R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(80,111,122,131,192,188,216,238,173,160,93,67,60,32,126,131,134,162,230,232,200,143,85,66,54,81,100,126,204,218,227,220,220,120,110,67,81,52,106,156,187,204,204,196,204,124,53,77,77,50,105,125,165,194,263,225,263,140,127,86,71,95,95,133,178,160,250,251,250,173,103,21,29,39,71,148,144,199,206,224,206,152,88,35,23,92,117,120,173,202,217,256,217,143,95,77,76,100,108,132,195,198,204,212,204,129,73,77,80,64,109,138,185,198,237,223,237,146,102,77,70,86,98,141,195,205,191,226,191,147,100,74,56,77,80,120,186,196,229,229,229,176,104,61,72,99,113,140,174,209,205,229,215,136,113,57,55,66,125,149,176,230,238,245,238,124,111,72,63,78,100,149,166,201,214,231,214,151,97,68,81,55,99,146,170,218,218,207,218,178,105,67,47,55,73,124,185,213,278,205,278,171,125,92,96,92,118,185,183,215,207,214,207,142,102,66,87,90,90,133,205,201,220,210,220,136,95,52,40,60,100,169,184,202,226,239,226,149,121,50)
> 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] 145.2917
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 4.103515
> (armose <- arm / armse)
[1] 35.40664
> (geo <- geomean(x))
[1] 129.113
> (har <- harmean(x))
[1] 110.6902
> (qua <- quamean(x))
[1] 158.5375
> (win <- winmean(x))
          [,1]     [,2]
 [1,] 145.3000 4.102467
 [2,] 145.2250 4.080360
 [3,] 145.2625 4.075945
 [4,] 145.1958 4.056478
 [5,] 145.1750 4.035487
 [6,] 145.1750 4.030014
 [7,] 145.3792 4.008382
 [8,] 145.3125 3.980403
 [9,] 145.0875 3.957443
[10,] 145.1292 3.945017
[11,] 145.1292 3.945017
[12,] 145.1792 3.940101
[13,] 145.1792 3.929503
[14,] 145.2375 3.923865
[15,] 144.9250 3.893954
[16,] 144.8583 3.887745
[17,] 144.8583 3.874381
[18,] 144.9333 3.867215
[19,] 145.0917 3.837635
[20,] 145.0917 3.837635
[21,] 145.1792 3.829552
[22,] 145.3625 3.812836
[23,] 145.2667 3.786751
[24,] 145.3667 3.759937
[25,] 145.3667 3.759937
[26,] 145.3667 3.759937
[27,] 145.3667 3.739979
[28,] 145.2500 3.729629
[29,] 145.1292 3.718998
[30,] 144.8792 3.675571
[31,] 145.1375 3.653151
[32,] 145.2708 3.641725
[33,] 145.2708 3.641725
[34,] 145.1292 3.605525
[35,] 145.1292 3.605525
[36,] 145.2792 3.592847
[37,] 145.2792 3.592847
[38,] 145.2792 3.566196
[39,] 145.6042 3.539234
[40,] 145.6042 3.511541
[41,] 145.4333 3.497267
[42,] 145.4333 3.497267
[43,] 145.2542 3.482411
[44,] 145.2542 3.482411
[45,] 145.2542 3.482411
[46,] 145.2542 3.450950
[47,] 145.4500 3.403167
[48,] 145.0500 3.370677
[49,] 144.8458 3.354277
[50,] 144.6375 3.304332
[51,] 144.6375 3.304332
[52,] 144.6375 3.304332
[53,] 145.3000 3.216650
[54,] 145.5250 3.199067
[55,] 145.2958 3.181005
[56,] 145.5292 3.162872
[57,] 145.7667 3.144550
[58,] 146.2500 3.107671
[59,] 146.0042 3.088290
[60,] 146.5042 3.050630
[61,] 146.5042 3.050630
[62,] 146.5042 3.050630
[63,] 146.7667 3.031077
[64,] 147.3000 2.991779
[65,] 146.7583 2.949074
[66,] 146.7583 2.949074
[67,] 146.4792 2.927256
[68,] 146.7625 2.906479
[69,] 146.7625 2.863112
[70,] 146.7625 2.819301
[71,] 146.7625 2.775049
[72,] 146.7625 2.775049
[73,] 146.4583 2.706376
[74,] 146.4583 2.706376
[75,] 146.1458 2.682501
[76,] 146.1458 2.682501
[77,] 145.8250 2.658113
[78,] 145.8250 2.562254
[79,] 145.4958 2.537494
[80,] 145.8292 2.513659
> (tri <- trimean(x))
          [,1]     [,2]
 [1,] 145.2563 4.066635
 [2,] 145.2119 4.028942
 [3,] 145.2051 4.001183
 [4,] 145.1853 3.973568
 [5,] 145.1826 3.949934
 [6,] 145.1842 3.929798
 [7,] 145.1858 3.909583
 [8,] 145.1562 3.891875
 [9,] 145.1351 3.877333
[10,] 145.1409 3.864997
[11,] 145.1422 3.853379
[12,] 145.1435 3.840956
[13,] 145.1402 3.828212
[14,] 145.1368 3.815672
[15,] 145.1286 3.802799
[16,] 145.1442 3.791761
[17,] 145.1650 3.780436
[18,] 145.1863 3.769380
[19,] 145.2030 3.758054
[20,] 145.2100 3.748163
[21,] 145.2172 3.737454
[22,] 145.2194 3.726472
[23,] 145.2113 3.715794
[24,] 145.2083 3.706046
[25,] 145.2000 3.697261
[26,] 145.1915 3.687654
[27,] 145.1828 3.677171
[28,] 145.1739 3.667044
[29,] 145.1703 3.656647
[30,] 145.1722 3.645962
[31,] 145.1854 3.636969
[32,] 145.1875 3.628427
[33,] 145.1839 3.619667
[34,] 145.1802 3.609978
[35,] 145.1824 3.601433
[36,] 145.1845 3.591939
[37,] 145.1807 3.582168
[38,] 145.1768 3.571347
[39,] 145.1728 3.560949
[40,] 145.1562 3.550983
[41,] 145.1392 3.541492
[42,] 145.1282 3.531715
[43,] 145.1169 3.520791
[44,] 145.1118 3.509492
[45,] 145.1067 3.496910
[46,] 145.1014 3.482942
[47,] 145.0959 3.469325
[48,] 145.0833 3.457008
[49,] 145.0845 3.445155
[50,] 145.0929 3.432822
[51,] 145.1087 3.421927
[52,] 145.1250 3.409592
[53,] 145.1418 3.395690
[54,] 145.1364 3.385375
[55,] 145.1231 3.374622
[56,] 145.1172 3.363417
[57,] 145.1032 3.351699
[58,] 145.0806 3.339411
[59,] 145.0410 3.327624
[60,] 145.0083 3.315305
[61,] 144.9576 3.303482
[62,] 144.9052 3.289777
[63,] 144.8509 3.273992
[64,] 144.7857 3.257193
[65,] 144.7000 3.240552
[66,] 144.6296 3.224538
[67,] 144.5566 3.206016
[68,] 144.4904 3.186363
[69,] 144.4118 3.165234
[70,] 144.3300 3.144245
[71,] 144.2449 3.123419
[72,] 144.1562 3.102783
[73,] 144.0638 3.078728
[74,] 143.9783 3.056678
[75,] 143.8889 3.030863
[76,] 143.8068 3.002996
[77,] 143.7209 2.970473
[78,] 143.6429 2.935071
[79,] 143.5610 2.903346
[80,] 143.4875 2.868698
> (midr <- midrange(x))
[1] 149.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 144.5935 145.4959 144.5935 145.4959 145.4959 144.5935 145.4959 144.5935
> postscript(file="/var/wessaorg/rcomp/tmp/133hs1324140145.ps",horizontal=F,onefile=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/wessaorg/rcomp/tmp/2lddi1324140145.ps",horizontal=F,onefile=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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3wyfl1324140145.tab") 
> 
> try(system("convert tmp/133hs1324140145.ps tmp/133hs1324140145.png",intern=TRUE))
character(0)
> try(system("convert tmp/2lddi1324140145.ps tmp/2lddi1324140145.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.260   0.137   1.394