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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: Tue, 27 Jul 2010 08:30:15 +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/27/t1280219546ufpvw7igjd5cmde.htm/, Retrieved Tue, 27 Jul 2010 10:32:26 +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/27/t1280219546ufpvw7igjd5cmde.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:
Patrick Fieremans
 
Dataseries X:
» Textbox « » Textfile « » CSV «
136 135 134 132 152 151 136 126 127 127 128 130 125 118 111 104 126 131 122 116 115 115 113 122 114 106 93 89 114 122 115 116 120 120 120 121 118 112 99 96 120 135 128 134 134 132 130 125 124 114 101 101 123 143 133 136 137 135 141 136 133 124 110 104 130 160 142 142 137 135 139 135 134 120 103 101 127 159 141 140 135 127 130 128 126 110 101 102 129 169 146 145 138 123 124 137 132 112 105 106 137 175 151 142 140 122 127 135 128 117 107 108 134 171 154 146 148 122 124 135
 
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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean126.9416666666671.4630507932796386.7650441459448
Geometric Mean125.937056321508
Harmonic Mean124.925738200123
Quadratic Mean127.941034595369
Winsorized Mean ( 1 / 40 )126.9416666666671.4472661290744187.7113504672785
Winsorized Mean ( 2 / 40 )126.9583333333331.4294029151167288.8191369911728
Winsorized Mean ( 3 / 40 )126.8083333333331.3652497864707692.8828809130522
Winsorized Mean ( 4 / 40 )126.8416666666671.3474218474259094.1365667396467
Winsorized Mean ( 5 / 40 )126.6333333333331.3081801102092096.8011456106622
Winsorized Mean ( 6 / 40 )126.5333333333331.2910993151742198.0043377346689
Winsorized Mean ( 7 / 40 )126.4751.2815739240048198.6872451374297
Winsorized Mean ( 8 / 40 )126.5416666666671.2705948139116399.5924627435698
Winsorized Mean ( 9 / 40 )126.3916666666671.22356048349453103.298258134071
Winsorized Mean ( 10 / 40 )126.3083333333331.18627750479979106.474524571424
Winsorized Mean ( 11 / 40 )126.3083333333331.18627750479979106.474524571424
Winsorized Mean ( 12 / 40 )126.3083333333331.15686937696907109.181153765392
Winsorized Mean ( 13 / 40 )126.21.11172765340714113.517010765390
Winsorized Mean ( 14 / 40 )126.0833333333331.09720700505941114.912986111045
Winsorized Mean ( 15 / 40 )126.2083333333331.07823487833023117.050872560143
Winsorized Mean ( 16 / 40 )126.3416666666671.05854505039519119.354076257311
Winsorized Mean ( 17 / 40 )126.4833333333331.00083881719379126.377325859497
Winsorized Mean ( 18 / 40 )126.4833333333331.00083881719379126.377325859497
Winsorized Mean ( 19 / 40 )126.4833333333330.960128327479592131.735862502215
Winsorized Mean ( 20 / 40 )126.650.937892774864407135.036758352585
Winsorized Mean ( 21 / 40 )126.4750.917382900731544137.865006966170
Winsorized Mean ( 22 / 40 )126.4750.872627836902247144.935784364816
Winsorized Mean ( 23 / 40 )126.4750.827144737858464152.905524524586
Winsorized Mean ( 24 / 40 )126.4750.827144737858464152.905524524586
Winsorized Mean ( 25 / 40 )126.4750.827144737858464152.905524524586
Winsorized Mean ( 26 / 40 )126.6916666666670.800104670440144158.343865930657
Winsorized Mean ( 27 / 40 )126.4666666666670.77630646484337162.908171442554
Winsorized Mean ( 28 / 40 )126.4666666666670.77630646484337162.908171442554
Winsorized Mean ( 29 / 40 )126.7083333333330.746738551336602169.682324699234
Winsorized Mean ( 30 / 40 )126.7083333333330.746738551336602169.682324699234
Winsorized Mean ( 31 / 40 )126.7083333333330.689293454816893183.823497014044
Winsorized Mean ( 32 / 40 )126.9750.658223406771051192.905628535579
Winsorized Mean ( 33 / 40 )126.9750.658223406771051192.905628535579
Winsorized Mean ( 34 / 40 )127.5416666666670.595489092738477214.179685609589
Winsorized Mean ( 35 / 40 )127.5416666666670.595489092738477214.179685609589
Winsorized Mean ( 36 / 40 )127.5416666666670.595489092738477214.179685609589
Winsorized Mean ( 37 / 40 )127.5416666666670.595489092738477214.179685609589
Winsorized Mean ( 38 / 40 )127.5416666666670.595489092738477214.179685609589
Winsorized Mean ( 39 / 40 )127.5416666666670.52738664311414241.837119562892
Winsorized Mean ( 40 / 40 )127.8750.493311354457785259.217629686533
Trimmed Mean ( 1 / 40 )126.8559322033901.3936943020550191.0213466585466
Trimmed Mean ( 2 / 40 )126.7672413793101.3334783768409495.0650896039473
Trimmed Mean ( 3 / 40 )126.6666666666671.2764613664495799.232667745351
Trimmed Mean ( 4 / 40 )126.6160714285711.23990424546437102.117620688645
Trimmed Mean ( 5 / 40 )126.5545454545451.20490977542380105.032383366658
Trimmed Mean ( 6 / 40 )126.5370370370371.17670550578265107.535008900018
Trimmed Mean ( 7 / 40 )126.5377358490571.14925457526192110.104182809295
Trimmed Mean ( 8 / 40 )126.5480769230771.12052610600414112.936303978097
Trimmed Mean ( 9 / 40 )126.5490196078431.09042063975943116.055231342432
Trimmed Mean ( 10 / 40 )126.571.06526944474109118.815010253826
Trimmed Mean ( 11 / 40 )126.6020408163271.04332204577945121.345121890666
Trimmed Mean ( 12 / 40 )126.6354166666671.01848268117662124.337329448124
Trimmed Mean ( 13 / 40 )126.6702127659570.994998738012342127.306907965532
Trimmed Mean ( 14 / 40 )126.7173913043480.97512370574659129.950067419731
Trimmed Mean ( 15 / 40 )126.7777777777780.95449233884474132.822205709081
Trimmed Mean ( 16 / 40 )126.8295454545450.933698277878985135.835685316519
Trimmed Mean ( 17 / 40 )126.8720930232560.912715542315406139.005075668376
Trimmed Mean ( 18 / 40 )126.9047619047620.89664048310541141.533607165764
Trimmed Mean ( 19 / 40 )126.9390243902440.878041461711276144.570649480315
Trimmed Mean ( 20 / 40 )126.9750.86199191602424147.304165665087
Trimmed Mean ( 21 / 40 )1270.846335463208128150.058700740948
Trimmed Mean ( 22 / 40 )127.0394736842110.83064988074202152.939856646613
Trimmed Mean ( 23 / 40 )127.0810810810810.818102471418989155.336385747204
Trimmed Mean ( 24 / 40 )127.1250.809020326622817157.134494420767
Trimmed Mean ( 25 / 40 )127.1714285714290.798023289917725159.358041523500
Trimmed Mean ( 26 / 40 )127.2205882352940.784744129417131162.1172857066
Trimmed Mean ( 27 / 40 )127.2575757575760.772580999913184164.717454573534
Trimmed Mean ( 28 / 40 )127.31250.760793693224907167.341686890619
Trimmed Mean ( 29 / 40 )127.3709677419350.74630550330705170.668670105641
Trimmed Mean ( 30 / 40 )127.4166666666670.733111805266233173.802502907990
Trimmed Mean ( 31 / 40 )127.4655172413790.716757974982754177.836203698251
Trimmed Mean ( 32 / 40 )127.5178571428570.705263638385634180.808778735210
Trimmed Mean ( 33 / 40 )127.5555555555560.695732557970297183.339925800916
Trimmed Mean ( 34 / 40 )127.5961538461540.683383702325262186.712316100016
Trimmed Mean ( 35 / 40 )127.60.677932029583124188.219459225823
Trimmed Mean ( 36 / 40 )127.6041666666670.670251608925439190.382484678022
Trimmed Mean ( 37 / 40 )127.6086956521740.65973077576564193.425409787924
Trimmed Mean ( 38 / 40 )127.6136363636360.645537543423501197.685847498286
Trimmed Mean ( 39 / 40 )127.6190476190480.626507363193099203.699198312077
Trimmed Mean ( 40 / 40 )127.6250.615700039354829207.284378499852
Median127
Midrange132
Midmean - Weighted Average at Xnp127.640625
Midmean - Weighted Average at X(n+1)p127.640625
Midmean - Empirical Distribution Function127.640625
Midmean - Empirical Distribution Function - Averaging127.640625
Midmean - Empirical Distribution Function - Interpolation127.640625
Midmean - Closest Observation127.640625
Midmean - True Basic - Statistics Graphics Toolkit127.640625
Midmean - MS Excel (old versions)127.640625
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jul/27/t1280219546ufpvw7igjd5cmde/1kllh1280219411.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/27/t1280219546ufpvw7igjd5cmde/1kllh1280219411.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jul/27/t1280219546ufpvw7igjd5cmde/2kllh1280219411.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/27/t1280219546ufpvw7igjd5cmde/2kllh1280219411.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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