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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: Wed, 04 Aug 2010 14:40:37 +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/04/t1280932817o9f0zmdksfl0c2w.htm/, Retrieved Wed, 04 Aug 2010 16:40:20 +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/04/t1280932817o9f0zmdksfl0c2w.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:
Keirsebelik gilian
 
Dataseries X:
» Textbox « » Textfile « » CSV «
668 667 666 664 684 683 668 658 659 659 660 662 659 655 655 655 674 674 665 644 638 648 641 637 651 649 652 650 661 666 652 624 613 623 615 613 621 612 611 609 631 632 624 596 584 587 581 574 593 582 571 572 594 588 571 546 535 537 527 515 545 538 520 523 541 529 504 473 455 458 450 442 469 455 439 443 461 451 425 393 366 359 351 343 366 355 344 351 367 364 353 313 278 274 261 255 274 262 265 274 291 289 277 238 203 198 190 187 201 181 181 196 207 202 186 154 120 107 99 100
 
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 Mean476.67516.098924588281029.6091206208263
Geometric Mean433.045752022036
Harmonic Mean376.569979032633
Quadratic Mean507.996973416181
Winsorized Mean ( 1 / 40 )476.67516.096384071650229.6137938730939
Winsorized Mean ( 2 / 40 )476.64166666666716.057803481102929.6828683466942
Winsorized Mean ( 3 / 40 )476.96666666666715.995893789154529.8180691215928
Winsorized Mean ( 4 / 40 )477.915.771288134193930.3019002591082
Winsorized Mean ( 5 / 40 )479.02515.583773174187930.7387045900688
Winsorized Mean ( 6 / 40 )478.97515.578690027829530.7455247613483
Winsorized Mean ( 7 / 40 )479.20833333333315.526199488763930.8644967289084
Winsorized Mean ( 8 / 40 )479.27515.515633042112030.8898127906974
Winsorized Mean ( 9 / 40 )479.42515.472568400209430.9854826683791
Winsorized Mean ( 10 / 40 )479.84166666666715.386122725549731.1866527536438
Winsorized Mean ( 11 / 40 )479.84166666666715.339391063009631.2816633134666
Winsorized Mean ( 12 / 40 )480.04166666666715.283251831049531.409654959124
Winsorized Mean ( 13 / 40 )480.04166666666715.255886478522531.4659962462672
Winsorized Mean ( 14 / 40 )480.04166666666715.226489871739731.5267452124748
Winsorized Mean ( 15 / 40 )480.54166666666715.150333939027631.7182227534127
Winsorized Mean ( 16 / 40 )484.67514.541783526694933.3298181141443
Winsorized Mean ( 17 / 40 )486.94166666666714.190349108453834.31498851403
Winsorized Mean ( 18 / 40 )487.39166666666714.022087897180834.7588511953814
Winsorized Mean ( 19 / 40 )487.5514.000629487648834.8234342198765
Winsorized Mean ( 20 / 40 )488.0513.933152984907635.0279653520388
Winsorized Mean ( 21 / 40 )489.113.670350668324435.778160477865
Winsorized Mean ( 22 / 40 )489.113.670350668324435.778160477865
Winsorized Mean ( 23 / 40 )488.90833333333313.651191941850435.8143329473297
Winsorized Mean ( 24 / 40 )489.30833333333313.552066809996036.1058088182106
Winsorized Mean ( 25 / 40 )489.30833333333313.503925126206536.2345265365662
Winsorized Mean ( 26 / 40 )491.47513.171673847570737.3130253366123
Winsorized Mean ( 27 / 40 )491.02513.024215017448437.7009285659197
Winsorized Mean ( 28 / 40 )495.45833333333312.303451360606940.269865650844
Winsorized Mean ( 29 / 40 )501.98333333333311.351538249722844.2216131673247
Winsorized Mean ( 30 / 40 )501.98333333333311.296996349352144.4351151235102
Winsorized Mean ( 31 / 40 )502.510.956643610873145.8625850987187
Winsorized Mean ( 32 / 40 )502.23333333333310.930200839088945.9491404345684
Winsorized Mean ( 33 / 40 )500.85833333333310.677637669219946.9072231938662
Winsorized Mean ( 34 / 40 )501.42510.611814029127947.2515819278081
Winsorized Mean ( 35 / 40 )502.310.448631181041048.0732826431293
Winsorized Mean ( 36 / 40 )503.210.218143088608249.2457382556129
Winsorized Mean ( 37 / 40 )501.9666666666679.9697507009093250.3489687681842
Winsorized Mean ( 38 / 40 )501.3333333333339.909593669033150.5907053384006
Winsorized Mean ( 39 / 40 )501.6583333333339.872318597293250.8146418077389
Winsorized Mean ( 40 / 40 )509.9916666666678.862144461610357.547207549582
Trimmed Mean ( 1 / 40 )478.11864406779715.9565276142129.963827696573
Trimmed Mean ( 2 / 40 )479.61206896551715.799406795991030.3563339534505
Trimmed Mean ( 3 / 40 )481.17543859649115.644917031123430.7560236746069
Trimmed Mean ( 4 / 40 )482.67857142857115.495776266205531.1490410765183
Trimmed Mean ( 5 / 40 )483.98181818181815.397431529894731.4326332441972
Trimmed Mean ( 6 / 40 )485.08333333333315.332950269493831.6366599256796
Trimmed Mean ( 7 / 40 )486.23584905660415.257911808499131.8677847374734
Trimmed Mean ( 8 / 40 )487.39423076923115.180365806688432.1068831262608
Trimmed Mean ( 9 / 40 )488.58823529411815.091221700747732.3756581794774
Trimmed Mean ( 10 / 40 )489.8114.994286420251132.6664428217451
Trimmed Mean ( 11 / 40 )491.03061224489814.894929390246332.9662933861533
Trimmed Mean ( 12 / 40 )492.30208333333314.785521603146833.2962269811677
Trimmed Mean ( 13 / 40 )493.60638297872314.665735017142033.6571186102691
Trimmed Mean ( 14 / 40 )494.96739130434814.529452197118134.0664867876108
Trimmed Mean ( 15 / 40 )496.38888888888914.374331179746434.5330076705277
Trimmed Mean ( 16 / 40 )497.82954545454514.204187404055835.0480834484342
Trimmed Mean ( 17 / 40 )498.97674418604714.089153076155235.4156663277742
Trimmed Mean ( 18 / 40 )499.98809523809513.998232554276635.7179446261839
Trimmed Mean ( 19 / 40 )501.01219512195113.908858206776436.021087257749
Trimmed Mean ( 20 / 40 )502.07513.802446295283236.3757981200461
Trimmed Mean ( 21 / 40 )503.15384615384613.682123074138636.7745446687939
Trimmed Mean ( 22 / 40 )504.21052631578913.569668392300837.1571737598149
Trimmed Mean ( 23 / 40 )505.32432432432413.432157175719337.6204892269855
Trimmed Mean ( 24 / 40 )506.51388888888913.267221557738138.1778420360716
Trimmed Mean ( 25 / 40 )507.74285714285713.080728570041538.8160991510618
Trimmed Mean ( 26 / 40 )509.04411764705912.861018987799339.5803876916726
Trimmed Mean ( 27 / 40 )510.27272727272712.643222300583840.3593890181909
Trimmed Mean ( 28 / 40 )511.60937512.397228656712641.2680437835584
Trimmed Mean ( 29 / 40 )512.72580645161312.205476169402842.0078495369917
Trimmed Mean ( 30 / 40 )513.46666666666712.106926314446142.410984698403
Trimmed Mean ( 31 / 40 )514.25862068965511.984931059518442.9087675294747
Trimmed Mean ( 32 / 40 )515.07142857142911.874830337622143.3750558051822
Trimmed Mean ( 33 / 40 )515.96296296296311.731832467942943.9797418155114
Trimmed Mean ( 34 / 40 )517.01923076923111.580054183394844.6473930588867
Trimmed Mean ( 35 / 40 )518.1211.390495142522945.4870480621831
Trimmed Mean ( 36 / 40 )519.2511.170245271820346.4851028213262
Trimmed Mean ( 37 / 40 )520.41304347826110.922943812603447.6440282406088
Trimmed Mean ( 38 / 40 )521.77272727272710.637743626710349.0491917818559
Trimmed Mean ( 39 / 40 )523.30952380952410.264079200276350.9845562956525
Trimmed Mean ( 40 / 40 )524.9759.7673899815294653.7477259526598
Median536
Midrange391.5
Midmean - Weighted Average at Xnp510.672131147541
Midmean - Weighted Average at X(n+1)p513.466666666667
Midmean - Empirical Distribution Function510.672131147541
Midmean - Empirical Distribution Function - Averaging513.466666666667
Midmean - Empirical Distribution Function - Interpolation513.466666666667
Midmean - Closest Observation510.672131147541
Midmean - True Basic - Statistics Graphics Toolkit513.466666666667
Midmean - MS Excel (old versions)512.725806451613
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Aug/04/t1280932817o9f0zmdksfl0c2w/1xekh1280932835.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/04/t1280932817o9f0zmdksfl0c2w/1xekh1280932835.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Aug/04/t1280932817o9f0zmdksfl0c2w/2xekh1280932835.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/04/t1280932817o9f0zmdksfl0c2w/2xekh1280932835.ps (open in new window)


 
Parameters (Session):
par1 = grey ;
 
Parameters (R input):
par1 = grey ;
 
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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