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Omzet product X

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 03 Aug 2010 13:12:06 +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/03/t1280841148m33xtkedtyck67c.htm/, Retrieved Tue, 03 Aug 2010 15:12:30 +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/03/t1280841148m33xtkedtyck67c.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:
Phiilppe De Vocht
 
Dataseries X:
» Textbox « » Textfile « » CSV «
73 72 71 69 89 88 73 63 64 64 65 67 69 71 70 72 88 83 76 70 75 71 75 81 87 90 80 85 105 104 98 94 107 112 121 118 120 122 109 112 132 127 116 113 123 125 137 127 123 128 114 120 143 135 119 117 132 139 158 141 139 150 142 149 166 150 139 140 158 169 186 177 175 187 176 185 204 188 171 171 182 185 200 192 185 195 190 195 213 194 171 171 186 182 193 185 172 185 179 182 193 173 155 164 188 186 200 185 173 190 190 193 195 178 163 165 188 182 200 177
 
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 Mean139.0754.1127179005387433.8158374494351
Geometric Mean130.848489987346
Harmonic Mean121.984202980677
Quadratic Mean146.132388607044
Winsorized Mean ( 1 / 40 )139.0083333333334.1007701646207733.8981039543796
Winsorized Mean ( 2 / 40 )138.9416666666674.0921509865283933.953211189927
Winsorized Mean ( 3 / 40 )138.9666666666674.0883268500989533.9910852928267
Winsorized Mean ( 4 / 40 )139.0333333333334.0783113804800534.090906839234
Winsorized Mean ( 5 / 40 )138.9083333333334.0408279761652634.3762056075342
Winsorized Mean ( 6 / 40 )138.9083333333334.0408279761652634.3762056075342
Winsorized Mean ( 7 / 40 )138.9666666666674.0323956592288534.4625573506451
Winsorized Mean ( 8 / 40 )138.94.0246683319340534.5121606413842
Winsorized Mean ( 9 / 40 )138.94.0053605537162434.6785259746781
Winsorized Mean ( 10 / 40 )138.94.0053605537162434.6785259746781
Winsorized Mean ( 11 / 40 )138.94.0053605537162434.6785259746781
Winsorized Mean ( 12 / 40 )138.93.9798934433886934.9004318773251
Winsorized Mean ( 13 / 40 )138.6833333333333.9559369865612535.0570127391957
Winsorized Mean ( 14 / 40 )138.83.9394862381696835.2330206551217
Winsorized Mean ( 15 / 40 )138.83.9394862381696835.2330206551217
Winsorized Mean ( 16 / 40 )138.83.8735185114135335.8330545190421
Winsorized Mean ( 17 / 40 )138.83.8735185114135335.8330545190421
Winsorized Mean ( 18 / 40 )138.953.8528400889084836.0643049785554
Winsorized Mean ( 19 / 40 )139.4253.7502691313321737.1773318440411
Winsorized Mean ( 20 / 40 )139.4253.71047163982137.5760856123202
Winsorized Mean ( 21 / 40 )139.7753.6645294732754238.1426868085923
Winsorized Mean ( 22 / 40 )140.1416666666673.6171722367980938.7434320215615
Winsorized Mean ( 23 / 40 )140.3333333333333.5480561082831939.5521742189237
Winsorized Mean ( 24 / 40 )140.5333333333333.5228929839916139.8914568145928
Winsorized Mean ( 25 / 40 )140.5333333333333.5228929839916139.8914568145928
Winsorized Mean ( 26 / 40 )140.753.4958408661357240.2621301682946
Winsorized Mean ( 27 / 40 )140.9753.4679497430280140.6508197771369
Winsorized Mean ( 28 / 40 )141.9083333333333.354268901655442.3067850234961
Winsorized Mean ( 29 / 40 )142.153.1619598662978744.9562948331897
Winsorized Mean ( 30 / 40 )143.652.9902654857169548.0392128010528
Winsorized Mean ( 31 / 40 )143.9083333333332.9616123777120148.5912114685682
Winsorized Mean ( 32 / 40 )144.4416666666672.9032676421348849.7514127083556
Winsorized Mean ( 33 / 40 )144.1666666666672.7552682751365352.3240034255911
Winsorized Mean ( 34 / 40 )144.7333333333332.6352154391683054.9227707086493
Winsorized Mean ( 35 / 40 )144.4416666666672.6044240489054955.4601186113944
Winsorized Mean ( 36 / 40 )144.7416666666672.5731727310517356.2502722495069
Winsorized Mean ( 37 / 40 )144.7416666666672.5089335016283157.6905153415698
Winsorized Mean ( 38 / 40 )145.0583333333332.4111463803372960.1615623656334
Winsorized Mean ( 39 / 40 )144.7333333333332.3109692551451162.628844157533
Winsorized Mean ( 40 / 40 )145.0666666666672.2775156415853163.6951351805822
Trimmed Mean ( 1 / 40 )139.0932203389834.0841323715657234.0569814307119
Trimmed Mean ( 2 / 40 )139.1810344827594.0650003390911634.2388740154143
Trimmed Mean ( 3 / 40 )139.3070175438604.0479222014370834.4144503306915
Trimmed Mean ( 4 / 40 )139.4285714285714.0296662577593734.6005258276893
Trimmed Mean ( 5 / 40 )139.5363636363644.0116319045457334.7829429410634
Trimmed Mean ( 6 / 40 )139.6759259259264.0000828284887434.9182584248378
Trimmed Mean ( 7 / 40 )139.8207547169813.9861123960706435.0769724543671
Trimmed Mean ( 8 / 40 )139.9615384615383.9710942849783035.2450806798971
Trimmed Mean ( 9 / 40 )140.1176470588243.9545391330634935.4321053210258
Trimmed Mean ( 10 / 40 )140.283.9380321189265335.621852682664
Trimmed Mean ( 11 / 40 )140.4489795918373.9183257063500335.8441309164844
Trimmed Mean ( 12 / 40 )140.6253.8950105848560136.103881346756
Trimmed Mean ( 13 / 40 )140.8085106382983.8711894377796336.3734487556002
Trimmed Mean ( 14 / 40 )141.0217391304353.8462128934581336.6650892804954
Trimmed Mean ( 15 / 40 )141.2333333333333.818937306020636.9823649921347
Trimmed Mean ( 16 / 40 )141.4545454545453.7867291881429337.3553371330251
Trimmed Mean ( 17 / 40 )141.6860465116283.7572460454716837.7100793498449
Trimmed Mean ( 18 / 40 )141.9285714285713.7222403676607338.1298780867738
Trimmed Mean ( 19 / 40 )142.1707317073173.68357785623738.5958264643694
Trimmed Mean ( 20 / 40 )142.38753.6510139804502338.9994398165633
Trimmed Mean ( 21 / 40 )142.6153846153853.6169040529365439.4302371663954
Trimmed Mean ( 22 / 40 )142.8289473684213.5818934597718139.8752640112083
Trimmed Mean ( 23 / 40 )143.0270270270273.5458582966565140.3363628946739
Trimmed Mean ( 24 / 40 )143.2222222222223.5110056242944440.7923647946317
Trimmed Mean ( 25 / 40 )143.4142857142863.4718324024498941.3079518507534
Trimmed Mean ( 26 / 40 )143.6176470588243.4240812621490441.9434108198372
Trimmed Mean ( 27 / 40 )143.8181818181823.3698864631195842.6774561671867
Trimmed Mean ( 28 / 40 )144.0156253.3080508596198143.5348884014896
Trimmed Mean ( 29 / 40 )144.1612903225813.249715730022944.3612002707587
Trimmed Mean ( 30 / 40 )144.33.2056006779096345.0149642762423
Trimmed Mean ( 31 / 40 )144.3448275862073.1752170733476445.4598297539461
Trimmed Mean ( 32 / 40 )144.3753.1398736946224245.9811489383371
Trimmed Mean ( 33 / 40 )144.3703703703703.102747401411346.5298497404922
Trimmed Mean ( 34 / 40 )144.3846153846153.0765931195632346.9300325956372
Trimmed Mean ( 35 / 40 )144.363.0588459875433747.1942688804475
Trimmed Mean ( 36 / 40 )144.3541666666673.037223206799247.5283365224893
Trimmed Mean ( 37 / 40 )144.3260869565223.0106179807340147.9390237752231
Trimmed Mean ( 38 / 40 )144.2954545454552.9833185874709148.3674305357311
Trimmed Mean ( 39 / 40 )144.2380952380952.9607987597852748.7159401703329
Trimmed Mean ( 40 / 40 )144.22.9446169922027648.9707151666368
Median140.5
Midrange138
Midmean - Weighted Average at Xnp144.161290322581
Midmean - Weighted Average at X(n+1)p144.918032786885
Midmean - Empirical Distribution Function144.161290322581
Midmean - Empirical Distribution Function - Averaging144.918032786885
Midmean - Empirical Distribution Function - Interpolation144.918032786885
Midmean - Closest Observation144.161290322581
Midmean - True Basic - Statistics Graphics Toolkit144.918032786885
Midmean - MS Excel (old versions)144.161290322581
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Aug/03/t1280841148m33xtkedtyck67c/1x9vp1280841124.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/03/t1280841148m33xtkedtyck67c/1x9vp1280841124.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Aug/03/t1280841148m33xtkedtyck67c/2x9vp1280841124.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Aug/03/t1280841148m33xtkedtyck67c/2x9vp1280841124.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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