R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(7
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+ ,28)
> 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] 10.84587
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.07046695
> (armose <- arm / armse)
[1] 153.9143
> (geo <- geomean(x))
[1] 10.66513
> (har <- harmean(x))
[1] 10.48723
> (qua <- quamean(x))
[1] 11.03266
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 10.83617 0.06822848
  [2,] 10.83131 0.06751881
  [3,] 10.83131 0.06751881
  [4,] 10.82646 0.06693349
  [5,] 10.82646 0.06693349
  [6,] 10.81917 0.06617880
  [7,] 10.81917 0.06617880
  [8,] 10.81917 0.06617880
  [9,] 10.81917 0.06617880
 [10,] 10.80704 0.06512609
 [11,] 10.80704 0.06512609
 [12,] 10.80704 0.06512609
 [13,] 10.80704 0.06512609
 [14,] 10.80704 0.06512609
 [15,] 10.80704 0.06512609
 [16,] 10.80704 0.06512609
 [17,] 10.80704 0.06512609
 [18,] 10.80704 0.06512609
 [19,] 10.80704 0.06512609
 [20,] 10.83131 0.06360527
 [21,] 10.83131 0.06360527
 [22,] 10.83131 0.06360527
 [23,] 10.83131 0.06360527
 [24,] 10.83131 0.06360527
 [25,] 10.83131 0.06360527
 [26,] 10.83131 0.06360527
 [27,] 10.83131 0.06360527
 [28,] 10.83131 0.06360527
 [29,] 10.83131 0.06360527
 [30,] 10.79490 0.06098713
 [31,] 10.79490 0.06098713
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 [65,] 10.79490 0.06098713
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 [67,] 10.79490 0.06098713
 [68,] 10.71238 0.05629086
 [69,] 10.71238 0.05629086
 [70,] 10.71238 0.05629086
 [71,] 10.71238 0.05629086
 [72,] 10.71238 0.05629086
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 [85,] 10.71238 0.05629086
 [86,] 10.71238 0.05629086
 [87,] 10.71238 0.05629086
 [88,] 10.71238 0.05629086
 [89,] 10.71238 0.05629086
 [90,] 10.71238 0.05629086
 [91,] 10.71238 0.05629086
 [92,] 10.71238 0.05629086
 [93,] 10.71238 0.05629086
 [94,] 10.59830 0.05154878
 [95,] 10.59830 0.05154878
 [96,] 10.59830 0.05154878
 [97,] 10.59830 0.05154878
 [98,] 10.59830 0.05154878
 [99,] 10.59830 0.05154878
[100,] 10.59830 0.05154878
[101,] 10.59830 0.05154878
[102,] 10.59830 0.05154878
[103,] 10.59830 0.05154878
[104,] 10.59830 0.05154878
[105,] 10.59830 0.05154878
[106,] 10.59830 0.05154878
[107,] 10.59830 0.05154878
[108,] 10.59830 0.05154878
[109,] 10.59830 0.05154878
[110,] 10.59830 0.05154878
[111,] 10.59830 0.05154878
[112,] 10.59830 0.05154878
[113,] 10.59830 0.05154878
[114,] 10.59830 0.05154878
[115,] 10.59830 0.05154878
[116,] 10.59830 0.05154878
[117,] 10.59830 0.05154878
[118,] 10.74150 0.04361354
[119,] 10.74150 0.04361354
[120,] 10.74150 0.04361354
[121,] 10.74150 0.04361354
[122,] 10.74150 0.04361354
[123,] 10.74150 0.04361354
[124,] 10.74150 0.04361354
[125,] 10.74150 0.04361354
[126,] 10.74150 0.04361354
[127,] 10.74150 0.04361354
[128,] 10.74150 0.04361354
[129,] 10.74150 0.04361354
[130,] 10.74150 0.04361354
[131,] 10.74150 0.04361354
[132,] 10.74150 0.04361354
[133,] 10.74150 0.04361354
[134,] 10.74150 0.04361354
[135,] 10.74150 0.04361354
[136,] 10.74150 0.04361354
[137,] 10.74150 0.04361354
[138,] 10.74150 0.04361354
[139,] 10.74150 0.04361354
[140,] 10.74150 0.04361354
[141,] 10.74150 0.04361354
[142,] 10.74150 0.04361354
[143,] 10.74150 0.04361354
[144,] 10.74150 0.04361354
[145,] 10.74150 0.04361354
[146,] 10.74150 0.04361354
[147,] 10.74150 0.04361354
[148,] 10.74150 0.04361354
[149,] 10.74150 0.04361354
[150,] 10.74150 0.04361354
[151,] 10.74150 0.04361354
[152,] 10.74150 0.04361354
[153,] 10.74150 0.04361354
[154,] 10.74150 0.04361354
[155,] 10.74150 0.04361354
[156,] 10.74150 0.04361354
[157,] 10.74150 0.04361354
[158,] 10.74150 0.04361354
[159,] 10.74150 0.04361354
[160,] 10.74150 0.04361354
[161,] 10.74150 0.04361354
[162,] 10.74150 0.04361354
[163,] 10.74150 0.04361354
[164,] 10.74150 0.04361354
[165,] 10.74150 0.04361354
[166,] 10.74150 0.04361354
[167,] 10.74150 0.04361354
[168,] 10.74150 0.04361354
[169,] 10.74150 0.04361354
[170,] 10.74150 0.04361354
[171,] 10.74150 0.04361354
[172,] 10.74150 0.04361354
[173,] 10.74150 0.04361354
[174,] 10.74150 0.04361354
[175,] 10.74150 0.04361354
[176,] 10.74150 0.04361354
[177,] 10.74150 0.04361354
[178,] 10.74150 0.04361354
[179,] 10.74150 0.04361354
[180,] 10.74150 0.04361354
[181,] 10.74150 0.04361354
[182,] 10.74150 0.04361354
[183,] 10.74150 0.04361354
[184,] 10.74150 0.04361354
[185,] 10.74150 0.04361354
[186,] 10.96723 0.03404706
[187,] 10.96723 0.03404706
[188,] 10.96723 0.03404706
[189,] 10.96723 0.03404706
[190,] 10.96723 0.03404706
[191,] 10.96723 0.03404706
[192,] 10.96723 0.03404706
[193,] 10.96723 0.03404706
[194,] 10.96723 0.03404706
[195,] 10.96723 0.03404706
[196,] 10.96723 0.03404706
[197,] 10.96723 0.03404706
[198,] 10.96723 0.03404706
[199,] 10.96723 0.03404706
[200,] 10.96723 0.03404706
[201,] 10.96723 0.03404706
[202,] 10.96723 0.03404706
[203,] 10.96723 0.03404706
[204,] 10.96723 0.03404706
[205,] 10.96723 0.03404706
[206,] 10.96723 0.03404706
[207,] 10.96723 0.03404706
[208,] 10.96723 0.03404706
[209,] 10.96723 0.03404706
[210,] 10.96723 0.03404706
[211,] 10.96723 0.03404706
[212,] 10.96723 0.03404706
[213,] 10.96723 0.03404706
[214,] 10.96723 0.03404706
[215,] 10.96723 0.03404706
[216,] 10.96723 0.03404706
[217,] 10.96723 0.03404706
[218,] 10.96723 0.03404706
[219,] 10.96723 0.03404706
[220,] 10.96723 0.03404706
[221,] 10.96723 0.03404706
[222,] 10.96723 0.03404706
[223,] 10.96723 0.03404706
[224,] 10.96723 0.03404706
[225,] 10.96723 0.03404706
[226,] 10.96723 0.03404706
[227,] 10.96723 0.03404706
[228,] 10.96723 0.03404706
[229,] 10.96723 0.03404706
[230,] 10.96723 0.03404706
[231,] 10.96723 0.03404706
[232,] 10.96723 0.03404706
[233,] 10.96723 0.03404706
[234,] 10.96723 0.03404706
[235,] 10.96723 0.03404706
[236,] 10.96723 0.03404706
[237,] 10.96723 0.03404706
[238,] 10.96723 0.03404706
[239,] 10.96723 0.03404706
[240,] 10.96723 0.03404706
[241,] 10.96723 0.03404706
[242,] 10.96723 0.03404706
[243,] 10.96723 0.03404706
[244,] 10.96723 0.03404706
[245,] 10.96723 0.03404706
[246,] 10.96723 0.03404706
[247,] 10.96723 0.03404706
[248,] 10.96723 0.03404706
[249,] 10.96723 0.03404706
[250,] 10.96723 0.03404706
[251,] 10.96723 0.03404706
[252,] 10.96723 0.03404706
[253,] 10.96723 0.03404706
[254,] 10.96723 0.03404706
[255,] 10.96723 0.03404706
[256,] 10.96723 0.03404706
[257,] 10.96723 0.03404706
[258,] 10.96723 0.03404706
[259,] 10.96723 0.03404706
[260,] 10.96723 0.03404706
[261,] 10.96723 0.03404706
[262,] 10.96723 0.03404706
[263,] 10.96723 0.03404706
[264,] 10.96723 0.03404706
[265,] 10.96723 0.03404706
[266,] 10.96723 0.03404706
[267,] 10.96723 0.03404706
[268,] 10.96723 0.03404706
[269,] 10.96723 0.03404706
[270,] 10.96723 0.03404706
[271,] 10.96723 0.03404706
[272,] 10.96723 0.03404706
[273,] 10.96723 0.03404706
[274,] 10.96723 0.03404706
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 10.84587 0.06731662
  [2,] 10.82968 0.06638195
  [3,] 10.81907 0.06579657
  [4,] 10.81907 0.06519938
  [5,] 10.81204 0.06474626
  [6,] 10.80911 0.06428487
  [7,] 10.80741 0.06395095
  [8,] 10.80741 0.06361149
  [9,] 10.80397 0.06326635
 [10,] 10.80224 0.06291539
 [11,] 10.80175 0.06267528
 [12,] 10.80125 0.06243142
 [13,] 10.80075 0.06218375
 [14,] 10.80025 0.06193216
 [15,] 10.80025 0.06167660
 [16,] 10.79975 0.06141696
 [17,] 10.79873 0.06115317
 [18,] 10.79822 0.06088513
 [19,] 10.79771 0.06061274
 [20,] 10.79719 0.06033592
 [21,] 10.79540 0.06014435
 [22,] 10.79359 0.05994973
 [23,] 10.79177 0.05975198
 [24,] 10.78995 0.05955105
 [25,] 10.78811 0.05934688
 [26,] 10.78627 0.05913939
 [27,] 10.78442 0.05892852
 [28,] 10.78255 0.05871420
 [29,] 10.78068 0.05849635
 [30,] 10.78068 0.05827491
 [31,] 10.77880 0.05816026
 [32,] 10.77822 0.05804377
 [33,] 10.77704 0.05792539
 [34,] 10.77646 0.05780510
 [35,] 10.77586 0.05768285
 [36,] 10.77527 0.05755861
 [37,] 10.77467 0.05743236
 [38,] 10.77406 0.05730404
 [39,] 10.77346 0.05717363
 [40,] 10.77285 0.05704109
 [41,] 10.77224 0.05690637
 [42,] 10.77162 0.05676945
 [43,] 10.77100 0.05663027
 [44,] 10.77038 0.05648879
 [45,] 10.76975 0.05634497
 [46,] 10.76913 0.05619877
 [47,] 10.76849 0.05605015
 [48,] 10.76786 0.05589904
 [49,] 10.76722 0.05574542
 [50,] 10.76657 0.05558922
 [51,] 10.76593 0.05543040
 [52,] 10.76528 0.05526890
 [53,] 10.76462 0.05510468
 [54,] 10.76397 0.05493767
 [55,] 10.76331 0.05476782
 [56,] 10.76264 0.05459507
 [57,] 10.76197 0.05441937
 [58,] 10.76130 0.05424065
 [59,] 10.76062 0.05405884
 [60,] 10.76062 0.05387389
 [61,] 10.75994 0.05368572
 [62,] 10.75926 0.05349426
 [63,] 10.75857 0.05329945
 [64,] 10.75788 0.05310121
 [65,] 10.75648 0.05289947
 [66,] 10.75578 0.05269414
 [67,] 10.75507 0.05248514
 [68,] 10.75436 0.05227240
 [69,] 10.75510 0.05216794
 [70,] 10.75585 0.05206158
 [71,] 10.75660 0.05195328
 [72,] 10.75735 0.05184300
 [73,] 10.75811 0.05173071
 [74,] 10.75888 0.05161636
 [75,] 10.75964 0.05149992
 [76,] 10.76042 0.05138135
 [77,] 10.76119 0.05126060
 [78,] 10.76198 0.05113762
 [79,] 10.76276 0.05101239
 [80,] 10.76355 0.05088484
 [81,] 10.76435 0.05075493
 [82,] 10.76515 0.05062261
 [83,] 10.76596 0.05048784
 [84,] 10.76677 0.05035056
 [85,] 10.76758 0.05021071
 [86,] 10.76840 0.05006826
 [87,] 10.76923 0.04992313
 [88,] 10.77006 0.04977527
 [89,] 10.77090 0.04962462
 [90,] 10.77174 0.04947113
 [91,] 10.77259 0.04931472
 [92,] 10.77344 0.04915534
 [93,] 10.77429 0.04899291
 [94,] 10.77516 0.04882737
 [95,] 10.77760 0.04874681
 [96,] 10.78006 0.04866440
 [97,] 10.78254 0.04858011
 [98,] 10.78503 0.04849389
 [99,] 10.78754 0.04840571
[100,] 10.79006 0.04831552
[101,] 10.79260 0.04822327
[102,] 10.79516 0.04812893
[103,] 10.79773 0.04803244
[104,] 10.80032 0.04793376
[105,] 10.80293 0.04783284
[106,] 10.80556 0.04772963
[107,] 10.80820 0.04762408
[108,] 10.81086 0.04751613
[109,] 10.81353 0.04740574
[110,] 10.81623 0.04729283
[111,] 10.81894 0.04717737
[112,] 10.82167 0.04705927
[113,] 10.82441 0.04693849
[114,] 10.82718 0.04681496
[115,] 10.82997 0.04668862
[116,] 10.83277 0.04655939
[117,] 10.83559 0.04642720
[118,] 10.83844 0.04629199
[119,] 10.83959 0.04630136
[120,] 10.83959 0.04631026
[121,] 10.84075 0.04631869
[122,] 10.84192 0.04632663
[123,] 10.84310 0.04633407
[124,] 10.84429 0.04634100
[125,] 10.84549 0.04634741
[126,] 10.84669 0.04635329
[127,] 10.84790 0.04635862
[128,] 10.84912 0.04636339
[129,] 10.85159 0.04636759
[130,] 10.85284 0.04637121
[131,] 10.85409 0.04637422
[132,] 10.85536 0.04637663
[133,] 10.85663 0.04637842
[134,] 10.85791 0.04637956
[135,] 10.85921 0.04638005
[136,] 10.86051 0.04637987
[137,] 10.86182 0.04637901
[138,] 10.86314 0.04637744
[139,] 10.86447 0.04637517
[140,] 10.86581 0.04637215
[141,] 10.86716 0.04636839
[142,] 10.86852 0.04636386
[143,] 10.86989 0.04635855
[144,] 10.87127 0.04635243
[145,] 10.87266 0.04634549
[146,] 10.87406 0.04633771
[147,] 10.87547 0.04632906
[148,] 10.87689 0.04631954
[149,] 10.87833 0.04630911
[150,] 10.87977 0.04629776
[151,] 10.88123 0.04628546
[152,] 10.88269 0.04627219
[153,] 10.88417 0.04625793
[154,] 10.88566 0.04624265
[155,] 10.88716 0.04622634
[156,] 10.88867 0.04620895
[157,] 10.89020 0.04619048
[158,] 10.89173 0.04617089
[159,] 10.89328 0.04615015
[160,] 10.89484 0.04612824
[161,] 10.89641 0.04610513
[162,] 10.89800 0.04608079
[163,] 10.89960 0.04605518
[164,] 10.90121 0.04602828
[165,] 10.90283 0.04600005
[166,] 10.90447 0.04597047
[167,] 10.90612 0.04593948
[168,] 10.90779 0.04590708
[169,] 10.90947 0.04587320
[170,] 10.91116 0.04583782
[171,] 10.91286 0.04580090
[172,] 10.91458 0.04576240
[173,] 10.91632 0.04572228
[174,] 10.91807 0.04568050
[175,] 10.91983 0.04563700
[176,] 10.92161 0.04559176
[177,] 10.92340 0.04554471
[178,] 10.92521 0.04549582
[179,] 10.92704 0.04544504
[180,] 10.92888 0.04539230
[181,] 10.93074 0.04533757
[182,] 10.93261 0.04528079
[183,] 10.93450 0.04522190
[184,] 10.93640 0.04516084
[185,] 10.93833 0.04509755
[186,] 10.94027 0.04503198
[187,] 10.94000 0.04512240
[188,] 10.93973 0.04521335
[189,] 10.93946 0.04530485
[190,] 10.93919 0.04539689
[191,] 10.93891 0.04548948
[192,] 10.93864 0.04558263
[193,] 10.93836 0.04567633
[194,] 10.93807 0.04577061
[195,] 10.93779 0.04586546
[196,] 10.93750 0.04596088
[197,] 10.93721 0.04605689
[198,] 10.93692 0.04615349
[199,] 10.93662 0.04625068
[200,] 10.93632 0.04634848
[201,] 10.93602 0.04644688
[202,] 10.93571 0.04654590
[203,] 10.93541 0.04664553
[204,] 10.93510 0.04674579
[205,] 10.93478 0.04684668
[206,] 10.93447 0.04694822
[207,] 10.93415 0.04705039
[208,] 10.93382 0.04715322
[209,] 10.93350 0.04725670
[210,] 10.93317 0.04736085
[211,] 10.93284 0.04746568
[212,] 10.93250 0.04757118
[213,] 10.93216 0.04767736
[214,] 10.93182 0.04778424
[215,] 10.93147 0.04789182
[216,] 10.93112 0.04800011
[217,] 10.93077 0.04810911
[218,] 10.93041 0.04821884
[219,] 10.93005 0.04832929
[220,] 10.92969 0.04844048
[221,] 10.92932 0.04855242
[222,] 10.92895 0.04866511
[223,] 10.92857 0.04877857
[224,] 10.92819 0.04889279
[225,] 10.92781 0.04900779
[226,] 10.92742 0.04912358
[227,] 10.92703 0.04924016
[228,] 10.92663 0.04935755
[229,] 10.92623 0.04947575
[230,] 10.92582 0.04959477
[231,] 10.92541 0.04971462
[232,] 10.92500 0.04983531
[233,] 10.92458 0.04995684
[234,] 10.92416 0.05007924
[235,] 10.92373 0.05020251
[236,] 10.92330 0.05032665
[237,] 10.92286 0.05045168
[238,] 10.92241 0.05057760
[239,] 10.92241 0.05070443
[240,] 10.92197 0.05083218
[241,] 10.92151 0.05096086
[242,] 10.92105 0.05109048
[243,] 10.92059 0.05122104
[244,] 10.92012 0.05135256
[245,] 10.91964 0.05148505
[246,] 10.91916 0.05161853
[247,] 10.91867 0.05175300
[248,] 10.91818 0.05188847
[249,] 10.91768 0.05202495
[250,] 10.91718 0.05216246
[251,] 10.91667 0.05230102
[252,] 10.91615 0.05244062
[253,] 10.91563 0.05258128
[254,] 10.91509 0.05272302
[255,] 10.91456 0.05286585
[256,] 10.91401 0.05300978
[257,] 10.91290 0.05315482
[258,] 10.91234 0.05330098
[259,] 10.91176 0.05344829
[260,] 10.91118 0.05359675
[261,] 10.91060 0.05374637
[262,] 10.91000 0.05389717
[263,] 10.90940 0.05404917
[264,] 10.90878 0.05420237
[265,] 10.90816 0.05435679
[266,] 10.90753 0.05451245
[267,] 10.90690 0.05466936
[268,] 10.90625 0.05482753
[269,] 10.90559 0.05498698
[270,] 10.90493 0.05514773
[271,] 10.90426 0.05530978
[272,] 10.90357 0.05547316
[273,] 10.90288 0.05563787
[274,] 10.90217 0.05580395
> (midr <- midrange(x))
[1] 17.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 11.11949 11.11949 11.11949 11.11949 11.11949 11.11949 11.11949 11.11949
> postscript(file="/var/www/html/freestat/rcomp/tmp/12br71246564026.ps",horizontal=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/www/html/freestat/rcomp/tmp/2w0xz1246564026.ps",horizontal=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/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/www/html/freestat/rcomp/tmp/3i3pz1246564026.tab") 
> 
> system("convert tmp/12br71246564026.ps tmp/12br71246564026.png")
> system("convert tmp/2w0xz1246564026.ps tmp/2w0xz1246564026.png")
> 
> 
> proc.time()
   user  system elapsed 
  8.129   0.648   8.401