R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(112,118,129,99,116,168,118,129,205,147,150,267,126,129,124,97,102,127,222,214,118,141,154,226,89,77,82,97,127,121,117,117,106,112,134,169,75,108,115,85,101,108,109,124,105,95,135,164,88,85,112,87,91,87,87,142,95,108,139,159,61,82,124,93,108,75,87,103,90,108,123,129,57,65,67,71,76,67,110,118,99,85,107,141,58,65,70,86,93,74,87,73,101,100,96,157,63,115,70,66,67,83,79,77,102,116,100,135,71,60,89,74,73,91,86,74,87,87,109,137,43,69,73,77,69,76,78,70,83,65,110,132,54,55,66,65,60,65,96,55,71,63,74,106,34,47,56,53,53,55,67,52,46,51,58,91,33,40,46,45,41,55,57,54,46,52,48,77,30,35,42,48,44,45,46)
> 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: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.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] 92.73714
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 2.933415
> (armose <- arm / armse)
[1] 31.61406
> (geo <- geomean(x))
[1] 85.50535
> (har <- harmean(x))
[1] 78.77265
> (qua <- quamean(x))
[1] 100.486
> (win <- winmean(x))
          [,1]     [,2]
 [1,] 92.52000 2.859810
 [2,] 92.48571 2.846342
 [3,] 92.36571 2.809324
 [4,] 92.27429 2.746491
 [5,] 91.27429 2.529931
 [6,] 91.27429 2.520021
 [7,] 91.15429 2.488085
 [8,] 90.97143 2.445510
 [9,] 90.92000 2.423590
[10,] 90.74857 2.397159
[11,] 90.56000 2.352968
[12,] 90.35429 2.323621
[13,] 89.98286 2.273160
[14,] 89.90286 2.262708
[15,] 89.98857 2.253230
[16,] 89.89714 2.219736
[17,] 89.70286 2.195357
[18,] 89.80571 2.137163
[19,] 89.91429 2.125934
[20,] 89.80000 2.112097
[21,] 89.68000 2.071292
[22,] 89.30286 2.027925
[23,] 89.43429 2.014520
[24,] 89.43429 2.014520
[25,] 89.57714 2.000203
[26,] 89.28000 1.966996
[27,] 89.28000 1.966996
[28,] 89.12000 1.949481
[29,] 88.95429 1.897260
[30,] 89.12571 1.880286
[31,] 89.12571 1.880286
[32,] 89.12571 1.843029
[33,] 88.74857 1.803727
[34,] 88.55429 1.707140
[35,] 88.55429 1.707140
[36,] 88.76000 1.687527
[37,] 89.18286 1.648228
[38,] 88.96571 1.626563
[39,] 89.41143 1.586399
[40,] 89.18286 1.563712
[41,] 89.18286 1.563712
[42,] 88.94286 1.540215
[43,] 88.94286 1.540215
[44,] 88.44000 1.445736
[45,] 88.44000 1.445736
[46,] 88.70286 1.422486
[47,] 88.16571 1.372641
[48,] 88.16571 1.372641
[49,] 87.88571 1.347231
[50,] 88.45714 1.297129
[51,] 88.16571 1.270793
[52,] 88.46286 1.245254
[53,] 88.46286 1.245254
[54,] 88.46286 1.245254
[55,] 88.77714 1.218687
[56,] 88.45714 1.189851
[57,] 88.13143 1.160855
[58,] 88.79429 1.105511
> (tri <- trimean(x))
          [,1]     [,2]
 [1,] 92.09249 2.765931
 [2,] 91.65497 2.663237
 [3,] 91.22485 2.558442
 [4,] 90.82635 2.458676
 [5,] 90.44242 2.369574
 [6,] 90.26380 2.329692
 [7,] 90.08075 2.288745
 [8,] 89.91195 2.250660
 [9,] 89.76433 2.216907
[10,] 89.61935 2.183866
[11,] 89.49020 2.152033
[12,] 89.37748 2.123655
[13,] 89.28188 2.096724
[14,] 89.21769 2.073716
[15,] 89.15862 2.049943
[16,] 89.09091 2.025128
[17,] 89.02837 2.001746
[18,] 88.97842 1.978839
[19,] 88.91971 1.959664
[20,] 88.85185 1.939737
[21,] 88.78947 1.919253
[22,] 88.73282 1.900639
[23,] 88.69767 1.884202
[24,] 88.65354 1.867247
[25,] 88.60800 1.848518
[26,] 88.55285 1.829068
[27,] 88.51240 1.810557
[28,] 88.47059 1.790033
[29,] 88.47059 1.768856
[30,] 88.40870 1.749965
[31,] 88.40870 1.730371
[32,] 88.33333 1.708500
[33,] 88.29358 1.687399
[34,] 88.27103 1.667343
[35,] 88.25714 1.653281
[36,] 88.24272 1.637328
[37,] 88.21782 1.620940
[38,] 88.17172 1.605690
[39,] 88.13402 1.590256
[40,] 88.07368 1.576013
[41,] 88.02151 1.561725
[42,] 87.96703 1.545204
[43,] 87.92135 1.528435
[44,] 87.87356 1.509022
[45,] 87.87356 1.495887
[46,] 87.81928 1.480418
[47,] 87.77778 1.464498
[48,] 87.75949 1.450941
[49,] 87.74026 1.434775
[50,] 87.73333 1.418327
[51,] 87.69863 1.404045
[52,] 87.67606 1.389784
[53,] 87.63768 1.375243
[54,] 87.59701 1.357436
[55,] 87.55385 1.335721
[56,] 87.49206 1.312602
[57,] 87.44262 1.288564
[58,] 87.44262 1.263413
> (midr <- midrange(x))
[1] 148.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 86.63043 87.23404 87.23404 87.23404 87.87356 86.63043 87.23404 87.23404
> postscript(file="/var/www/html/rcomp/tmp/1bmcr1268842854.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/2ryze1268842854.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 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> 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/3dcu51268842854.tab") 
> 
> try(system("convert tmp/1bmcr1268842854.ps tmp/1bmcr1268842854.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ryze1268842854.ps tmp/2ryze1268842854.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.910   0.333   1.199