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Tijdreeks 2 - Stap 9

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 20 Jul 2010 11:06:17 +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/20/t1279624487ce37l5paf5jcqvk.htm/, Retrieved Tue, 20 Jul 2010 13:14:49 +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/20/t1279624487ce37l5paf5jcqvk.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:
Van Puyenbroeck Cassandra
 
Dataseries X:
» Textbox « » Textfile « » CSV «
349 348 347 345 365 364 349 339 340 340 341 343 341 343 341 335 355 357 337 325 336 338 337 328 326 327 319 310 320 322 303 292 303 315 311 307 308 312 309 310 309 304 287 275 290 298 294 286 294 292 287 281 280 271 264 259 271 279 279 273 286 286 280 277 269 255 252 245 257 267 261 258 271 262 258 253 236 228 235 226 231 235 227 222 233 221 218 220 204 196 208 190 191 194 179 162 179 176 168 170 153 142 155 136 136 144 135 114 135 132 123 123 103 97 113 108 111 121 111 97
 
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'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean254.8756.9238915979342136.8109460402360
Geometric Mean241.070059591576
Harmonic Mean224.583816220851
Quadratic Mean265.831071045755
Winsorized Mean ( 1 / 40 )254.8666666666676.9227827233649836.8156385735566
Winsorized Mean ( 2 / 40 )254.856.8889414285216736.9940726952427
Winsorized Mean ( 3 / 40 )254.9256.8599348562863937.161431608405
Winsorized Mean ( 4 / 40 )254.8256.8182041560197737.3742108873369
Winsorized Mean ( 5 / 40 )254.8256.8182041560197737.3742108873369
Winsorized Mean ( 6 / 40 )254.8756.7947867075104137.5103753762103
Winsorized Mean ( 7 / 40 )254.8756.7778842300421737.6039175868919
Winsorized Mean ( 8 / 40 )255.2083333333336.6825989156894538.1899821541217
Winsorized Mean ( 9 / 40 )255.2083333333336.6405921725722438.4315625325442
Winsorized Mean ( 10 / 40 )255.2083333333336.6405921725722438.4315625325442
Winsorized Mean ( 11 / 40 )255.856.4850469029401339.4522975437549
Winsorized Mean ( 12 / 40 )256.156.4372498999580439.7918371945867
Winsorized Mean ( 13 / 40 )256.156.4372498999580439.7918371945867
Winsorized Mean ( 14 / 40 )256.156.4059523484175339.9862481123946
Winsorized Mean ( 15 / 40 )256.156.4059523484175339.9862481123946
Winsorized Mean ( 16 / 40 )256.8166666666676.2666247614666640.981657023064
Winsorized Mean ( 17 / 40 )256.9583333333336.2075719082637441.394338580478
Winsorized Mean ( 18 / 40 )258.1583333333335.988153522556943.1115088083282
Winsorized Mean ( 19 / 40 )258.4755.9416155941248343.5024777192898
Winsorized Mean ( 20 / 40 )259.4755.7546104096095545.0899333804954
Winsorized Mean ( 21 / 40 )260.355.5873337397481246.5964648125237
Winsorized Mean ( 22 / 40 )259.4333333333335.3957101610375148.0814064489054
Winsorized Mean ( 23 / 40 )260.3916666666675.2169098013878949.9130091529267
Winsorized Mean ( 24 / 40 )260.7916666666675.114362922193450.9920141832290
Winsorized Mean ( 25 / 40 )260.5833333333335.0921285899019851.1737535163756
Winsorized Mean ( 26 / 40 )262.3166666666674.7084610552568255.7117630555316
Winsorized Mean ( 27 / 40 )262.0916666666674.6318226357491656.5849962914816
Winsorized Mean ( 28 / 40 )262.5583333333334.5175319206983558.1198623368544
Winsorized Mean ( 29 / 40 )262.0754.3557837286481960.1671286561637
Winsorized Mean ( 30 / 40 )263.3254.0280209447186965.3732946312647
Winsorized Mean ( 31 / 40 )264.13.8749428476855268.1558439391553
Winsorized Mean ( 32 / 40 )266.53.5310943701606775.4723527787998
Winsorized Mean ( 33 / 40 )267.053.4679979532752977.004082354717
Winsorized Mean ( 34 / 40 )267.053.4063470580832078.3977661249448
Winsorized Mean ( 35 / 40 )267.3416666666673.37330714538579.2520974653657
Winsorized Mean ( 36 / 40 )268.2416666666673.2079207781605683.6185446014905
Winsorized Mean ( 37 / 40 )268.2416666666673.1418160066742685.3779044020504
Winsorized Mean ( 38 / 40 )267.6083333333333.0093061968136788.926920635954
Winsorized Mean ( 39 / 40 )268.2583333333332.8691221935517693.4983995928208
Winsorized Mean ( 40 / 40 )268.9252.7967608940700496.1558782412185
Trimmed Mean ( 1 / 40 )255.2796610169496.8484334659643337.275628402561
Trimmed Mean ( 2 / 40 )255.7068965517246.7656312124852937.7949800278565
Trimmed Mean ( 3 / 40 )256.1578947368426.6927325269142138.2740373542087
Trimmed Mean ( 4 / 40 )256.5982142857146.6227453585751338.7449917508109
Trimmed Mean ( 5 / 40 )257.0818181818186.5570840645229939.2067290356632
Trimmed Mean ( 6 / 40 )257.5833333333336.483051965694339.7318014256805
Trimmed Mean ( 7 / 40 )258.0943396226416.4049555205688140.296039339196
Trimmed Mean ( 8 / 40 )258.6256.32023179984240.9201763780982
Trimmed Mean ( 9 / 40 )259.1274509803926.2425831988753041.5096511692593
Trimmed Mean ( 10 / 40 )259.656.1617486531541142.1390119292011
Trimmed Mean ( 11 / 40 )260.1938775510206.0698067341450642.8669130579277
Trimmed Mean ( 12 / 40 )260.68755.9901108654034643.5196452716141
Trimmed Mean ( 13 / 40 )261.1702127659575.9063971209077944.2181938362141
Trimmed Mean ( 14 / 40 )261.6739130434785.8104949098904245.0347030849414
Trimmed Mean ( 15 / 40 )262.25.7049861013834945.9597964553174
Trimmed Mean ( 16 / 40 )262.755.5836764348174447.0568098039496
Trimmed Mean ( 17 / 40 )263.2674418604655.4644335516737648.1783590871603
Trimmed Mean ( 18 / 40 )263.7976190476195.3350662281369349.445987691092
Trimmed Mean ( 19 / 40 )264.2560975609765.2172267803123750.6506825730036
Trimmed Mean ( 20 / 40 )264.71255.0870023549100952.0370311494929
Trimmed Mean ( 21 / 40 )265.1153846153854.9624289639102253.4245198356417
Trimmed Mean ( 22 / 40 )265.4736842105264.8409247226019254.8394572159012
Trimmed Mean ( 23 / 40 )265.9189189189194.7237164927022456.2944281964724
Trimmed Mean ( 24 / 40 )266.3194444444444.6114619730947957.7516297430759
Trimmed Mean ( 25 / 40 )266.7142857142864.4932036488315159.3594919259105
Trimmed Mean ( 26 / 40 )267.1470588235294.3549828517579261.342849769361
Trimmed Mean ( 27 / 40 )267.4848484848484.2486933367303562.9569675392707
Trimmed Mean ( 28 / 40 )267.8593754.1315104459783464.8332803468371
Trimmed Mean ( 29 / 40 )268.2258064516134.0076882324084966.9278124686905
Trimmed Mean ( 30 / 40 )268.653.8813493634760569.2156193225036
Trimmed Mean ( 31 / 40 )269.0172413793103.7810214276681171.1493564703818
Trimmed Mean ( 32 / 40 )269.3571428571433.6826575465041273.1420555551897
Trimmed Mean ( 33 / 40 )269.5555555555563.6187711048560174.4881474249201
Trimmed Mean ( 34 / 40 )269.7307692307693.5481088566990176.0209960079167
Trimmed Mean ( 35 / 40 )269.923.4680865747261777.8296602994439
Trimmed Mean ( 36 / 40 )270.1041666666673.3714013626895880.1162892249612
Trimmed Mean ( 37 / 40 )270.2391304347833.2792989681221982.4075917022987
Trimmed Mean ( 38 / 40 )270.3863636363643.1721595323067885.237315741097
Trimmed Mean ( 39 / 40 )270.5952380952383.0586712523918888.4682320414895
Trimmed Mean ( 40 / 40 )270.7752.9407585581675992.0765831822394
Median272
Midrange231
Midmean - Weighted Average at Xnp267.459016393443
Midmean - Weighted Average at X(n+1)p268.65
Midmean - Empirical Distribution Function267.459016393443
Midmean - Empirical Distribution Function - Averaging268.65
Midmean - Empirical Distribution Function - Interpolation268.65
Midmean - Closest Observation267.459016393443
Midmean - True Basic - Statistics Graphics Toolkit268.65
Midmean - MS Excel (old versions)268.225806451613
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jul/20/t1279624487ce37l5paf5jcqvk/124hs1279623974.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/20/t1279624487ce37l5paf5jcqvk/124hs1279623974.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jul/20/t1279624487ce37l5paf5jcqvk/224hs1279623974.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/20/t1279624487ce37l5paf5jcqvk/224hs1279623974.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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