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(13408,7820,9079,8307,7865,10028,9054,7143,8006,7638,7600,2904,13224,8079,9678,7746,9007,8362,7458,7753,7352,7117,6971,3304,11812,6867,8296,6489,7784,7506,6514,6323,6201,7169,6744,2087,10668,6406,7730,7105,7694,7160,6820,6025,5877,7191,5778,2273,11321,6759,7150,6363,6442,6453,6228,5325,6504,6817,5789,1894,11068,7174,8269,7060,6681,8953,7815,5925,6805,7044,7169,2824,10717,5245,6237,5871,5508,15801,1236,2656,3425,3533,4287,1380,8584,5522,6423,5173,5583,5716,4752,4977,4999,5285,5747,1713,9923,6737,7433,6388,6855,7658,6585,6847,6353,7361,6929,1714,11798,8378,8131,7676,7505,8168,6455,6141,6554,6888,5339,1624,9187,5047,5289,4169,3862,4253,3768,3066,4108,3890,3420,1221,5984,4064,5151,4027,3530,4819,3855,3584,4322,4154,4656,1464,7780,5060,6084,4778,4989,4903,4142,4101,4595,5034,5407,1782,8395,5291,6116,4210,4621,5299,4293,4542,3831,4360,4088,1508,6743,4159,5105,4283,4019,4206,3948,3407,3701,4159,4208,2622,6229,4432,4986,4226,4349,4688,4002,3381,4250,4154,4350,2713)
> 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] 5924.391
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 172.053
> (armose <- arm / armse)
[1] 34.43352
> (geo <- geomean(x))
[1] 5409.435
> (har <- harmean(x))
[1] 4797.009
> (qua <- quamean(x))
[1] 6383.763
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 5912.005 168.71504
 [2,] 5911.589 168.05908
 [3,] 5890.839 163.25954
 [4,] 5891.464 163.07462
 [5,] 5882.062 160.37080
 [6,] 5876.938 158.60687
 [7,] 5864.177 156.46603
 [8,] 5864.969 155.74425
 [9,] 5840.219 150.41079
[10,] 5844.802 148.26085
[11,] 5841.422 144.88231
[12,] 5832.547 138.06285
[13,] 5827.536 136.86314
[14,] 5829.870 136.13550
[15,] 5834.870 134.65399
[16,] 5837.036 133.32697
[17,] 5818.708 127.83999
[18,] 5823.302 123.41834
[19,] 5829.240 122.42880
[20,] 5830.281 121.96475
[21,] 5825.688 121.16751
[22,] 5825.000 120.97301
[23,] 5834.344 119.33816
[24,] 5822.094 117.96858
[25,] 5823.917 116.79794
[26,] 5832.719 114.50438
[27,] 5831.875 112.54646
[28,] 5820.500 109.62465
[29,] 5817.328 108.62109
[30,] 5817.641 108.44235
[31,] 5817.156 107.53584
[32,] 5826.156 106.57243
[33,] 5830.797 105.27762
[34,] 5832.568 104.88601
[35,] 5831.109 104.47601
[36,] 5831.297 103.21134
[37,] 5832.453 102.47066
[38,] 5831.464 101.90669
[39,] 5828.823 101.39995
[40,] 5827.990 100.03585
[41,] 5810.479  97.96893
[42,] 5810.260  97.94911
[43,] 5800.854  96.90186
[44,] 5795.125  96.39053
[45,] 5780.594  94.69395
[46,] 5787.302  93.71900
[47,] 5748.380  90.30344
[48,] 5744.630  89.90415
[49,] 5747.438  89.43363
[50,] 5753.688  88.87848
[51,] 5752.094  88.60880
[52,] 5757.510  87.66593
[53,] 5756.682  87.40814
[54,] 5751.057  86.65417
[55,] 5755.927  85.64052
[56,] 5750.677  83.87317
[57,] 5746.224  83.45971
[58,] 5727.193  81.41484
[59,] 5736.411  78.44917
[60,] 5757.974  74.46385
[61,] 5768.141  72.50092
[62,] 5772.661  71.48384
[63,] 5781.521  70.31002
[64,] 5783.188  68.70531
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 5897.163 163.99386
 [2,] 5882.005 158.89280
 [3,] 5866.737 153.74474
 [4,] 5858.353 150.09909
 [5,] 5849.621 146.22965
 [6,] 5842.700 142.75401
 [7,] 5836.545 139.40012
 [8,] 5832.239 136.20786
 [9,] 5827.724 132.89414
[10,] 5826.174 130.18911
[11,] 5824.071 127.59576
[12,] 5822.268 125.27137
[13,] 5821.277 123.64153
[14,] 5820.713 122.03162
[15,] 5819.938 120.38159
[16,] 5818.744 118.76593
[17,] 5817.354 117.16373
[18,] 5817.256 115.98753
[19,] 5816.838 115.13415
[20,] 5816.013 114.29728
[21,] 5815.100 113.42865
[22,] 5814.446 112.55328
[23,] 5813.815 111.61685
[24,] 5812.625 110.73383
[25,] 5812.092 109.88370
[26,] 5811.443 109.04905
[27,] 5810.304 108.31710
[28,] 5809.176 107.66490
[29,] 5808.597 107.16779
[30,] 5808.159 106.68772
[31,] 5807.692 106.16288
[32,] 5807.234 105.64292
[33,] 5806.333 105.13037
[34,] 5805.185 104.64868
[35,] 5803.918 104.13238
[36,] 5802.675 103.57919
[37,] 5801.381 103.04814
[38,] 5799.991 102.50049
[39,] 5798.596 101.92059
[40,] 5797.268 101.30027
[41,] 5795.927 100.69982
[42,] 5795.296 100.17453
[43,] 5794.651  99.57084
[44,] 5794.385  98.96055
[45,] 5794.353  98.29902
[46,] 5794.940  97.67444
[47,] 5795.265  97.03133
[48,] 5797.260  96.55916
[49,] 5799.500  96.02998
[50,] 5801.717  95.44369
[51,] 5803.767  94.80056
[52,] 5805.977  94.06526
[53,] 5808.058  93.28783
[54,] 5810.274  92.39595
[55,] 5812.841  91.41881
[56,] 5815.325  90.37289
[57,] 5818.167  89.32082
[58,] 5821.355  88.11691
[59,] 5825.568  86.90619
[60,] 5829.597  85.80700
[61,] 5832.871  84.95520
[62,] 5835.868  84.14422
[63,] 5838.833  83.26454
[64,] 5841.562  82.32505
> (midr <- midrange(x))
[1] 8511
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 5780.876 5797.260 5780.876 5797.260 5797.260 5780.876 5797.260 5795.265
> postscript(file="/var/wessaorg/rcomp/tmp/129qr1452124398.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/22p2u1452124398.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/3j1at1452124398.tab") 
> 
> try(system("convert tmp/129qr1452124398.ps tmp/129qr1452124398.png",intern=TRUE))
character(0)
> try(system("convert tmp/22p2u1452124398.ps tmp/22p2u1452124398.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.485   0.192   1.677