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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+ ,15)
> 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] 10.74174
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.06411495
> (armose <- arm / armse)
[1] 167.5387
> (geo <- geomean(x))
[1] 10.58114
> (har <- harmean(x))
[1] 10.41615
> (qua <- quamean(x))
[1] 10.89676
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 10.74174 0.06411495
  [2,] 10.74174 0.06411495
  [3,] 10.74174 0.06411495
  [4,] 10.74174 0.06411495
  [5,] 10.74174 0.06411495
  [6,] 10.74174 0.06411495
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 [14,] 10.74174 0.06411495
 [15,] 10.74174 0.06411495
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 [17,] 10.74174 0.06411495
 [18,] 10.74174 0.06411495
 [19,] 10.74174 0.06411495
 [20,] 10.71726 0.06232575
 [21,] 10.71726 0.06232575
 [22,] 10.71726 0.06232575
 [23,] 10.74541 0.06051065
 [24,] 10.74541 0.06051065
 [25,] 10.74541 0.06051065
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 [55,] 10.74541 0.06051065
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 [57,] 10.74541 0.06051065
 [58,] 10.67442 0.05635661
 [59,] 10.67442 0.05635661
 [60,] 10.67442 0.05635661
 [61,] 10.67442 0.05635661
 [62,] 10.67442 0.05635661
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 [70,] 10.67442 0.05635661
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 [75,] 10.67442 0.05635661
 [76,] 10.67442 0.05635661
 [77,] 10.67442 0.05635661
 [78,] 10.67442 0.05635661
 [79,] 10.67442 0.05635661
 [80,] 10.67442 0.05635661
 [81,] 10.67442 0.05635661
 [82,] 10.67442 0.05635661
 [83,] 10.67442 0.05635661
 [84,] 10.57160 0.05199106
 [85,] 10.57160 0.05199106
 [86,] 10.57160 0.05199106
 [87,] 10.57160 0.05199106
 [88,] 10.57160 0.05199106
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 [90,] 10.57160 0.05199106
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 [96,] 10.57160 0.05199106
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 [99,] 10.57160 0.05199106
[100,] 10.57160 0.05199106
[101,] 10.57160 0.05199106
[102,] 10.57160 0.05199106
[103,] 10.57160 0.05199106
[104,] 10.57160 0.05199106
[105,] 10.57160 0.05199106
[106,] 10.57160 0.05199106
[107,] 10.57160 0.05199106
[108,] 10.57160 0.05199106
[109,] 10.57160 0.05199106
[110,] 10.57160 0.05199106
[111,] 10.57160 0.05199106
[112,] 10.57160 0.05199106
[113,] 10.57160 0.05199106
[114,] 10.57160 0.05199106
[115,] 10.57160 0.05199106
[116,] 10.57160 0.05199106
[117,] 10.57160 0.05199106
[118,] 10.57160 0.05199106
[119,] 10.57160 0.05199106
[120,] 10.57160 0.05199106
[121,] 10.71971 0.04386575
[122,] 10.71971 0.04386575
[123,] 10.71971 0.04386575
[124,] 10.71971 0.04386575
[125,] 10.71971 0.04386575
[126,] 10.71971 0.04386575
[127,] 10.71971 0.04386575
[128,] 10.71971 0.04386575
[129,] 10.71971 0.04386575
[130,] 10.71971 0.04386575
[131,] 10.71971 0.04386575
[132,] 10.71971 0.04386575
[133,] 10.71971 0.04386575
[134,] 10.71971 0.04386575
[135,] 10.71971 0.04386575
[136,] 10.71971 0.04386575
[137,] 10.71971 0.04386575
[138,] 10.71971 0.04386575
[139,] 10.71971 0.04386575
[140,] 10.71971 0.04386575
[141,] 10.71971 0.04386575
[142,] 10.71971 0.04386575
[143,] 10.71971 0.04386575
[144,] 10.71971 0.04386575
[145,] 10.71971 0.04386575
[146,] 10.71971 0.04386575
[147,] 10.71971 0.04386575
[148,] 10.71971 0.04386575
[149,] 10.71971 0.04386575
[150,] 10.71971 0.04386575
[151,] 10.71971 0.04386575
[152,] 10.71971 0.04386575
[153,] 10.71971 0.04386575
[154,] 10.71971 0.04386575
[155,] 10.71971 0.04386575
[156,] 10.71971 0.04386575
[157,] 10.71971 0.04386575
[158,] 10.71971 0.04386575
[159,] 10.71971 0.04386575
[160,] 10.71971 0.04386575
[161,] 10.71971 0.04386575
[162,] 10.71971 0.04386575
[163,] 10.71971 0.04386575
[164,] 10.71971 0.04386575
[165,] 10.71971 0.04386575
[166,] 10.71971 0.04386575
[167,] 10.71971 0.04386575
[168,] 10.71971 0.04386575
[169,] 10.71971 0.04386575
[170,] 10.71971 0.04386575
[171,] 10.71971 0.04386575
[172,] 10.71971 0.04386575
[173,] 10.71971 0.04386575
[174,] 10.71971 0.04386575
[175,] 10.71971 0.04386575
[176,] 10.71971 0.04386575
[177,] 10.71971 0.04386575
[178,] 10.71971 0.04386575
[179,] 10.71971 0.04386575
[180,] 10.71971 0.04386575
[181,] 10.71971 0.04386575
[182,] 10.71971 0.04386575
[183,] 10.71971 0.04386575
[184,] 10.71971 0.04386575
[185,] 10.71971 0.04386575
[186,] 10.71971 0.04386575
[187,] 10.71971 0.04386575
[188,] 10.71971 0.04386575
[189,] 10.95104 0.03416216
[190,] 10.95104 0.03416216
[191,] 10.95104 0.03416216
[192,] 10.95104 0.03416216
[193,] 10.95104 0.03416216
[194,] 10.95104 0.03416216
[195,] 10.95104 0.03416216
[196,] 10.95104 0.03416216
[197,] 10.95104 0.03416216
[198,] 10.95104 0.03416216
[199,] 10.95104 0.03416216
[200,] 10.95104 0.03416216
[201,] 10.95104 0.03416216
[202,] 10.95104 0.03416216
[203,] 10.95104 0.03416216
[204,] 10.95104 0.03416216
[205,] 10.95104 0.03416216
[206,] 10.95104 0.03416216
[207,] 10.95104 0.03416216
[208,] 10.95104 0.03416216
[209,] 10.95104 0.03416216
[210,] 10.95104 0.03416216
[211,] 10.95104 0.03416216
[212,] 10.95104 0.03416216
[213,] 10.95104 0.03416216
[214,] 10.95104 0.03416216
[215,] 10.95104 0.03416216
[216,] 10.95104 0.03416216
[217,] 10.95104 0.03416216
[218,] 10.95104 0.03416216
[219,] 10.95104 0.03416216
[220,] 10.95104 0.03416216
[221,] 10.95104 0.03416216
[222,] 10.95104 0.03416216
[223,] 10.95104 0.03416216
[224,] 10.95104 0.03416216
[225,] 10.95104 0.03416216
[226,] 10.95104 0.03416216
[227,] 10.95104 0.03416216
[228,] 10.95104 0.03416216
[229,] 10.95104 0.03416216
[230,] 10.95104 0.03416216
[231,] 10.95104 0.03416216
[232,] 10.95104 0.03416216
[233,] 10.95104 0.03416216
[234,] 10.95104 0.03416216
[235,] 10.95104 0.03416216
[236,] 10.95104 0.03416216
[237,] 10.95104 0.03416216
[238,] 10.95104 0.03416216
[239,] 10.95104 0.03416216
[240,] 10.95104 0.03416216
[241,] 10.95104 0.03416216
[242,] 10.95104 0.03416216
[243,] 10.95104 0.03416216
[244,] 10.95104 0.03416216
[245,] 10.95104 0.03416216
[246,] 10.95104 0.03416216
[247,] 10.95104 0.03416216
[248,] 10.95104 0.03416216
[249,] 10.95104 0.03416216
[250,] 10.95104 0.03416216
[251,] 10.95104 0.03416216
[252,] 10.95104 0.03416216
[253,] 10.95104 0.03416216
[254,] 10.95104 0.03416216
[255,] 10.95104 0.03416216
[256,] 10.95104 0.03416216
[257,] 10.95104 0.03416216
[258,] 10.95104 0.03416216
[259,] 10.95104 0.03416216
[260,] 10.95104 0.03416216
[261,] 10.95104 0.03416216
[262,] 10.95104 0.03416216
[263,] 10.95104 0.03416216
[264,] 10.95104 0.03416216
[265,] 10.95104 0.03416216
[266,] 10.95104 0.03416216
[267,] 10.95104 0.03416216
[268,] 10.95104 0.03416216
[269,] 10.95104 0.03416216
[270,] 10.95104 0.03416216
[271,] 10.95104 0.03416216
[272,] 10.95104 0.03416216
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 10.74174 0.06389446
  [2,] 10.74110 0.06367063
  [3,] 10.73983 0.06344338
  [4,] 10.73983 0.06321265
  [5,] 10.73854 0.06297836
  [6,] 10.73789 0.06274046
  [7,] 10.73789 0.06249886
  [8,] 10.73724 0.06225349
  [9,] 10.73592 0.06200426
 [10,] 10.73526 0.06175111
 [11,] 10.73459 0.06149393
 [12,] 10.73392 0.06123266
 [13,] 10.73325 0.06096720
 [14,] 10.73325 0.06069745
 [15,] 10.73189 0.06042333
 [16,] 10.73189 0.06014473
 [17,] 10.73052 0.05986155
 [18,] 10.72983 0.05957369
 [19,] 10.72914 0.05928104
 [20,] 10.72844 0.05898349
 [21,] 10.72903 0.05878797
 [22,] 10.72962 0.05858935
 [23,] 10.73022 0.05838758
 [24,] 10.72952 0.05827651
 [25,] 10.72881 0.05816365
 [26,] 10.72810 0.05804898
 [27,] 10.72739 0.05793246
 [28,] 10.72739 0.05781406
 [29,] 10.72596 0.05769375
 [30,] 10.72523 0.05757149
 [31,] 10.72450 0.05744724
 [32,] 10.72450 0.05732098
 [33,] 10.72304 0.05719267
 [34,] 10.72230 0.05706226
 [35,] 10.72155 0.05692973
 [36,] 10.72081 0.05679503
 [37,] 10.72005 0.05665813
 [38,] 10.71930 0.05651897
 [39,] 10.71854 0.05637753
 [40,] 10.71777 0.05623375
 [41,] 10.71701 0.05608759
 [42,] 10.71623 0.05593902
 [43,] 10.71546 0.05578797
 [44,] 10.71468 0.05563441
 [45,] 10.71389 0.05547828
 [46,] 10.71310 0.05531953
 [47,] 10.71231 0.05515812
 [48,] 10.71151 0.05499398
 [49,] 10.71071 0.05482707
 [50,] 10.70990 0.05465733
 [51,] 10.70909 0.05448470
 [52,] 10.70827 0.05430911
 [53,] 10.70745 0.05413052
 [54,] 10.70663 0.05394885
 [55,] 10.70580 0.05376405
 [56,] 10.70580 0.05357603
 [57,] 10.70413 0.05338474
 [58,] 10.70328 0.05319011
 [59,] 10.70328 0.05310012
 [60,] 10.70445 0.05300849
 [61,] 10.70504 0.05291519
 [62,] 10.70563 0.05282019
 [63,] 10.70622 0.05272346
 [64,] 10.70622 0.05262496
 [65,] 10.70742 0.05252467
 [66,] 10.70803 0.05242255
 [67,] 10.70864 0.05231856
 [68,] 10.70925 0.05221267
 [69,] 10.70987 0.05210485
 [70,] 10.71049 0.05199505
 [71,] 10.71111 0.05188324
 [72,] 10.71174 0.05176938
 [73,] 10.71237 0.05165343
 [74,] 10.71300 0.05153535
 [75,] 10.71364 0.05141509
 [76,] 10.71429 0.05129261
 [77,] 10.71493 0.05116787
 [78,] 10.71558 0.05104082
 [79,] 10.71624 0.05091142
 [80,] 10.71689 0.05077961
 [81,] 10.71756 0.05064535
 [82,] 10.71822 0.05050858
 [83,] 10.71889 0.05036925
 [84,] 10.71957 0.05022731
 [85,] 10.72179 0.05016762
 [86,] 10.72403 0.05010648
 [87,] 10.72628 0.05004385
 [88,] 10.72855 0.04997970
 [89,] 10.73083 0.04991402
 [90,] 10.73312 0.04984676
 [91,] 10.73543 0.04977789
 [92,] 10.73776 0.04970737
 [93,] 10.74010 0.04963519
 [94,] 10.74245 0.04956129
 [95,] 10.74482 0.04948565
 [96,] 10.74720 0.04940823
 [97,] 10.74960 0.04932899
 [98,] 10.75201 0.04924789
 [99,] 10.75444 0.04916489
[100,] 10.75689 0.04907995
[101,] 10.75935 0.04899303
[102,] 10.76183 0.04890409
[103,] 10.76432 0.04881308
[104,] 10.76683 0.04871995
[105,] 10.76936 0.04862466
[106,] 10.77190 0.04852716
[107,] 10.77190 0.04842741
[108,] 10.77704 0.04832534
[109,] 10.77963 0.04822091
[110,] 10.78224 0.04811407
[111,] 10.78487 0.04800475
[112,] 10.78487 0.04789290
[113,] 10.79019 0.04777846
[114,] 10.79287 0.04766137
[115,] 10.79557 0.04754157
[116,] 10.79829 0.04741899
[117,] 10.80103 0.04729357
[118,] 10.80103 0.04716522
[119,] 10.80656 0.04703390
[120,] 10.80936 0.04689951
[121,] 10.81217 0.04676198
[122,] 10.81326 0.04677244
[123,] 10.81326 0.04678243
[124,] 10.81547 0.04679193
[125,] 10.81658 0.04680093
[126,] 10.81770 0.04680942
[127,] 10.81883 0.04681740
[128,] 10.81883 0.04682484
[129,] 10.82111 0.04683174
[130,] 10.82226 0.04683808
[131,] 10.82342 0.04684384
[132,] 10.82459 0.04684903
[133,] 10.82577 0.04685362
[134,] 10.82696 0.04685760
[135,] 10.82815 0.04686095
[136,] 10.82936 0.04686366
[137,] 10.83057 0.04686572
[138,] 10.83179 0.04686711
[139,] 10.83302 0.04686782
[140,] 10.83426 0.04686782
[141,] 10.83551 0.04686710
[142,] 10.83677 0.04686565
[143,] 10.83804 0.04686344
[144,] 10.83932 0.04686047
[145,] 10.84061 0.04685670
[146,] 10.84190 0.04685213
[147,] 10.84321 0.04684673
[148,] 10.84453 0.04684049
[149,] 10.84586 0.04683337
[150,] 10.84720 0.04682537
[151,] 10.84854 0.04681646
[152,] 10.84990 0.04680662
[153,] 10.85127 0.04679583
[154,] 10.85265 0.04678406
[155,] 10.85404 0.04677128
[156,] 10.85545 0.04675749
[157,] 10.85686 0.04674264
[158,] 10.85828 0.04672671
[159,] 10.85972 0.04670969
[160,] 10.86117 0.04669153
[161,] 10.86263 0.04667221
[162,] 10.86410 0.04665171
[163,] 10.86558 0.04662999
[164,] 10.86708 0.04660702
[165,] 10.86858 0.04658278
[166,] 10.87010 0.04655722
[167,] 10.87164 0.04653032
[168,] 10.87318 0.04650204
[169,] 10.87474 0.04647234
[170,] 10.87631 0.04644120
[171,] 10.87789 0.04640856
[172,] 10.87949 0.04637440
[173,] 10.88110 0.04633868
[174,] 10.88273 0.04630134
[175,] 10.88437 0.04626236
[176,] 10.88602 0.04622168
[177,] 10.88769 0.04617927
[178,] 10.88937 0.04613507
[179,] 10.89107 0.04608903
[180,] 10.89278 0.04604112
[181,] 10.89451 0.04599127
[182,] 10.89625 0.04593944
[183,] 10.89800 0.04588557
[184,] 10.89978 0.04582960
[185,] 10.90157 0.04577147
[186,] 10.90337 0.04571113
[187,] 10.90519 0.04564852
[188,] 10.90703 0.04558356
[189,] 10.90888 0.04551620
[190,] 10.90847 0.04560886
[191,] 10.90805 0.04570208
[192,] 10.90762 0.04579584
[193,] 10.90719 0.04589016
[194,] 10.90676 0.04598504
[195,] 10.90632 0.04608050
[196,] 10.90588 0.04617652
[197,] 10.90544 0.04627313
[198,] 10.90499 0.04637032
[199,] 10.90453 0.04646810
[200,] 10.90408 0.04656648
[201,] 10.90361 0.04666546
[202,] 10.90315 0.04676504
[203,] 10.90268 0.04686524
[204,] 10.90220 0.04696606
[205,] 10.90172 0.04706750
[206,] 10.90123 0.04716957
[207,] 10.90074 0.04727229
[208,] 10.90025 0.04737564
[209,] 10.89975 0.04747964
[210,] 10.89924 0.04758430
[211,] 10.89873 0.04768963
[212,] 10.89822 0.04779562
[213,] 10.89822 0.04790228
[214,] 10.89770 0.04800963
[215,] 10.89664 0.04811767
[216,] 10.89610 0.04822640
[217,] 10.89556 0.04833584
[218,] 10.89501 0.04844598
[219,] 10.89446 0.04855684
[220,] 10.89390 0.04866842
[221,] 10.89333 0.04878074
[222,] 10.89276 0.04889379
[223,] 10.89218 0.04900759
[224,] 10.89218 0.04912214
[225,] 10.89160 0.04923745
[226,] 10.89041 0.04935352
[227,] 10.88981 0.04947038
[228,] 10.88920 0.04958801
[229,] 10.88858 0.04970644
[230,] 10.88796 0.04982567
[231,] 10.88732 0.04994570
[232,] 10.88669 0.05006655
[233,] 10.88604 0.05018822
[234,] 10.88539 0.05031072
[235,] 10.88539 0.05043406
[236,] 10.88473 0.05055825
[237,] 10.88338 0.05068330
[238,] 10.88270 0.05080921
[239,] 10.88201 0.05093600
[240,] 10.88131 0.05106367
[241,] 10.88060 0.05119223
[242,] 10.87988 0.05132169
[243,] 10.87915 0.05145206
[244,] 10.87842 0.05158335
[245,] 10.87768 0.05171557
[246,] 10.87768 0.05184872
[247,] 10.87692 0.05198282
[248,] 10.87539 0.05211788
[249,] 10.87461 0.05225390
[250,] 10.87382 0.05239089
[251,] 10.87302 0.05252887
[252,] 10.87220 0.05266785
[253,] 10.87138 0.05280782
[254,] 10.87055 0.05294881
[255,] 10.86971 0.05309082
[256,] 10.86971 0.05323387
[257,] 10.86799 0.05337796
[258,] 10.86711 0.05352310
[259,] 10.86622 0.05366930
[260,] 10.86532 0.05381657
[261,] 10.86441 0.05396493
[262,] 10.86348 0.05411438
[263,] 10.86254 0.05426492
[264,] 10.86159 0.05441659
[265,] 10.86063 0.05456937
[266,] 10.85965 0.05472328
[267,] 10.85866 0.05487834
[268,] 10.85765 0.05503454
[269,] 10.85663 0.05519191
[270,] 10.85560 0.05535044
[271,] 10.85455 0.05551016
[272,] 10.85348 0.05567106
> (midr <- midrange(x))
[1] 11
> 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/1smbl1249436495.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/2heb31249436495.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/3ejrf1249436495.tab") 
> 
> system("convert tmp/1smbl1249436495.ps tmp/1smbl1249436495.png")
> system("convert tmp/2heb31249436495.ps tmp/2heb31249436495.png")
> 
> 
> proc.time()
   user  system elapsed 
  8.000   0.652   8.197