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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 25 Jan 2017 10:08:39 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/25/t1485335333mramrz0hxxn1r27.htm/, Retrieved Tue, 14 May 2024 08:38:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=305909, Retrieved Tue, 14 May 2024 08:38:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vraag 3] [2017-01-25 09:08:39] [2a3a89286ec83ecc146a1d371615e68b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.2
0
3
0
3.7
0
3.6
0
3.8
0
3.7
0
2.8
0
4.3
0
3.6
0
3.3
0

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305909&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=305909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305909&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.750.4070114.29964
Geometric Mean0
Harmonic Mean0
Quadratic Mean2.49199
Winsorized Mean ( 1 / 6 )1.7250.3994654.31827
Winsorized Mean ( 2 / 6 )1.7150.3967814.32228
Winsorized Mean ( 3 / 6 )1.7150.3967814.32228
Winsorized Mean ( 4 / 6 )1.6950.3915884.32853
Winsorized Mean ( 5 / 6 )1.6950.3915884.32853
Winsorized Mean ( 6 / 6 )1.6050.3691724.34756
Trimmed Mean ( 1 / 6 )1.705560.4175464.08471
Trimmed Mean ( 2 / 6 )1.681250.4380093.83839
Trimmed Mean ( 3 / 6 )1.657140.4637063.57369
Trimmed Mean ( 4 / 6 )1.6250.4939213.29
Trimmed Mean ( 5 / 6 )1.590.5338442.9784
Trimmed Mean ( 6 / 6 )1.53750.5833822.63549
Median1.4
Midrange2.15
Midmean - Weighted Average at Xnp1.21875
Midmean - Weighted Average at X(n+1)p1.21875
Midmean - Empirical Distribution Function1.21875
Midmean - Empirical Distribution Function - Averaging1.21875
Midmean - Empirical Distribution Function - Interpolation1.21875
Midmean - Closest Observation1.21875
Midmean - True Basic - Statistics Graphics Toolkit1.21875
Midmean - MS Excel (old versions)1.21875
Number of observations20

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.75 & 0.407011 & 4.29964 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.49199 &  &  \tabularnewline
Winsorized Mean ( 1 / 6 ) & 1.725 & 0.399465 & 4.31827 \tabularnewline
Winsorized Mean ( 2 / 6 ) & 1.715 & 0.396781 & 4.32228 \tabularnewline
Winsorized Mean ( 3 / 6 ) & 1.715 & 0.396781 & 4.32228 \tabularnewline
Winsorized Mean ( 4 / 6 ) & 1.695 & 0.391588 & 4.32853 \tabularnewline
Winsorized Mean ( 5 / 6 ) & 1.695 & 0.391588 & 4.32853 \tabularnewline
Winsorized Mean ( 6 / 6 ) & 1.605 & 0.369172 & 4.34756 \tabularnewline
Trimmed Mean ( 1 / 6 ) & 1.70556 & 0.417546 & 4.08471 \tabularnewline
Trimmed Mean ( 2 / 6 ) & 1.68125 & 0.438009 & 3.83839 \tabularnewline
Trimmed Mean ( 3 / 6 ) & 1.65714 & 0.463706 & 3.57369 \tabularnewline
Trimmed Mean ( 4 / 6 ) & 1.625 & 0.493921 & 3.29 \tabularnewline
Trimmed Mean ( 5 / 6 ) & 1.59 & 0.533844 & 2.9784 \tabularnewline
Trimmed Mean ( 6 / 6 ) & 1.5375 & 0.583382 & 2.63549 \tabularnewline
Median & 1.4 &  &  \tabularnewline
Midrange & 2.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.21875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.21875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.21875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.21875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.21875 &  &  \tabularnewline
Midmean - Closest Observation & 1.21875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.21875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.21875 &  &  \tabularnewline
Number of observations & 20 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305909&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.75[/C][C]0.407011[/C][C]4.29964[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.49199[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 6 )[/C][C]1.725[/C][C]0.399465[/C][C]4.31827[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 6 )[/C][C]1.715[/C][C]0.396781[/C][C]4.32228[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 6 )[/C][C]1.715[/C][C]0.396781[/C][C]4.32228[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 6 )[/C][C]1.695[/C][C]0.391588[/C][C]4.32853[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 6 )[/C][C]1.695[/C][C]0.391588[/C][C]4.32853[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 6 )[/C][C]1.605[/C][C]0.369172[/C][C]4.34756[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 6 )[/C][C]1.70556[/C][C]0.417546[/C][C]4.08471[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 6 )[/C][C]1.68125[/C][C]0.438009[/C][C]3.83839[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 6 )[/C][C]1.65714[/C][C]0.463706[/C][C]3.57369[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 6 )[/C][C]1.625[/C][C]0.493921[/C][C]3.29[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 6 )[/C][C]1.59[/C][C]0.533844[/C][C]2.9784[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 6 )[/C][C]1.5375[/C][C]0.583382[/C][C]2.63549[/C][/ROW]
[ROW][C]Median[/C][C]1.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]20[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305909&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.750.4070114.29964
Geometric Mean0
Harmonic Mean0
Quadratic Mean2.49199
Winsorized Mean ( 1 / 6 )1.7250.3994654.31827
Winsorized Mean ( 2 / 6 )1.7150.3967814.32228
Winsorized Mean ( 3 / 6 )1.7150.3967814.32228
Winsorized Mean ( 4 / 6 )1.6950.3915884.32853
Winsorized Mean ( 5 / 6 )1.6950.3915884.32853
Winsorized Mean ( 6 / 6 )1.6050.3691724.34756
Trimmed Mean ( 1 / 6 )1.705560.4175464.08471
Trimmed Mean ( 2 / 6 )1.681250.4380093.83839
Trimmed Mean ( 3 / 6 )1.657140.4637063.57369
Trimmed Mean ( 4 / 6 )1.6250.4939213.29
Trimmed Mean ( 5 / 6 )1.590.5338442.9784
Trimmed Mean ( 6 / 6 )1.53750.5833822.63549
Median1.4
Midrange2.15
Midmean - Weighted Average at Xnp1.21875
Midmean - Weighted Average at X(n+1)p1.21875
Midmean - Empirical Distribution Function1.21875
Midmean - Empirical Distribution Function - Averaging1.21875
Midmean - Empirical Distribution Function - Interpolation1.21875
Midmean - Closest Observation1.21875
Midmean - True Basic - Statistics Graphics Toolkit1.21875
Midmean - MS Excel (old versions)1.21875
Number of observations20


Figures (Output of Computation)

Input Parameters & R Code

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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')