R version 2.5.1 (2007-06-27)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(0.0257493744938832
+ ,0.021734532514729
+ ,0.0181409407214812
+ ,0.0152701505942662
+ ,0.0130169628370724
+ ,0.0113755336274530
+ ,0.0104102672587416
+ ,0.0100957980377989
+ ,0.0102701844619835
+ ,0.0107193845356072
+ ,0.0112601657760742
+ ,0.0117752995862039
+ ,0.0122043778163178
+ ,0.0125298799458765
+ ,0.0127639590477691
+ ,0.012937217037477
+ ,0.0130890257027324
+ ,0.0132543391742880
+ ,0.0134562040704081
+ ,0.0137014134900641
+ ,0.0139761760838112
+ ,0.014254906668871
+ ,0.0145009100196785
+ ,0.0146742460172555
+ ,0.0147425838993809
+ ,0.0146806157352704
+ ,0.0144813558459163
+ ,0.0141518828509622
+ ,0.0137166291746623
+ ,0.0132144865802642
+ ,0.0126954985073174
+ ,0.0122127590106538
+ ,0.0118197530780406
+ ,0.0115605302029674
+ ,0.0114653295564385
+ ,0.0115477666075857
+ ,0.0118008984086779
+ ,0.0122015373336842
+ ,0.0127161972913673
+ ,0.0133047190084541
+ ,0.0139270942039374
+ ,0.0145468382768111
+ ,0.0151326313986313
+ ,0.0156627183912659
+ ,0.0161249314936152
+ ,0.0165157734928721
+ ,0.0168385143727890
+ ,0.0171040905359246
+ ,0.0173246160284153
+ ,0.0175143229302128
+ ,0.0176871470530748
+ ,0.0178499332357475
+ ,0.0180101805121891
+ ,0.0181670326317408
+ ,0.0183152217343903
+ ,0.0184445154323164
+ ,0.0185417822082271
+ ,0.0185853019135757
+ ,0.0185546256675338
+ ,0.0184274237550889
+ ,0.0181815126038245
+ ,0.0178003184355686
+ ,0.0172750557804465
+ ,0.0166064564640451
+ ,0.0158060406733841
+ ,0.0148957772281856
+ ,0.0139084949432564
+ ,0.0128841617006653
+ ,0.0118732217969068
+ ,0.0109276070046339
+ ,0.0101118222886584
+ ,0.0094955906524746
+ ,0.00916083841819465
+ ,0.00919703433683982
+ ,0.00968438506916855
+ ,0.0106742913471305
+ ,0.0121649595096515
+ ,0.0140954137567437
+ ,0.0163422947029298
+ ,0.0187253547553665
+ ,0.0210153504000639
+ ,0.0229581518854807
+ ,0.0243101462873557
+ ,0.024886670194248
+ ,0.0246046329518060
+ ,0.0235246397989794
+ ,0.0218629790162297
+ ,0.0199805985887911
+ ,0.0183298783311204
+ ,0.0173304254644116
+ ,0.0171531920939682
+ ,0.0175490373660681
+ ,0.0179383444747054
+ ,0.0177538738190025
+ ,0.0168765909408637
+ ,0.0161209786732948
+ ,0.0174324825582754
+ ,0.0223196274919401
+ ,0.0295050170940449)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa, P., (2007), Central Tendency (v1.0.2) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_centraltendency.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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))
[1] 0.01557588
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.0004081118
> (armose <- arm / armse)
[1] 38.16571
> (geo <- geomean(x))
[1] 0.01508576
> (har <- harmean(x))
[1] 0.01462557
> (qua <- quamean(x))
[1] 0.01609131
> (win <- winmean(x))
            [,1]         [,2]
 [1,] 0.01553831 0.0003964379
 [2,] 0.01552691 0.0003910512
 [3,] 0.01552408 0.0003880977
 [4,] 0.01552881 0.0003828042
 [5,] 0.01548995 0.0003736876
 [6,] 0.01546521 0.0003649206
 [7,] 0.01542997 0.0003542720
 [8,] 0.01541440 0.0003440371
 [9,] 0.01540682 0.0003412401
[10,] 0.01535521 0.0003249651
[11,] 0.01527719 0.0003004328
[12,] 0.01513902 0.0002761871
[13,] 0.01513242 0.0002721476
[14,] 0.01513974 0.0002699940
[15,] 0.01513973 0.0002694808
[16,] 0.01515872 0.0002628328
[17,] 0.01516018 0.0002618824
[18,] 0.01514588 0.0002591930
[19,] 0.01515332 0.0002575017
[20,] 0.01518525 0.0002466185
[21,] 0.01518994 0.0002452707
[22,] 0.01518477 0.0002444755
[23,] 0.01515634 0.0002405193
[24,] 0.01521580 0.0002290031
[25,] 0.01523530 0.0002213513
[26,] 0.01522770 0.0002191495
[27,] 0.01522806 0.0002161161
[28,] 0.01524319 0.0002099427
[29,] 0.01521827 0.0002033937
[30,] 0.01523192 0.0001994120
[31,] 0.01522886 0.0001938797
[32,] 0.01523642 0.0001855277
[33,] 0.01524777 0.0001838310
> (tri <- trimean(x))
            [,1]         [,2]
 [1,] 0.01549841 0.0003849849
 [2,] 0.01545684 0.0003719157
 [3,] 0.01541954 0.0003602863
 [4,] 0.01538163 0.0003482440
 [5,] 0.01534070 0.0003362325
 [6,] 0.01530673 0.0003251482
 [7,] 0.01527597 0.0003146773
 [8,] 0.01524973 0.0003051306
 [9,] 0.01522457 0.0002963120
[10,] 0.01519919 0.0002866221
[11,] 0.01517914 0.0002785683
[12,] 0.01516737 0.0002736784
[13,] 0.01517057 0.0002719288
[14,] 0.01517466 0.0002703548
[15,] 0.01517824 0.0002686705
[16,] 0.01518204 0.0002665950
[17,] 0.01518426 0.0002649539
[18,] 0.01518648 0.0002629487
[19,] 0.01519014 0.0002607535
[20,] 0.01519339 0.0002581706
[21,] 0.01519410 0.0002564843
[22,] 0.01519446 0.0002543820
[23,] 0.01519528 0.0002516758
[24,] 0.01519857 0.0002487201
[25,] 0.01519712 0.0002466777
[26,] 0.01519390 0.0002450462
[27,] 0.01519390 0.0002429721
[28,] 0.01518788 0.0002404671
[29,] 0.01518311 0.0002379748
[30,] 0.01518003 0.0002355607
[31,] 0.01517541 0.0002326662
[32,] 0.01517053 0.0002294636
[33,] 0.01516435 0.0002264791
> (midr <- midrange(x))
[1] 0.01933293
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 0.01514377 0.01519857 0.01519857 0.01519857 0.01519712 0.01514377 0.01519857
[8] 0.01519857
> postscript(file="/var/www/html/rcomp/tmp/12psv1192985821.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> 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()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2cotz1192985821.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> 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()
null device 
          1 
> load(file='/var/www/html/rcomp/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="/var/www/html/rcomp/tmp/3qsjy1192985822.tab") 
> 
> system("convert tmp/12psv1192985821.ps tmp/12psv1192985821.png")
> system("convert tmp/2cotz1192985821.ps tmp/2cotz1192985821.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.917   0.327   1.007