R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree"
Copyright (C) 2015 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(283411
+ ,234585
+ ,207695
+ ,204000
+ ,220791
+ ,222335
+ ,303510
+ ,201602
+ ,218279
+ ,207253
+ ,217639
+ ,231043
+ ,302988
+ ,221415
+ ,213989
+ ,190507
+ ,199397
+ ,201077
+ ,261048
+ ,241508
+ ,194637
+ ,240044
+ ,253534
+ ,269220
+ ,270820
+ ,354121
+ ,315233
+ ,297098
+ ,258289
+ ,276246
+ ,246652
+ ,242945
+ ,210838
+ ,246343
+ ,234636
+ ,229011
+ ,238756
+ ,283696
+ ,226656
+ ,229790
+ ,219831
+ ,232331
+ ,315447
+ ,251031
+ ,297019
+ ,208424
+ ,311626
+ ,352320
+ ,375214
+ ,419501
+ ,664867
+ ,483142
+ ,312717
+ ,228228
+ ,230978
+ ,218033
+ ,225566
+ ,207708
+ ,241861
+ ,208381
+ ,209071
+ ,214514
+ ,195868
+ ,190208
+ ,187651
+ ,215934
+ ,213012
+ ,236845
+ ,154595
+ ,193485
+ ,231875
+ ,192259
+ ,191609
+ ,212911
+ ,238596
+ ,203033
+ ,258272
+ ,314681
+ ,289789
+ ,297541
+ ,239578
+ ,207798
+ ,254091
+ ,242544
+ ,218067
+ ,217463
+ ,229438
+ ,216485
+ ,238410
+ ,223108
+ ,221267
+ ,224802
+ ,233630
+ ,235134
+ ,309660
+ ,253229
+ ,293530
+ ,273323
+ ,297578
+ ,341589
+ ,389911
+ ,398685
+ ,629637
+ ,522502
+ ,358941
+ ,252783
+ ,236585
+ ,224995
+ ,225721
+ ,223338
+ ,228952
+ ,212759
+ ,200270
+ ,211925
+ ,191206
+ ,200511
+ ,205944
+ ,289288
+ ,186209
+ ,197515
+ ,182038
+ ,181606
+ ,223337
+ ,201213
+ ,220700
+ ,194043
+ ,224593
+ ,249907
+ ,238613
+ ,266200
+ ,274197
+ ,288601
+ ,242662
+ ,232105
+ ,267842
+ ,219037
+ ,198404
+ ,203910
+ ,209685
+ ,214274
+ ,215376
+ ,217711
+ ,224819
+ ,217142
+ ,221445
+ ,213483
+ ,282063
+ ,236194
+ ,297296
+ ,255885
+ ,264502
+ ,311580
+ ,416595
+ ,356762
+ ,537286
+ ,532855)
> 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] 256672.9
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 6322.25
> (armose <- arm / armse)
[1] 40.59835
> (geo <- geomean(x))
[1] 248078
> (har <- harmean(x))
[1] 241698.4
> (qua <- quamean(x))
[1] 268470.6
> (win <- winmean(x))
          [,1]     [,2]
 [1,] 256620.2 6215.690
 [2,] 255441.8 5798.902
 [3,] 255436.8 5765.934
 [4,] 255208.3 5681.590
 [5,] 254028.7 5307.613
 [6,] 251592.5 4678.867
 [7,] 251493.4 4646.190
 [8,] 250595.6 4440.197
 [9,] 250126.9 4329.775
[10,] 249263.4 4132.088
[11,] 248155.3 3910.718
[12,] 248033.4 3876.163
[13,] 247915.9 3827.489
[14,] 247902.1 3785.810
[15,] 246955.7 3598.989
[16,] 244376.3 3166.209
[17,] 244448.2 3154.174
[18,] 244412.3 3142.459
[19,] 244242.0 3101.968
[20,] 244119.6 3080.555
[21,] 244165.7 3074.988
[22,] 244096.8 3019.002
[23,] 243319.3 2882.984
[24,] 243252.9 2870.964
[25,] 242697.4 2729.206
[26,] 242909.4 2709.666
[27,] 242943.5 2697.681
[28,] 242910.3 2692.867
[29,] 242912.4 2689.551
[30,] 242353.5 2593.832
[31,] 241618.7 2499.556
[32,] 241648.6 2475.467
[33,] 241633.2 2446.459
[34,] 240815.4 2294.576
[35,] 240995.4 2266.492
[36,] 240876.8 2213.186
[37,] 239533.1 2047.455
[38,] 239058.6 1988.050
[39,] 238957.9 1953.260
[40,] 238445.8 1870.050
[41,] 238100.2 1817.002
[42,] 237793.8 1770.721
[43,] 237578.8 1701.298
[44,] 237257.3 1636.338
[45,] 236419.9 1517.187
[46,] 235800.1 1416.444
[47,] 235891.6 1407.726
[48,] 235211.3 1328.572
[49,] 234670.5 1270.553
[50,] 234595.1 1244.107
[51,] 234506.5 1233.373
[52,] 234428.5 1212.761
> (tri <- trimean(x))
          [,1]     [,2]
 [1,] 254685.1 5786.148
 [2,] 252699.1 5290.099
 [3,] 251273.0 4987.804
 [4,] 249810.0 4658.739
 [5,] 248368.0 4312.217
 [6,] 247141.5 4033.072
 [7,] 246326.5 3883.306
 [8,] 245504.1 3723.545
 [9,] 244784.6 3587.832
[10,] 244103.7 3457.527
[11,] 243503.0 3347.291
[12,] 243003.2 3260.943
[13,] 242500.2 3170.428
[14,] 241992.4 3076.882
[15,] 241469.8 2978.377
[16,] 241009.7 2894.794
[17,] 240740.7 2857.400
[18,] 240457.1 2817.155
[19,] 240166.7 2773.715
[20,] 239878.2 2729.911
[21,] 239588.0 2683.462
[22,] 239284.4 2632.076
[23,] 238974.2 2580.631
[24,] 238701.3 2538.162
[25,] 238422.2 2491.705
[26,] 238165.7 2454.602
[27,] 237886.6 2414.357
[28,] 237594.4 2369.887
[29,] 237292.2 2319.866
[30,] 236977.3 2263.180
[31,] 236977.3 2209.778
[32,] 236409.7 2160.059
[33,] 236126.0 2105.571
[34,] 235830.1 2046.077
[35,] 235564.2 1996.217
[36,] 235276.0 1941.277
[37,] 234980.0 1883.827
[38,] 234740.0 1839.124
[39,] 234512.7 1794.636
[40,] 234278.8 1746.725
[41,] 234059.2 1701.562
[42,] 233845.6 1655.447
[43,] 233636.1 1607.237
[44,] 233425.8 1559.478
[45,] 233425.8 1511.847
[46,] 233046.6 1473.071
[47,] 232896.0 1441.404
[48,] 232730.3 1403.576
[49,] 232591.3 1370.425
[50,] 232473.1 1339.271
[51,] 232350.4 1304.664
[52,] 232223.6 1263.058
> (midr <- midrange(x))
[1] 409731
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 234240.6 234512.7 234240.6 234512.7 234512.7 234240.6 234512.7 234740.0
> postscript(file="/var/wessaorg/rcomp/tmp/14vvv1457101052.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/272w21457101052.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/3vv711457101052.tab") 
> 
> try(system("convert tmp/14vvv1457101052.ps tmp/14vvv1457101052.png",intern=TRUE))
character(0)
> try(system("convert tmp/272w21457101052.ps tmp/272w21457101052.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.252   0.145   1.404