Winsorized & trimmed mean

*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Sat, 18 Dec 2010 17:27:55 +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/Dec/18/t1292693283zmh7po3of336eaz.htm/, Retrieved Sat, 18 Dec 2010 18:28:03 +0100

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/Dec/18/t1292693283zmh7po3of336eaz.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:

Dataseries X:

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13 16 19 15 14 13 19 15 14 15 16 16 16 17 15 15 20 18 16 16 19 16 17 17 16 15 14 15 12 14 16 14 7 10 14 16 16 16 14 20 14 14 11 15 16 14 16 14 12 16 9 14 16 16 15 16 12 16 16 14 16 17 18 18 12 16 10 14 18 18 16 16 16 13 16 16 20 16 15 15 16 14 15 12 17 16 15 13 16 16 16 16 14 16 16 20 15 16 13 17 16 12 16 16 17 13 12 18 14 14 13 16 13 16 13 16 15 16 15 17 15 12 16 10 16 14 15 13 15 11 12 8 16 15 17 16 10 18 13 15 16 16 14 10 17 13 15 16 12 13

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 14.96 0.185583305582593 80.6106990768205 Geometric Mean 14.7676609687896 Harmonic Mean 14.5463336247130 Quadratic Mean 15.130543061415 Winsorized Mean ( 1 / 50 ) 14.9666666666667 0.18377514387111 81.4401031140723 Winsorized Mean ( 2 / 50 ) 14.98 0.180595584388631 82.9477644800214 Winsorized Mean ( 3 / 50 ) 15 0.176467956290414 85.0012677390248 Winsorized Mean ( 4 / 50 ) 14.9733333333333 0.171829650481194 87.1405679485574 Winsorized Mean ( 5 / 50 ) 14.9733333333333 0.171829650481194 87.1405679485574 Winsorized Mean ( 6 / 50 ) 14.9733333333333 0.171829650481194 87.1405679485574 Winsorized Mean ( 7 / 50 ) 14.9266666666667 0.165232306580634 90.3374586699385 Winsorized Mean ( 8 / 50 ) 14.98 0.155285693263863 96.4673543656456 Winsorized Mean ( 9 / 50 ) 14.98 0.155285693263863 96.4673543656456 Winsorized Mean ( 10 / 50 ) 15.0466666666667 0.144809267957899 103.906793251943 Winsorized Mean ( 11 / 50 ) 15.0466666666667 0.144809267957899 103.906793251943 Winsorized Mean ( 12 / 50 ) 15.0466666666667 0.144809267957899 103.906793251943 Winsorized Mean ( 13 / 50 ) 15.0466666666667 0.144809267957899 103.906793251943 Winsorized Mean ( 14 / 50 ) 14.9533333333333 0.133557976306353 111.961364995780 Winsorized Mean ( 15 / 50 ) 14.9533333333333 0.133557976306353 111.961364995780 Winsorized Mean ( 16 / 50 ) 14.9533333333333 0.133557976306353 111.961364995780 Winsorized Mean ( 17 / 50 ) 14.9533333333333 0.133557976306353 111.961364995780 Winsorized Mean ( 18 / 50 ) 14.9533333333333 0.133557976306353 111.961364995780 Winsorized Mean ( 19 / 50 ) 14.9533333333333 0.133557976306353 111.961364995780 Winsorized Mean ( 20 / 50 ) 15.0866666666667 0.115445510614118 130.682142479273 Winsorized Mean ( 21 / 50 ) 15.0866666666667 0.115445510614118 130.682142479273 Winsorized Mean ( 22 / 50 ) 15.0866666666667 0.115445510614118 130.682142479273 Winsorized Mean ( 23 / 50 ) 15.0866666666667 0.115445510614118 130.682142479273 Winsorized Mean ( 24 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 25 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 26 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 27 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 28 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 29 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 30 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 31 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 32 / 50 ) 14.9266666666667 0.100600731032461 148.375330014752 Winsorized Mean ( 33 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 34 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 35 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 36 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 37 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 38 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 39 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 40 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 41 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 42 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 43 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 44 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 45 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 46 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 47 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 48 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 49 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Winsorized Mean ( 50 / 50 ) 15.1466666666667 0.0747174643440306 202.719227688523 Trimmed Mean ( 1 / 50 ) 14.9797297297297 0.176914992990591 84.671906413983 Trimmed Mean ( 2 / 50 ) 14.9931506849315 0.169329047825954 88.5444693478834 Trimmed Mean ( 3 / 50 ) 15 0.162834736819732 92.1179368294486 Trimmed Mean ( 4 / 50 ) 15 0.157393614784805 95.3024684038717 Trimmed Mean ( 5 / 50 ) 15.0071428571429 0.152908233626357 98.1447663165997 Trimmed Mean ( 6 / 50 ) 15.0144927536232 0.147973906757126 101.467164601303 Trimmed Mean ( 7 / 50 ) 15.0220588235294 0.142521225635005 105.402256797880 Trimmed Mean ( 8 / 50 ) 15.0373134328358 0.137880258991412 109.060670054097 Trimmed Mean ( 9 / 50 ) 15.0454545454545 0.134695635497317 111.699644089465 Trimmed Mean ( 10 / 50 ) 15.0538461538462 0.131189475222852 114.748886130340 Trimmed Mean ( 11 / 50 ) 15.0546875 0.129024101311507 116.681204108161 Trimmed Mean ( 12 / 50 ) 15.0555555555556 0.126644386790206 118.880559471585 Trimmed Mean ( 13 / 50 ) 15.0564516129032 0.124023814449464 121.399681825124 Trimmed Mean ( 14 / 50 ) 15.0573770491803 0.121130910633449 124.306644525649 Trimmed Mean ( 15 / 50 ) 15.0666666666667 0.119366519648819 126.221881235990 Trimmed Mean ( 16 / 50 ) 15.0762711864407 0.117408876246647 128.408274300907 Trimmed Mean ( 17 / 50 ) 15.0862068965517 0.115233265487223 130.918852579288 Trimmed Mean ( 18 / 50 ) 15.0964912280702 0.112810353191718 133.821859438859 Trimmed Mean ( 19 / 50 ) 15.1071428571429 0.110104915785969 137.206797256077 Trimmed Mean ( 20 / 50 ) 15.1181818181818 0.107074072855514 141.193674761792 Trimmed Mean ( 21 / 50 ) 15.1203703703704 0.105833317055945 142.869663268492 Trimmed Mean ( 22 / 50 ) 15.1226415094340 0.104441207825005 144.795735556529 Trimmed Mean ( 23 / 50 ) 15.125 0.102878202601791 147.018509436291 Trimmed Mean ( 24 / 50 ) 15.1274509803922 0.101121231792389 149.597178676088 Trimmed Mean ( 25 / 50 ) 15.14 0.100523880272553 150.610978793801 Trimmed Mean ( 26 / 50 ) 15.1530612244898 0.099812617218106 151.815087579339 Trimmed Mean ( 27 / 50 ) 15.1666666666667 0.0989713172460936 153.243051509101 Trimmed Mean ( 28 / 50 ) 15.1808510638298 0.0979809509468221 154.936759820478 Trimmed Mean ( 29 / 50 ) 15.1956521739130 0.0968188846503415 156.949258698772 Trimmed Mean ( 30 / 50 ) 15.2111111111111 0.0954579532310812 159.348808519795 Trimmed Mean ( 31 / 50 ) 15.2272727272727 0.0938652081762732 162.224886335700 Trimmed Mean ( 32 / 50 ) 15.2441860465116 0.092000188115593 165.697335611512 Trimmed Mean ( 33 / 50 ) 15.2619047619048 0.0898124641702 169.930809747994 Trimmed Mean ( 34 / 50 ) 15.2682926829268 0.0902483783487627 169.180798173712 Trimmed Mean ( 35 / 50 ) 15.275 0.0906638666110196 168.479467851677 Trimmed Mean ( 36 / 50 ) 15.2820512820513 0.0910541292018138 167.834796906134 Trimmed Mean ( 37 / 50 ) 15.2894736842105 0.09141344189553 167.256295870402 Trimmed Mean ( 38 / 50 ) 15.2972972972973 0.091734953207778 166.755383443094 Trimmed Mean ( 39 / 50 ) 15.3055555555556 0.0920104285970553 166.345878276296 Trimmed Mean ( 40 / 50 ) 15.3142857142857 0.0922299249992391 166.044651065390 Trimmed Mean ( 41 / 50 ) 15.3235294117647 0.0923813727394815 165.87250175398 Trimmed Mean ( 42 / 50 ) 15.3333333333333 0.0924500327042048 165.855358671344 Trimmed Mean ( 43 / 50 ) 15.34375 0.092417783066811 166.025947505229 Trimmed Mean ( 44 / 50 ) 15.3548387096774 0.0922621692570532 166.426161809583 Trimmed Mean ( 45 / 50 ) 15.3666666666667 0.0919551188323559 167.110508493625 Trimmed Mean ( 46 / 50 ) 15.3793103448276 0.091461171655996 168.151250048188 Trimmed Mean ( 47 / 50 ) 15.3928571428571 0.0907349909901436 169.646318083938 Trimmed Mean ( 48 / 50 ) 15.4074074074074 0.0897177752083877 171.731937975731 Trimmed Mean ( 49 / 50 ) 15.4230769230769 0.088331926820046 174.603651004891 Trimmed Mean ( 50 / 50 ) 15.44 0.0864728340024089 178.553185842965 Median 15.5 Midrange 13.5 Midmean - Weighted Average at Xnp 15.3333333333333 Midmean - Weighted Average at X(n+1)p 15.3333333333333 Midmean - Empirical Distribution Function 15.3333333333333 Midmean - Empirical Distribution Function - Averaging 15.3333333333333 Midmean - Empirical Distribution Function - Interpolation 15.3333333333333 Midmean - Closest Observation 15.3333333333333 Midmean - True Basic - Statistics Graphics Toolkit 15.3333333333333 Midmean - MS Excel (old versions) 15.3333333333333 Number of observations 150

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292693283zmh7po3of336eaz/1b2hz1292693272.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292693283zmh7po3of336eaz/1b2hz1292693272.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292693283zmh7po3of336eaz/2mugk1292693272.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292693283zmh7po3of336eaz/2mugk1292693272.ps (open in new window)

Parameters (Session):

par1 = 20 ;

Parameters (R input):

par1 = 20 ;

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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