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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: Sun, 15 Aug 2010 18:11:00 +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/t12818961584o11iqi69a83zib.htm/, Retrieved Sun, 15 Aug 2010 20:16:00 +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/t12818961584o11iqi69a83zib.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:
De Cock Nicola
 
Dataseries X:
» Textbox « » Textfile « » CSV «
252 251 250 248 268 267 252 242 243 243 244 246 236 241 240 239 253 249 232 229 221 222 224 224 215 225 225 221 238 234 228 227 216 219 225 227 205 215 214 209 222 216 206 199 189 198 203 211 199 211 210 203 214 202 193 193 176 192 200 195 180 197 194 194 212 202 195 198 170 187 190 189 176 188 195 194 211 203 194 194 163 183 181 184 171 178 179 186 205 204 195 186 156 167 164 165 153 160 154 169 186 188 187 169 131 146 145 137 119 118 113 123 142 141 138 124 83 100 96 98
 
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 Mean195.3416666666673.5404721993011455.1739021436817
Geometric Mean190.884230416638
Harmonic Mean185.584928714322
Quadratic Mean199.123140292634
Winsorized Mean ( 1 / 40 )195.4416666666673.5117010456985755.6544148044892
Winsorized Mean ( 2 / 40 )195.2416666666673.4674758502656656.3065685523689
Winsorized Mean ( 3 / 40 )195.2666666666673.4523108270671956.5611488790973
Winsorized Mean ( 4 / 40 )195.73.3571404732097158.2936584160549
Winsorized Mean ( 5 / 40 )195.8666666666673.3091193352577459.1899677294082
Winsorized Mean ( 6 / 40 )195.8666666666673.2923162674975159.492056884178
Winsorized Mean ( 7 / 40 )196.0416666666673.2392765522102860.5202005777802
Winsorized Mean ( 8 / 40 )196.0416666666673.2175855170127860.9281915368244
Winsorized Mean ( 9 / 40 )196.4166666666673.1013592243211763.3324463436379
Winsorized Mean ( 10 / 40 )196.752.9928076715859465.7409434852654
Winsorized Mean ( 11 / 40 )196.752.9653992036443966.34857113275
Winsorized Mean ( 12 / 40 )197.052.9161928386629267.5709772644349
Winsorized Mean ( 13 / 40 )197.052.8844907895235168.3136173343618
Winsorized Mean ( 14 / 40 )197.2833333333332.8138359468456970.1118818083506
Winsorized Mean ( 15 / 40 )197.2833333333332.7781455872268871.0125971224783
Winsorized Mean ( 16 / 40 )198.0833333333332.6207955079144275.5813770037192
Winsorized Mean ( 17 / 40 )198.0833333333332.5818962298906376.7200986004478
Winsorized Mean ( 18 / 40 )198.0833333333332.5005484925856179.2159535880513
Winsorized Mean ( 19 / 40 )198.42.3725023723914083.6247846614459
Winsorized Mean ( 20 / 40 )198.5666666666672.2637607010616987.7153961430374
Winsorized Mean ( 21 / 40 )198.2166666666672.1768511982040391.056599013383
Winsorized Mean ( 22 / 40 )198.2166666666672.1310753763230793.0125085526855
Winsorized Mean ( 23 / 40 )198.4083333333332.0589524352735796.363728435024
Winsorized Mean ( 24 / 40 )198.8083333333332.0083612281150398.9903263169083
Winsorized Mean ( 25 / 40 )198.3916666666671.96000971219416101.219736531088
Winsorized Mean ( 26 / 40 )198.6083333333331.93288277735590102.752394330411
Winsorized Mean ( 27 / 40 )198.8333333333331.90507700474922104.370234293761
Winsorized Mean ( 28 / 40 )199.7666666666671.73914131446278114.865114758299
Winsorized Mean ( 29 / 40 )199.7666666666671.73914131446278114.865114758299
Winsorized Mean ( 30 / 40 )199.7666666666671.62420992787958122.993132376345
Winsorized Mean ( 31 / 40 )200.0251.59535664198512125.379488658477
Winsorized Mean ( 32 / 40 )200.0251.5352288171502130.290024369983
Winsorized Mean ( 33 / 40 )200.31.50534063260382133.059585094396
Winsorized Mean ( 34 / 40 )200.31.37990784411978145.154620907143
Winsorized Mean ( 35 / 40 )199.7166666666671.25139604581925159.595091684917
Winsorized Mean ( 36 / 40 )200.3166666666671.18935423321376168.424730893999
Winsorized Mean ( 37 / 40 )200.0083333333331.15545811263182173.098731270984
Winsorized Mean ( 38 / 40 )200.0083333333331.15545811263182173.098731270984
Winsorized Mean ( 39 / 40 )200.0083333333331.08726366332003183.955686261596
Winsorized Mean ( 40 / 40 )200.0083333333331.08726366332003183.955686261596
Trimmed Mean ( 1 / 40 )195.6779661016953.4158173832569257.2858394189445
Trimmed Mean ( 2 / 40 )195.9224137931033.3088892781691559.2109307149467
Trimmed Mean ( 3 / 40 )196.2807017543863.2155283451907861.0415087921549
Trimmed Mean ( 4 / 40 )196.6428571428573.1172615161671263.0819249918572
Trimmed Mean ( 5 / 40 )196.93.0390549318934564.7898785683758
Trimmed Mean ( 6 / 40 )197.1296296296302.9648363971714366.4892099333706
Trimmed Mean ( 7 / 40 )197.3679245283022.8855785255438268.3980431588171
Trimmed Mean ( 8 / 40 )197.5865384615382.8081754970582670.3611788752245
Trimmed Mean ( 9 / 40 )197.8137254901962.7252256889563872.5861811342121
Trimmed Mean ( 10 / 40 )1982.653794691121874.6101424734941
Trimmed Mean ( 11 / 40 )198.153061224492.5923446525419676.4377765241163
Trimmed Mean ( 12 / 40 )198.31252.5272771779546778.4688366317202
Trimmed Mean ( 13 / 40 )198.4468085106382.4614909661716580.6205715307914
Trimmed Mean ( 14 / 40 )198.5869565217392.391513911679183.0381774289198
Trimmed Mean ( 15 / 40 )198.7111111111112.3226209120807085.5546895653745
Trimmed Mean ( 16 / 40 )198.8409090909092.2490498611317988.4110719496659
Trimmed Mean ( 17 / 40 )198.9069767441862.1884929699080690.8876471065576
Trimmed Mean ( 18 / 40 )198.9761904761902.1244267014092193.6611229487007
Trimmed Mean ( 19 / 40 )199.0487804878052.0622576186559396.5198424712497
Trimmed Mean ( 20 / 40 )199.12.0087309426600799.1173062412935
Trimmed Mean ( 21 / 40 )199.1410256410261.96181703027181101.508460049118
Trimmed Mean ( 22 / 40 )199.2105263157891.91891012464940103.814412023172
Trimmed Mean ( 23 / 40 )199.2837837837841.87488321445704106.291305104833
Trimmed Mean ( 24 / 40 )199.3472222222221.83313696368547108.746496400051
Trimmed Mean ( 25 / 40 )199.3857142857141.79097031858340111.328318630887
Trimmed Mean ( 26 / 40 )199.4558823529411.74749712194023114.138031959382
Trimmed Mean ( 27 / 40 )199.5151515151521.69961498783487117.388439701460
Trimmed Mean ( 28 / 40 )199.56251.64643599574816121.208780976218
Trimmed Mean ( 29 / 40 )199.5483870967741.60786627569773124.107576676537
Trimmed Mean ( 30 / 40 )199.5333333333331.56090417565409127.831891569974
Trimmed Mean ( 31 / 40 )199.5172413793101.52181979835832131.104380160215
Trimmed Mean ( 32 / 40 )199.4821428571431.47819455326127134.949856510454
Trimmed Mean ( 33 / 40 )199.4444444444441.43424880974837139.058469554830
Trimmed Mean ( 34 / 40 )199.3846153846151.38434302667389144.028330798667
Trimmed Mean ( 35 / 40 )199.321.34450962155314148.247358594393
Trimmed Mean ( 36 / 40 )199.2916666666671.31748953100304151.266224115603
Trimmed Mean ( 37 / 40 )199.2173913043481.29283160874803154.093843278838
Trimmed Mean ( 38 / 40 )199.1590909090911.26672455620301157.223675765841
Trimmed Mean ( 39 / 40 )199.0952380952381.23151112702747161.667429327901
Trimmed Mean ( 40 / 40 )199.0251.19908485403640165.980747175678
Median198
Midrange175.5
Midmean - Weighted Average at Xnp198.774193548387
Midmean - Weighted Average at X(n+1)p199.533333333333
Midmean - Empirical Distribution Function198.774193548387
Midmean - Empirical Distribution Function - Averaging199.533333333333
Midmean - Empirical Distribution Function - Interpolation199.533333333333
Midmean - Closest Observation198.774193548387
Midmean - True Basic - Statistics Graphics Toolkit199.533333333333
Midmean - MS Excel (old versions)199.5625
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Aug/15/t12818961584o11iqi69a83zib/19t3b1281895858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/15/t12818961584o11iqi69a83zib/19t3b1281895858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Aug/15/t12818961584o11iqi69a83zib/29t3b1281895858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/15/t12818961584o11iqi69a83zib/29t3b1281895858.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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