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Centrumaten 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: Sun, 11 Jul 2010 13:41:39 +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/11/t12788557808efj6paszf8insa.htm/, Retrieved Sun, 11 Jul 2010 15:43:03 +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/11/t12788557808efj6paszf8insa.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:
Febiri Lordina
 
Dataseries X:
» Textbox « » Textfile « » CSV «
213 212 211 209 229 228 213 203 204 204 205 207 205 208 201 201 220 218 203 185 179 182 182 185 183 192 177 172 188 182 162 150 141 135 139 148 142 156 143 134 146 142 117 106 104 99 105 106 96 104 96 85 91 98 73 70 62 60 70 82 72 73 68 53 61 73 46 50 52 45 58 73 58 49 44 35 46 61 29 33 37 31 44 57 42 34 27 22 30 47 12 13 18 11 26 41 21 24 30 34 48 64 35 44 55 53 73 94 73 78 87 87 91 104 73 84 103 111 131 155
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.7166666666675.9438217733690617.7859752020701
Geometric Mean83.86383665002
Harmonic Mean62.2515439217573
Quadratic Mean124.016799937213
Winsorized Mean ( 1 / 40 )105.7166666666675.9412646058489417.7936304271977
Winsorized Mean ( 2 / 40 )105.65.9167000038513217.8477867614147
Winsorized Mean ( 3 / 40 )105.6755.892598054740717.9335157460778
Winsorized Mean ( 4 / 40 )105.6083333333335.8540763148823818.0401360783175
Winsorized Mean ( 5 / 40 )105.655.8490422735869618.0627861893037
Winsorized Mean ( 6 / 40 )105.75.8294576961165418.1320468403802
Winsorized Mean ( 7 / 40 )105.7583333333335.8069430556642618.2123937361799
Winsorized Mean ( 8 / 40 )105.6916666666675.7791133123462318.2885610567406
Winsorized Mean ( 9 / 40 )105.7666666666675.7508826911490418.3913796102028
Winsorized Mean ( 10 / 40 )105.7666666666675.7291667812579618.4610905398435
Winsorized Mean ( 11 / 40 )105.5833333333335.7021248107709618.5164893504072
Winsorized Mean ( 12 / 40 )105.6833333333335.6910414554636518.5701218591323
Winsorized Mean ( 13 / 40 )105.7916666666675.651514953105318.7191695579852
Winsorized Mean ( 14 / 40 )105.9083333333335.6389501256949218.7815694362577
Winsorized Mean ( 15 / 40 )105.7833333333335.6207297308934718.8202134594573
Winsorized Mean ( 16 / 40 )105.9166666666675.6064886294870618.8918008518920
Winsorized Mean ( 17 / 40 )105.6333333333335.5654739660565718.9801145378783
Winsorized Mean ( 18 / 40 )105.9333333333335.5337737329382819.1430547119760
Winsorized Mean ( 19 / 40 )105.1416666666675.2664879924838619.9642848928396
Winsorized Mean ( 20 / 40 )104.6416666666675.1579776376008720.2873439977415
Winsorized Mean ( 21 / 40 )104.4666666666675.0516926377273920.6795373666406
Winsorized Mean ( 22 / 40 )104.4666666666675.0516926377273920.6795373666406
Winsorized Mean ( 23 / 40 )104.0833333333335.0005963696630820.8141840770776
Winsorized Mean ( 24 / 40 )104.0833333333334.9539982343627321.0099657709552
Winsorized Mean ( 25 / 40 )104.2916666666674.9332149822089621.1407098702939
Winsorized Mean ( 26 / 40 )104.2916666666674.9332149822089621.1407098702939
Winsorized Mean ( 27 / 40 )103.8416666666674.8220141170183821.5349155242365
Winsorized Mean ( 28 / 40 )103.6083333333334.7380144500664321.8674582834758
Winsorized Mean ( 29 / 40 )102.6416666666674.5582257936198122.5178986987295
Winsorized Mean ( 30 / 40 )100.3916666666674.2198891457510623.790119408172
Winsorized Mean ( 31 / 40 )99.35833333333333.9803050822877824.962491889246
Winsorized Mean ( 32 / 40 )99.35833333333333.9218877977609125.3343130800578
Winsorized Mean ( 33 / 40 )97.98333333333333.7599537986115926.0597173745898
Winsorized Mean ( 34 / 40 )97.98333333333333.6376490571427926.9358950778762
Winsorized Mean ( 35 / 40 )97.98333333333333.5128811252569827.8925844170618
Winsorized Mean ( 36 / 40 )97.38333333333333.3807658152651928.805110633105
Winsorized Mean ( 37 / 40 )97.0753.3458901270509329.0132061465993
Winsorized Mean ( 38 / 40 )97.70833333333333.2842548543994229.7505332762007
Winsorized Mean ( 39 / 40 )97.70833333333333.2161923098372430.3801277785774
Winsorized Mean ( 40 / 40 )97.04166666666673.1410670062005430.8944910997136
Trimmed Mean ( 1 / 40 )105.4745762711865.898370439942917.8819857696505
Trimmed Mean ( 2 / 40 )105.2241379310345.8502307929575817.9863225323865
Trimmed Mean ( 3 / 40 )105.0263157894745.8102327505161918.0760944181011
Trimmed Mean ( 4 / 40 )104.7946428571435.774465861307618.1479370341992
Trimmed Mean ( 5 / 40 )104.5727272727275.745527456489918.2007183961164
Trimmed Mean ( 6 / 40 )104.3333333333335.7134014422366918.2611592040500
Trimmed Mean ( 7 / 40 )104.0754716981135.6807029498267418.3208790562244
Trimmed Mean ( 8 / 40 )103.7980769230775.647346985095718.3799715507153
Trimmed Mean ( 9 / 40 )103.5196078431375.6137524645367118.4403584762764
Trimmed Mean ( 10 / 40 )103.225.5793736298091818.5002845926148
Trimmed Mean ( 11 / 40 )102.9081632653065.5427130300013118.5663884650513
Trimmed Mean ( 12 / 40 )102.6041666666675.5041148715307418.6413563418475
Trimmed Mean ( 13 / 40 )102.2765957446815.4606054526258518.7299003072084
Trimmed Mean ( 14 / 40 )101.9239130434785.4152955699395618.8214866071689
Trimmed Mean ( 15 / 40 )101.5444444444445.363984048418518.9307879232757
Trimmed Mean ( 16 / 40 )101.1590909090915.3066588944117719.0626706788366
Trimmed Mean ( 17 / 40 )100.7441860465125.2415572410255219.2202777560053
Trimmed Mean ( 18 / 40 )100.3333333333335.1712867763188119.4020052789947
Trimmed Mean ( 19 / 40 )99.87804878048785.0930040474174619.6108323988341
Trimmed Mean ( 20 / 40 )99.46255.0365419040514119.7481728326319
Trimmed Mean ( 21 / 40 )99.06410256410264.9835673940019519.8781504757682
Trimmed Mean ( 22 / 40 )98.65789473684214.9335070843600919.9975175974919
Trimmed Mean ( 23 / 40 )98.22972972972974.8730475940111320.1577612027537
Trimmed Mean ( 24 / 40 )97.80555555555564.807305623602520.3451919252560
Trimmed Mean ( 25 / 40 )97.35714285714294.7340900911814820.5651225435056
Trimmed Mean ( 26 / 40 )96.86764705882354.6480571909634920.8404593745423
Trimmed Mean ( 27 / 40 )96.34848484848484.5439317573548221.2037702134358
Trimmed Mean ( 28 / 40 )95.8281254.4346307338699321.6090427254976
Trimmed Mean ( 29 / 40 )95.29032258064524.3144136996890622.0865056560322
Trimmed Mean ( 30 / 40 )94.78333333333334.1969919054739622.5836350100441
Trimmed Mean ( 31 / 40 )94.3965517241384.10921232424122.9719333720663
Trimmed Mean ( 32 / 40 )94.05357142857144.0381636918103423.2911735646869
Trimmed Mean ( 33 / 40 )93.68518518518523.9572156382132423.674521115429
Trimmed Mean ( 34 / 40 )93.38461538461543.8830134235509024.0495216468291
Trimmed Mean ( 35 / 40 )93.063.807876905916524.4388151978883
Trimmed Mean ( 36 / 40 )92.70833333333333.7316879527044224.8435385027695
Trimmed Mean ( 37 / 40 )92.36956521739133.6565550556536525.2613631714836
Trimmed Mean ( 38 / 40 )92.02272727272733.5636004307417425.8229644600120
Trimmed Mean ( 39 / 40 )91.59523809523813.4500011822801826.5493352772421
Trimmed Mean ( 40 / 40 )91.1253.3118256449523627.5150354424262
Median89
Midrange120
Midmean - Weighted Average at Xnp94.032786885246
Midmean - Weighted Average at X(n+1)p94.7833333333333
Midmean - Empirical Distribution Function94.032786885246
Midmean - Empirical Distribution Function - Averaging94.7833333333333
Midmean - Empirical Distribution Function - Interpolation94.7833333333333
Midmean - Closest Observation94.032786885246
Midmean - True Basic - Statistics Graphics Toolkit94.7833333333333
Midmean - MS Excel (old versions)95.2903225806452
Number of observations120
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jul/11/t12788557808efj6paszf8insa/1exe31278855694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/11/t12788557808efj6paszf8insa/1exe31278855694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jul/11/t12788557808efj6paszf8insa/276vo1278855694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jul/11/t12788557808efj6paszf8insa/276vo1278855694.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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