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(221102
+ ,220892
+ ,225537
+ ,219334
+ ,216126
+ ,224573
+ ,213991
+ ,221865
+ ,215382
+ ,213962
+ ,217009
+ ,318110
+ ,219662
+ ,212650
+ ,209307
+ ,210541
+ ,210609
+ ,208910
+ ,207541
+ ,207699
+ ,205005
+ ,205747
+ ,203644
+ ,229937
+ ,214446
+ ,210194
+ ,206535
+ ,216524
+ ,198243
+ ,208274
+ ,207493
+ ,215525
+ ,207562
+ ,213355
+ ,209048
+ ,220497
+ ,214563
+ ,211571
+ ,216385
+ ,211496
+ ,209683
+ ,206304
+ ,213925
+ ,204829
+ ,205729
+ ,200296
+ ,207960
+ ,207729
+ ,208327
+ ,207794
+ ,213700
+ ,213136
+ ,210354
+ ,202205
+ ,220425
+ ,210038
+ ,205201
+ ,197441
+ ,200021
+ ,203165
+ ,201699
+ ,201003
+ ,232308
+ ,211412
+ ,209661
+ ,213587
+ ,193611
+ ,192543
+ ,196040
+ ,191407
+ ,189726
+ ,191272
+ ,187924
+ ,198213
+ ,199352
+ ,199289
+ ,195475
+ ,198045
+ ,197615
+ ,189015
+ ,189668
+ ,189120
+ ,194168
+ ,192304
+ ,185913
+ ,197599
+ ,186085
+ ,190566
+ ,187054
+ ,193222
+ ,189856
+ ,190608
+ ,190588
+ ,186773
+ ,183510
+ ,180106
+ ,180150
+ ,178412
+ ,182353
+ ,203805
+ ,186054
+ ,184290
+ ,187483
+ ,187111
+ ,189561
+ ,184439
+ ,182985
+ ,183828
+ ,184036
+ ,183214
+ ,183464
+ ,173718
+ ,180210
+ ,171252
+ ,172705
+ ,174006
+ ,172043
+ ,169445
+ ,169449
+ ,177073
+ ,170799
+ ,171648
+ ,172220
+ ,165795
+ ,167466
+ ,165528
+ ,162851
+ ,165864
+ ,162094
+ ,162385
+ ,164293
+ ,165983
+ ,159680
+ ,161739
+ ,159302
+ ,167795
+ ,164242
+ ,159743
+ ,160887
+ ,163844
+ ,161172
+ ,159330
+ ,155570
+ ,156749
+ ,155012
+ ,163419
+ ,153630
+ ,154535
+ ,151543
+ ,152955
+ ,150166
+ ,151416
+ ,150332
+ ,152196
+ ,153422
+ ,147435)
> 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] 191728
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 1895.908
> (armose <- arm / armse)
[1] 101.1273
> (geo <- geomean(x))
[1] 190305.4
> (har <- harmean(x))
[1] 188896.2
> (qua <- quamean(x))
[1] 193175.5
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 191195.5 1729.3009
 [2,] 191167.2 1724.4395
 [3,] 191103.5 1709.6491
 [4,] 191082.0 1705.9905
 [5,] 191016.1 1692.2750
 [6,] 191016.0 1684.5706
 [7,] 191027.5 1680.4475
 [8,] 191017.9 1676.6000
 [9,] 191066.0 1668.6855
[10,] 191047.7 1658.8859
[11,] 191063.9 1650.8353
[12,] 190975.7 1619.1989
[13,] 191148.1 1586.7292
[14,] 191138.1 1585.1194
[15,] 191146.8 1578.2254
[16,] 191091.7 1571.1544
[17,] 191200.8 1553.7193
[18,] 191139.1 1540.2047
[19,] 191193.9 1530.1846
[20,] 191181.1 1518.8614
[21,] 191216.4 1513.6561
[22,] 191276.9 1505.1081
[23,] 191327.5 1491.7368
[24,] 191375.5 1482.1915
[25,] 191402.1 1470.9836
[26,] 191374.1 1466.4665
[27,] 191503.7 1433.2033
[28,] 191358.0 1409.4183
[29,] 191356.8 1406.6290
[30,] 191363.6 1402.4641
[31,] 191498.7 1353.7517
[32,] 191552.2 1344.7704
[33,] 191861.7 1301.8696
[34,] 191827.7 1298.5839
[35,] 192095.6 1262.0521
[36,] 192118.2 1243.2105
[37,] 192206.9 1232.5955
[38,] 192216.9 1214.4087
[39,] 192196.4 1203.8054
[40,] 192285.4 1187.3366
[41,] 192398.4 1145.3684
[42,] 192461.7 1135.9444
[43,] 193220.5 1041.4313
[44,] 193551.4  999.7961
[45,] 194021.3  951.1117
[46,] 194025.4  949.0651
[47,] 194002.2  943.5283
[48,] 194655.1  882.1200
[49,] 194838.5  862.9684
[50,] 194604.9  827.6510
[51,] 194611.1  813.3956
[52,] 194440.8  794.9080
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 191195.0 1710.4782
 [2,] 191194.4 1690.1202
 [3,] 191208.6 1670.8017
 [4,] 191245.5 1655.5478
 [5,] 191289.1 1640.0513
 [6,] 191348.3 1626.5381
 [7,] 191409.1 1613.4065
 [8,] 191469.9 1599.8153
 [9,] 191533.7 1585.5836
[10,] 191593.3 1571.2389
[11,] 191656.9 1556.9183
[12,] 191720.6 1542.2871
[13,] 191795.1 1530.2236
[14,] 191855.7 1520.8642
[15,] 191919.2 1510.6072
[16,] 191984.0 1499.9477
[17,] 192055.3 1488.7995
[18,] 192120.6 1478.2318
[19,] 192192.7 1467.7500
[20,] 192263.4 1457.0027
[21,] 192337.5 1446.0221
[22,] 192411.8 1434.1682
[23,] 192485.0 1421.6650
[24,] 192557.7 1408.8766
[25,] 192630.2 1395.3659
[26,] 192703.8 1381.1738
[27,] 192782.1 1365.5131
[28,] 192855.9 1351.0682
[29,] 192941.1 1336.8200
[30,] 193029.9 1320.7954
[31,] 193029.9 1302.8843
[32,] 193210.8 1287.3590
[33,] 193300.7 1270.4180
[34,] 193378.0 1255.4686
[35,] 193460.7 1238.4313
[36,] 193533.1 1222.6724
[37,] 193607.9 1206.2838
[38,] 193681.7 1188.3224
[39,] 193758.8 1169.2936
[40,] 193841.1 1148.1101
[41,] 193923.0 1125.1880
[42,] 194003.6 1103.3281
[43,] 194085.4 1078.5878
[44,] 194131.6 1061.8409
[45,] 194131.6 1047.0390
[46,] 194170.4 1035.2717
[47,] 194178.3 1020.9142
[48,] 194188.1 1003.8916
[49,] 194161.9  991.3719
[50,] 194123.4  978.0834
[51,] 194095.6  966.4838
[52,] 194065.3  953.5290
> (midr <- midrange(x))
[1] 232772.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 193483.9 193758.8 193483.9 193758.8 193758.8 193483.9 193758.8 193681.7
> postscript(file="/var/fisher/rcomp/tmp/1x6h21381579279.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/2sv0c1381579279.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/3sxw21381579279.tab") 
> 
> try(system("convert tmp/1x6h21381579279.ps tmp/1x6h21381579279.png",intern=TRUE))
character(0)
> try(system("convert tmp/2sv0c1381579279.ps tmp/2sv0c1381579279.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.719   0.249   1.950