Mini-Tutorial 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: Mon, 15 Nov 2010 22:47:45 +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/Nov/15/t1289861175lh22by21s0i8f7p.htm/, Retrieved Mon, 15 Nov 2010 23:46:17 +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/Nov/15/t1289861175lh22by21s0i8f7p.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:

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Dataseries X:

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3 4 3 1 3 4 3 4 3 4 3 3 4 4 4 3 4 4 4 3 4 3 1 2 4 3 4 4 4 3 3 4 4 3 3 4 3 4 3 3 4 3 2 2 4 3 4 4 2 3 4 3 3 4 3 3 3 4 4 3 4 4 4 3 3 2 4 4 4 2 4 4 3 4 2 3 3 3 4 4 4 4 3 3 4 3 4 3 3 3 4 4 4 4 4 3 2 4 4 3 3 4 3 2 4 2 4 4 4 4 3 3 3 4 3 4 3 2 3 4 3 3 4 4 4 4 3 4 3 4 4 3 4 2 3 4 4 3 3 4 4 3 3 2 3 4 4 2 2 4 4 4 4

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3.37254901960784 0.0578260806392441 58.3222826504177 Geometric Mean 3.27854839280002 Harmonic Mean 3.15463917525773 Quadratic Mean 3.44707889976085 Winsorized Mean ( 1 / 51 ) 3.37254901960784 0.0578260806392441 58.3222826504177 Winsorized Mean ( 2 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 3 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 4 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 5 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 6 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 7 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 8 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 9 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 10 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 11 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 12 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 13 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 14 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 15 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 16 / 51 ) 3.38562091503268 0.0549604910214374 61.6009946801988 Winsorized Mean ( 17 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 18 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 19 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 20 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 21 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 22 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 23 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 24 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 25 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 26 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 27 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 28 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 29 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 30 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 31 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 32 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 33 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 34 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 35 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 36 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 37 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 38 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 39 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 40 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 41 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 42 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 43 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 44 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 45 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 46 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 47 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 48 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 49 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 50 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Winsorized Mean ( 51 / 51 ) 3.49673202614379 0.0405544890391858 86.2230571507157 Trimmed Mean ( 1 / 51 ) 3.3841059602649 0.0562719093675444 60.1384598159154 Trimmed Mean ( 2 / 51 ) 3.39597315436242 0.0545572286479298 62.2460714835316 Trimmed Mean ( 3 / 51 ) 3.40136054421769 0.0543168310804706 62.6207471341352 Trimmed Mean ( 4 / 51 ) 3.40689655172414 0.0540474388299253 63.0353005707606 Trimmed Mean ( 5 / 51 ) 3.41258741258741 0.0537463531284278 63.4943063845276 Trimmed Mean ( 6 / 51 ) 3.41843971631206 0.053410558675166 64.0030698256207 Trimmed Mean ( 7 / 51 ) 3.41843971631206 0.0530366748758623 64.4542615899896 Trimmed Mean ( 8 / 51 ) 3.43065693430657 0.0526208972519826 65.1957133660869 Trimmed Mean ( 9 / 51 ) 3.43703703703704 0.0521589264704335 65.8954711996486 Trimmed Mean ( 10 / 51 ) 3.44360902255639 0.0516458816127508 66.6773209212911 Trimmed Mean ( 11 / 51 ) 3.45038167938931 0.0510761931367766 67.5536187700904 Trimmed Mean ( 12 / 51 ) 3.45736434108527 0.0504434693210092 68.5393845352606 Trimmed Mean ( 13 / 51 ) 3.46456692913386 0.0497403275652223 69.6530782711659 Trimmed Mean ( 14 / 51 ) 3.46456692913386 0.0489581783342319 70.7658464226683 Trimmed Mean ( 15 / 51 ) 3.47967479674797 0.0480869440816827 72.3621528296169 Trimmed Mean ( 16 / 51 ) 3.48760330578512 0.0471146869875677 74.0236968295133 Trimmed Mean ( 17 / 51 ) 3.49579831932773 0.046027105672703 75.950861307383 Trimmed Mean ( 18 / 51 ) 3.49572649572650 0.046422138851283 75.3030037440829 Trimmed Mean ( 19 / 51 ) 3.49565217391304 0.0468275200620392 74.6495259471748 Trimmed Mean ( 20 / 51 ) 3.49557522123894 0.0472437090797846 73.9902791149538 Trimmed Mean ( 21 / 51 ) 3.49549549549550 0.0476711947939566 73.32510776379 Trimmed Mean ( 22 / 51 ) 3.4954128440367 0.048110497622484 72.6538493005141 Trimmed Mean ( 23 / 51 ) 3.49532710280374 0.0485621721748283 71.9763335589734 Trimmed Mean ( 24 / 51 ) 3.49523809523810 0.0490268101951762 71.2923822970232 Trimmed Mean ( 25 / 51 ) 3.49514563106796 0.0495050438212892 70.6018086497462 Trimmed Mean ( 26 / 51 ) 3.49504950495050 0.0499975491998123 69.9044165341532 Trimmed Mean ( 27 / 51 ) 3.49494949494949 0.0505050505050505 69.2 Trimmed Mean ( 28 / 51 ) 3.49494949494949 0.0510283244155241 68.4903832328511 Trimmed Mean ( 29 / 51 ) 3.49473684210526 0.0515682051112248 67.7692162170013 Trimmed Mean ( 30 / 51 ) 3.49462365591398 0.0521255898646917 67.0423810068216 Trimmed Mean ( 31 / 51 ) 3.49450549450549 0.0527014453111288 66.3075836701498 Trimmed Mean ( 32 / 51 ) 3.49438202247191 0.0532968144972199 65.5645568208244 Trimmed Mean ( 33 / 51 ) 3.49425287356322 0.0539128248255567 64.8130177721056 Trimmed Mean ( 34 / 51 ) 3.49411764705882 0.0545506970323277 64.0526672828424 Trimmed Mean ( 35 / 51 ) 3.49397590361446 0.0552117553609137 63.2831881684378 Trimmed Mean ( 36 / 51 ) 3.49382716049383 0.055897439124305 62.5042437583631 Trimmed Mean ( 37 / 51 ) 3.49367088607595 0.0566093158860706 61.7154761789942 Trimmed Mean ( 38 / 51 ) 3.49350649350649 0.0573490965345964 60.9165044369792 Trimmed Mean ( 39 / 51 ) 3.49333333333333 0.0581186525805423 60.1069222740872 Trimmed Mean ( 40 / 51 ) 3.49315068493151 0.0589200360756344 59.2862957593478 Trimmed Mean ( 41 / 51 ) 3.49295774647887 0.0597555026354829 58.4541605780879 Trimmed Mean ( 42 / 51 ) 3.49275362318841 0.0606275381546432 57.6100189699178 Trimmed Mean ( 43 / 51 ) 3.49253731343284 0.061538889934592 56.7533362585019 Trimmed Mean ( 44 / 51 ) 3.49230769230769 0.0624926031125843 55.8835369046171 Trimmed Mean ( 45 / 51 ) 3.49206349206349 0.0634920634920635 55 Trimmed Mean ( 46 / 51 ) 3.49180327868852 0.0645410481476378 54.1020541020811 Trimmed Mean ( 47 / 51 ) 3.49152542372881 0.0656437855289393 53.1889712879152 Trimmed Mean ( 48 / 51 ) 3.49122807017544 0.0668050272444203 52.2599602781696 Trimmed Mean ( 49 / 51 ) 3.49122807017544 0.0680301343049808 51.3188472409032 Trimmed Mean ( 50 / 51 ) 3.49056603773585 0.0693251813995239 50.3506224905431 Trimmed Mean ( 51 / 51 ) 3.49019607843137 0.0706970838326272 49.3683174640454 Median 3 Midrange 2.5 Midmean - Weighted Average at Xnp 3.55882352941176 Midmean - Weighted Average at X(n+1)p 3.55882352941176 Midmean - Empirical Distribution Function 3.55882352941176 Midmean - Empirical Distribution Function - Averaging 3.55882352941176 Midmean - Empirical Distribution Function - Interpolation 3.55882352941176 Midmean - Closest Observation 3.55882352941176 Midmean - True Basic - Statistics Graphics Toolkit 3.55882352941176 Midmean - MS Excel (old versions) 3.55882352941176 Number of observations 153

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289861175lh22by21s0i8f7p/11byt1289861262.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/15/t1289861175lh22by21s0i8f7p/11byt1289861262.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/15/t1289861175lh22by21s0i8f7p/21byt1289861262.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/15/t1289861175lh22by21s0i8f7p/21byt1289861262.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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