R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(-0.236493005027621
+ ,-4.93891480965441
+ ,-3.95116239084637
+ ,1.9753875025203
+ ,-1.7798512823075
+ ,2.37611897412902
+ ,0.311940513005736
+ ,-7.15597025619578
+ ,8.46791076910932
+ ,-1.41127366738798e-10
+ ,4.90820820490978
+ ,3.24776205176132
+ ,4.99999999991935
+ ,-3.06417846121247
+ ,10.3119405129169
+ ,-1.22014871767994
+ ,-2.62388102585579
+ ,-4.4402974353625
+ ,-1.31194051292749
+ ,4.6880594870725
+ ,1.06417846121749
+ ,2.84402974353625
+ ,-3.22014871768125
+ ,0.311940512927502
+ ,-6.53208923060875
+ ,2.376118974145
+ ,-2
+ ,1.90820820475374
+ ,9.46791076939125
+ ,3.6880594870725
+ ,1.46791076939125
+ ,11.4037323081738
+ ,-4.37611897414499
+ ,-5.84402974353625
+ ,6.55970256463751
+ ,5.22014871768124
+ ,9.06417846121749
+ ,-6.22014871768125
+ ,-6.06417846121749
+ ,-3.44029743536249
+ ,-0.0917917952462566
+ ,0.908208204753743
+ ,9.22014871768125
+ ,7.15597025646375
+ ,-6.6880594870725
+ ,-3.44029743536249
+ ,2.09179179524626
+ ,-1.09179179524626
+ ,1.22014871768125
+ ,2.15597025646375
+ ,-4
+ ,10.3119405129275
+ ,-0.688059487072498
+ ,5.376118974145
+ ,4.55970256463751
+ ,-1.15597025646375
+ ,0.935821538782506
+ ,-1.53208923060875
+ ,7.84402974353625
+ ,-6
+ ,1.6880594870725
+ ,-4.75223794828999
+ ,0.0641784612174945
+ ,2.3119405129275
+ ,-7.93582153878251
+ ,9.15597025646375
+ ,-1.6880594870725
+ ,-5.09179179524626
+ ,4.40373230817376
+ ,2.6880594870725
+ ,0.376118974144996
+ ,-3.53208923060875
+ ,-8.53208923060875
+ ,1.15597025646375
+ ,9.376118974145
+ ,-7.40373230817376
+ ,-5.84402974353625
+ ,1.55970256463751
+ ,-8.93582153878251
+ ,5.06417846121749
+ ,-7
+ ,2.75223794828999
+ ,5.93582153878251
+ ,-6.09179179524626
+ ,-3.376118974145
+ ,7.77985128231875
+ ,6.22014871768125
+ ,2.376118974145
+ ,-5.90820820475374
+ ,-7.90820820475374
+ ,4.46791076939125
+ ,-2.09179179524626
+ ,-2.40373230817376
+ ,2.623881025855
+ ,1.84402974353625
+ ,6.84402974353625
+ ,-0.688059487072498
+ ,-3.6880594870725
+ ,3.09179179524626
+ ,-0.155970256463751
+ ,-0.623881025855004
+ ,1.3119405129275
+ ,-1
+ ,2
+ ,3.15597025646375
+ ,-10.1559702564638
+ ,-1.6880594870725
+ ,-1.53208923060875)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.2.291 ()
> #Author: root
> #To cite this work: Wessa, P., (2012), Central Tendency (v1.0.4) 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
> #
> 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] 0.3292179
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.4796622
> (armose <- arm / armse)
[1] 0.6863537
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] -1.524176e-08
> (qua <- quamean(x))
[1] 4.972575
> (win <- winmean(x))
            [,1]      [,2]
 [1,] 0.33040644 0.4753957
 [2,] 0.33788296 0.4740610
 [3,] 0.33100068 0.4667908
 [4,] 0.32862370 0.4660023
 [5,] 0.34475822 0.4609332
 [6,] 0.35495731 0.4581565
 [7,] 0.35911703 0.4555537
 [8,] 0.33805575 0.4443798
 [9,] 0.29906319 0.4337902
[10,] 0.32200412 0.4286383
[11,] 0.27153407 0.4166973
[12,] 0.23994216 0.4109794
[13,] 0.21344278 0.4047939
[14,] 0.18132548 0.3967306
[15,] 0.15074927 0.3899034
[16,] 0.06783037 0.3787188
[17,] 0.16168732 0.3587389
[18,] 0.16117178 0.3518637
[19,] 0.18272242 0.3459803
[20,] 0.22349070 0.3361706
[21,] 0.19316315 0.3290310
[22,] 0.24363320 0.3159081
[23,] 0.23448555 0.3121164
[24,] 0.27869098 0.3030642
[25,] 0.14913020 0.2782110
[26,] 0.06523069 0.2631704
[27,] 0.04228275 0.2605923
[28,] 0.04228275 0.2566648
[29,] 0.01763495 0.2441681
[30,] 0.03546230 0.2360743
[31,] 0.14342238 0.2188506
[32,] 0.18963578 0.2091478
[33,] 0.20924587 0.1900723
[34,] 0.23814329 0.1868197
[35,] 0.30948778 0.1789306
[36,] 0.31869222 0.1733007
> (tri <- trimean(x))
           [,1]      [,2]
 [1,] 0.3236583 0.4668883
 [2,] 0.3166506 0.4573543
 [3,] 0.3054099 0.4474351
 [4,] 0.2961972 0.4393020
 [5,] 0.2872633 0.4303838
 [6,] 0.2743270 0.4217022
 [7,] 0.2588871 0.4125296
 [8,] 0.2420784 0.4026710
 [9,] 0.2276818 0.3937336
[10,] 0.2179479 0.3855487
[11,] 0.2048804 0.3770795
[12,] 0.1970897 0.3694110
[13,] 0.1923864 0.3615108
[14,] 0.1901998 0.3533642
[15,] 0.1910775 0.3451784
[16,] 0.1948981 0.3366966
[17,] 0.2064887 0.3284753
[18,] 0.2104418 0.3218822
[19,] 0.2146649 0.3151026
[20,] 0.2173350 0.3079282
[21,] 0.2168314 0.3008539
[22,] 0.2187333 0.2934527
[23,] 0.2167617 0.2865631
[24,] 0.2153746 0.2787826
[25,] 0.2104622 0.2707495
[26,] 0.2151935 0.2649710
[27,] 0.2267291 0.2601398
[28,] 0.2409173 0.2544042
[29,] 0.2562405 0.2477813
[30,] 0.2747530 0.2415420
[31,] 0.2934801 0.2350026
[32,] 0.3053615 0.2299773
[33,] 0.3146609 0.2252224
[34,] 0.3232857 0.2226085
[35,] 0.3304029 0.2194189
[36,] 0.3321956 0.2164892
> (midr <- midrange(x))
[1] 0.623881
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 0.1600559 0.1600559 0.1600559 0.1600559 0.1600559 0.1600559 0.1600559
[8] 0.2151935
> postscript(file="/var/fisher/rcomp/tmp/1hu581387556831.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/fisher/rcomp/tmp/2t7671387556831.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/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/fisher/rcomp/tmp/3pfkw1387556831.tab") 
> 
> try(system("convert tmp/1hu581387556831.ps tmp/1hu581387556831.png",intern=TRUE))
character(0)
> try(system("convert tmp/2t7671387556831.ps tmp/2t7671387556831.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.597   0.890   4.451