733215857
Trimmed Mean ( 32 / 40 )658.30357142857117.538397941815937.5349888634362
Trimmed Mean ( 33 / 40 )659.83333333333317.273719248027638.1986834369024
Trimmed Mean ( 34 / 40 )661.4807692307716.950342041170839.0246266195747
Trimmed Mean ( 35 / 40 )663.2216.565597249869940.0359848181875
Trimmed Mean ( 36 / 40 )664.60416666666716.247333103126440.9054312143559
Trimmed Mean ( 37 / 40 )665.60869565217415.989956940447441.6266721749877
Trimmed Mean ( 38 / 40 )666.68181818181815.648246689243942.6042502665856
Trimmed Mean ( 39 / 40 )667.5238095238115.319904161751443.5723228080232
Trimmed Mean ( 40 / 40 )668.514.912221798724744.8290006025240
Median681
Midrange470
Midmean - Weighted Average at Xnp651.327868852459
Midmean - Weighted Average at X(n+1)p655.766666666667
Midmean - Empirical Distribution Function651.327868852459
Midmean - Empirical Distribution Function - Averaging655.766666666667
Midmean - Empirical Distribution Function - Interpolation655.766666666667
Midmean - Closest Observation651.327868852459
Midmean - True Basic - Statistics Graphics Toolkit655.766666666667
Midmean - MS Excel (old versions)657.825396825397
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jul/24/t12799794017zzpaki9ccwy4tz/1an4f1279979368.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/24/t12799794017zzpaki9ccwy4tz/1an4f1279979368.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jul/24/t12799794017zzpaki9ccwy4tz/23w301279979368.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/24/t12799794017zzpaki9ccwy4tz/23w301279979368.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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