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.

  Natural language support but running in an English locale

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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(109
+ ,110.73
+ ,110.92
+ ,111.35
+ ,111.28
+ ,112.5
+ ,113.97
+ ,114.09
+ ,113.72
+ ,112.5
+ ,113.21
+ ,113.31
+ ,112.59
+ ,112.78
+ ,113.48
+ ,112.44
+ ,112.88
+ ,114.41
+ ,115.15
+ ,113.67
+ ,113.18
+ ,111.94
+ ,111.87
+ ,112.57
+ ,112.78
+ ,113.11
+ ,113.21
+ ,113.18
+ ,113.65
+ ,112.59
+ ,113.16
+ ,113
+ ,114.28
+ ,114.43
+ ,114.23
+ ,113.35
+ ,114.24
+ ,114.21
+ ,115.1
+ ,114.98
+ ,114.8
+ ,114.1
+ ,114.26
+ ,113.68
+ ,113.85
+ ,113.22
+ ,113.52
+ ,113.2
+ ,112.49
+ ,113.14
+ ,112.05
+ ,112.07
+ ,111.98
+ ,111.93
+ ,111.04
+ ,107.04
+ ,107.69
+ ,106.84
+ ,106.46
+ ,106.41
+ ,106.86
+ ,108.42
+ ,108.38
+ ,107.81
+ ,107.54
+ ,107.07
+ ,107.54
+ ,107.74
+ ,107.15
+ ,106.49
+ ,106.19
+ ,108.23
+ ,108.54
+ ,109.82
+ ,109.93
+ ,109.66
+ ,109.49
+ ,109.78
+ ,109.5
+ ,110.56
+ ,113.23
+ ,113.48
+ ,113.14
+ ,113.66
+ ,112.92
+ ,113.51
+ ,113.27
+ ,112.62
+ ,113.64
+ ,114.01
+ ,113.79
+ ,112.31
+ ,112.48
+ ,111.57
+ ,111.52
+ ,111.5
+ ,112.84
+ ,112.54
+ ,113.11
+ ,112.49
+ ,110.95
+ ,111.35
+ ,111.85
+ ,111.49
+ ,109.56
+ ,110.46
+ ,109.93
+ ,109.88
+ ,108.14
+ ,108.79
+ ,108.31
+ ,110.25
+ ,109.99
+ ,109.59
+ ,110.76
+ ,111.09
+ ,113.1
+ ,112.12
+ ,112.89
+ ,112.15
+ ,111.77
+ ,112.43
+ ,111.13
+ ,109.84
+ ,109.99
+ ,109.32
+ ,109.86
+ ,111.73
+ ,113.74
+ ,112.36
+ ,110.65
+ ,112.62
+ ,113.06
+ ,110.79
+ ,111.35
+ ,109.53
+ ,111.63
+ ,112.08
+ ,111.93
+ ,112.49
+ ,115.32
+ ,114.17
+ ,115.55
+ ,116.99
+ ,118.06
+ ,117.38
+ ,120.97
+ ,117.84
+ ,119.34
+ ,122.66
+ ,123.66
+ ,124.95
+ ,125.81
+ ,124.76
+ ,124.48
+ ,124.7
+ ,125.46
+ ,125.11
+ ,124.03
+ ,124.65
+ ,125.32
+ ,123.5
+ ,125.3
+ ,126.18
+ ,127.42
+ ,126.34
+ ,126.99
+ ,125.34
+ ,123.76
+ ,125.04
+ ,126.04
+ ,126.28
+ ,125.93
+ ,124.8
+ ,124.75
+ ,124
+ ,123.44
+ ,122.62
+ ,122.16
+ ,121.25
+ ,122.86
+ ,123.33
+ ,124.43
+ ,124.22
+ ,124.3
+ ,124.57
+ ,123.84
+ ,123.16
+ ,121.72
+ ,123.48
+ ,121.48
+ ,120.86
+ ,121.1
+ ,120.68
+ ,120.67
+ ,120.92
+ ,120.66
+ ,122.16
+ ,123.19
+ ,124.38
+ ,124.17
+ ,123.3
+ ,124.69
+ ,122.68
+ ,122.42
+ ,122.33
+ ,123.03
+ ,123.01
+ ,123.4
+ ,122.07
+ ,122.49
+ ,125.68
+ ,126.73
+ ,126.2
+ ,125.6
+ ,126.15
+ ,126.36
+ ,125.95
+ ,126.31
+ ,127.74
+ ,127.35
+ ,129.14
+ ,128.65
+ ,129.79
+ ,130.33
+ ,130.76
+ ,132.88
+ ,133.02
+ ,132.41
+ ,134.23
+ ,133.36
+ ,133.5
+ ,132.69
+ ,132.54
+ ,133.62
+ ,133.16
+ ,132.35
+ ,132.44
+ ,131.86
+ ,131.73
+ ,130.95
+ ,130.83
+ ,130.1
+ ,129.68
+ ,129.27
+ ,130.61
+ ,130.22
+ ,129.55
+ ,131.13
+ ,130.03
+ ,129.91
+ ,130.74
+ ,133.24
+ ,133.08
+ ,133.17
+ ,131.55
+ ,131.02
+ ,129.77
+ ,129.2
+ ,130.7
+ ,132.1
+ ,132.57
+ ,133.03
+ ,131.87
+ ,132.05
+ ,133.39
+ ,132.76
+ ,134.02
+ ,133.51
+ ,134.32
+ ,135.11
+ ,134.51
+ ,134.81
+ ,134.76
+ ,134.3
+ ,134.3
+ ,132.25
+ ,132.95
+ ,134.66
+ ,135.13
+ ,134.76
+ ,136.91
+ ,138.09
+ ,137.97
+ ,136.9
+ ,135.82
+ ,135.53
+ ,135.66
+ ,135.6
+ ,134.07
+ ,133.39
+ ,133.02
+ ,132.99
+ ,131.12
+ ,130.46
+ ,130.68
+ ,131.21
+ ,131.41
+ ,129.95
+ ,130.78
+ ,131.07
+ ,130.91
+ ,131.15
+ ,132.59
+ ,133.85
+ ,134.96
+ ,135.09
+ ,135.46
+ ,134.17
+ ,134.38
+ ,132.6
+ ,133.26
+ ,132.3
+ ,132.62
+ ,133.92
+ ,134.13
+ ,133.57
+ ,133.33
+ ,132.45
+ ,132.47
+ ,131.63
+ ,133.26
+ ,133.1
+ ,134.75
+ ,133.61
+ ,134.32
+ ,135.05
+ ,135.57
+ ,134.19
+ ,134.11
+ ,132.55
+ ,134.12
+ ,132.94
+ ,135.61
+ ,137.52
+ ,135.77
+ ,136.72
+ ,138.01
+ ,136.89
+ ,137.31
+ ,137.38
+ ,136.22
+ ,135.86
+ ,135.33
+ ,133.89
+ ,133.86
+ ,134.53
+ ,135.61
+ ,134.92
+ ,134.23
+ ,132.49
+ ,134.1
+ ,134.44
+ ,132.06
+ ,132.63
+ ,131.57
+ ,130.34
+ ,129.03
+ ,128.21
+ ,130.05
+ ,131.02
+ ,133.61
+ ,132.44
+ ,134.32
+ ,135.95
+ ,136.53
+ ,135.51
+ ,134.03
+ ,134.5
+ ,134.34
+ ,133.77
+ ,133.49
+ ,133.02
+ ,134.84
+ ,133.57
+ ,133.28
+ ,134.78
+ ,136.08
+ ,137.55
+ ,137.39
+ ,138.03
+ ,136.8
+ ,136.53
+ ,137.48
+ ,136.32
+ ,136.33
+ ,136.09
+ ,134.89
+ ,135.22
+ ,134.38
+ ,132.48
+ ,132.06
+ ,133.22
+ ,131.41
+ ,130.84
+ ,131.06
+ ,130.91
+ ,129.28
+ ,128.67
+ ,129.41
+ ,130.9
+ ,132.9
+ ,132.82
+ ,133.36
+ ,132.72
+ ,131.17
+ ,132.59
+ ,131.52
+ ,130.34
+ ,128.53
+ ,125.08
+ ,126.82
+ ,128.3
+ ,128.28
+ ,126.85
+ ,126.82
+ ,127.8
+ ,129.67
+ ,130.5
+ ,130.7
+ ,132.57
+ ,133.05
+ ,132.37
+ ,132.8
+ ,136.02
+ ,134.08
+ ,133.48
+ ,130.86
+ ,131.17
+ ,127.93
+ ,129.91
+ ,133.63
+ ,132.24
+ ,132.68
+ ,131.12
+ ,129.87
+ ,129.67
+ ,128.94
+ ,128.1
+ ,128.51
+ ,127.03
+ ,124.3
+ ,125.35
+ ,125.45
+ ,124.4
+ ,122.53
+ ,124.71
+ ,124.67
+ ,123.64
+ ,122.52
+ ,123.23
+ ,125.33
+ ,123.76
+ ,122.4
+ ,121.09
+ ,118.62
+ ,118.99
+ ,116.83
+ ,116.2
+ ,117.33
+ ,117.59
+ ,115.46
+ ,116.5
+ ,118.39
+ ,119.21
+ ,116.7
+ ,115.04
+ ,114.28
+ ,115.02
+ ,114.04
+ ,114.98
+ ,118.07
+ ,118.57
+ ,117.59
+ ,115.82
+ ,113.65
+ ,114.98
+ ,116.11
+ ,116.9
+ ,119.16
+ ,120.11
+ ,116.97
+ ,117.66
+ ,118.54
+ ,120.48
+ ,124.4
+ ,124.34
+ ,126.77
+ ,125.84
+ ,126.81
+ ,126.64)
> 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: Wessa, P., (2007), Central Tendency (v1.0.2) 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
> #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] 123.8762
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.4230923
> (armose <- arm / armse)
[1] 292.7876
> (geo <- geomean(x))
[1] 123.5161
> (har <- harmean(x))
[1] 123.1509
> (qua <- quamean(x))
[1] 124.2297
> (win <- winmean(x))
           [,1]      [,2]
  [1,] 123.8765 0.4230459
  [2,] 123.8766 0.4230232
  [3,] 123.8766 0.4229912
  [4,] 123.8760 0.4225250
  [5,] 123.8759 0.4224881
  [6,] 123.8776 0.4222760
  [7,] 123.8767 0.4221571
  [8,] 123.8779 0.4220408
  [9,] 123.8837 0.4213852
 [10,] 123.8756 0.4208628
 [11,] 123.8787 0.4205836
 [12,] 123.8797 0.4204723
 [13,] 123.8792 0.4201774
 [14,] 123.8863 0.4193068
 [15,] 123.8833 0.4187364
 [16,] 123.8859 0.4185379
 [17,] 123.8814 0.4179302
 [18,] 123.8825 0.4177971
 [19,] 123.8832 0.4172132
 [20,] 123.8881 0.4161358
 [21,] 123.8967 0.4154490
 [22,] 123.9083 0.4142485
 [23,] 123.9130 0.4134837
 [24,] 123.9091 0.4131884
 [25,] 123.9086 0.4129597
 [26,] 123.9075 0.4126913
 [27,] 123.9031 0.4122209
 [28,] 123.9043 0.4117728
 [29,] 123.9114 0.4112742
 [30,] 123.9132 0.4110675
 [31,] 123.9126 0.4108694
 [32,] 123.9113 0.4106276
 [33,] 123.9113 0.4104562
 [34,] 123.9113 0.4100156
 [35,] 123.9020 0.4094854
 [36,] 123.8983 0.4087218
 [37,] 123.8915 0.4083396
 [38,] 123.9101 0.4068643
 [39,] 123.9252 0.4056386
 [40,] 123.9301 0.4049053
 [41,] 123.9301 0.4039800
 [42,] 123.9335 0.4033314
 [43,] 123.9335 0.4030101
 [44,] 123.9317 0.4025827
 [45,] 123.9409 0.4016398
 [46,] 123.9409 0.4012989
 [47,] 123.9476 0.4006256
 [48,] 123.9525 0.4003046
 [49,] 123.9555 0.3999881
 [50,] 123.9616 0.3984889
 [51,] 123.9554 0.3972807
 [52,] 123.9532 0.3971657
 [53,] 123.9522 0.3971071
 [54,] 123.9610 0.3957563
 [55,] 123.9554 0.3953218
 [56,] 123.9576 0.3951752
 [57,] 123.9588 0.3945532
 [58,] 123.9635 0.3939729
 [59,] 123.9755 0.3932072
 [60,] 123.9804 0.3928968
 [61,] 123.9879 0.3921343
 [62,] 123.9904 0.3919749
 [63,] 123.9891 0.3910086
 [64,] 123.9891 0.3910086
 [65,] 123.9852 0.3906426
 [66,] 123.9878 0.3901613
 [67,] 123.9919 0.3892719
 [68,] 123.9933 0.3890250
 [69,] 123.9933 0.3888625
 [70,] 123.9976 0.3884306
 [71,] 123.9990 0.3880066
 [72,] 124.0210 0.3864722
 [73,] 124.0225 0.3856978
 [74,] 124.0316 0.3849680
 [75,] 124.0178 0.3840678
 [76,] 124.0194 0.3834431
 [77,] 124.0162 0.3830998
 [78,] 124.0146 0.3830166
 [79,] 124.0018 0.3823437
 [80,] 123.9806 0.3810595
 [81,] 123.9789 0.3809743
 [82,] 123.9840 0.3804776
 [83,] 123.9890 0.3801665
 [84,] 123.9856 0.3796038
 [85,] 123.9856 0.3796038
 [86,] 123.9803 0.3787415
 [87,] 123.9786 0.3786505
 [88,] 124.0055 0.3768090
 [89,] 124.0036 0.3767159
 [90,] 123.9981 0.3752030
 [91,] 124.0056 0.3747534
 [92,] 124.0018 0.3743529
 [93,] 124.0075 0.3740089
 [94,] 124.0171 0.3727908
 [95,] 124.0190 0.3715987
 [96,] 124.0229 0.3709295
 [97,] 124.0249 0.3708108
 [98,] 124.0209 0.3706081
 [99,] 124.0229 0.3700402
[100,] 124.0127 0.3695244
[101,] 124.0148 0.3691734
[102,] 124.0065 0.3682951
[103,] 124.0023 0.3680838
[104,] 124.0002 0.3675101
[105,] 123.9980 0.3671670
[106,] 123.9959 0.3670586
[107,] 123.9980 0.3669280
[108,] 124.0002 0.3667961
[109,] 124.0025 0.3659303
[110,] 124.0025 0.3649454
[111,] 124.0092 0.3642920
[112,] 124.0298 0.3620686
[113,] 124.0252 0.3618386
[114,] 124.0182 0.3607297
[115,] 124.0159 0.3603573
[116,] 124.0348 0.3582053
[117,] 124.0276 0.3575908
[118,] 124.0204 0.3572334
[119,] 124.0204 0.3569698
[120,] 124.0106 0.3562209
[121,] 124.0106 0.3559532
[122,] 124.0156 0.3551196
[123,] 124.0181 0.3546997
[124,] 124.0307 0.3539535
[125,] 124.0409 0.3528011
[126,] 124.0717 0.3509890
[127,] 124.0769 0.3501261
[128,] 124.0821 0.3495386
[129,] 124.0821 0.3481207
[130,] 124.0821 0.3478351
[131,] 124.0981 0.3466108
[132,] 124.1035 0.3457175
[133,] 124.1062 0.3452678
[134,] 124.1089 0.3451085
[135,] 124.1062 0.3443814
[136,] 124.1006 0.3435135
[137,] 124.0951 0.3432394
[138,] 124.1175 0.3404206
[139,] 124.1090 0.3393974
[140,] 124.2117 0.3331459
[141,] 124.2232 0.3281970
[142,] 124.2116 0.3276310
[143,] 124.2116 0.3276310
[144,] 124.2204 0.3268133
[145,] 124.1732 0.3238851
[146,] 124.1880 0.3227148
[147,] 124.1641 0.3199711
[148,] 124.1852 0.3155763
[149,] 124.2095 0.3122675
[150,] 124.2308 0.3104028
[151,] 124.3046 0.3052333
[152,] 124.3604 0.2985128
[153,] 124.3884 0.2969327
[154,] 124.4198 0.2886306
[155,] 124.4703 0.2844967
[156,] 124.5116 0.2821983
[157,] 124.5276 0.2806479
[158,] 124.5437 0.2790895
[159,] 124.5469 0.2785749
[160,] 124.6577 0.2724672
[161,] 124.6577 0.2707747
[162,] 124.7237 0.2668245
[163,] 124.7104 0.2661815
> (tri <- trimean(x))
           [,1]      [,2]
  [1,] 123.8762 0.4222775
  [2,] 123.8833 0.4214876
  [3,] 123.8969 0.4206874
  [4,] 123.8969 0.4198759
  [5,] 123.9109 0.4191642
  [6,] 123.9181 0.4184395
  [7,] 123.9251 0.4177316
  [8,] 123.9251 0.4170212
  [9,] 123.9393 0.4163056
 [10,] 123.9457 0.4156493
 [11,] 123.9530 0.4150307
 [12,] 123.9601 0.4144211
 [13,] 123.9672 0.4138027
 [14,] 123.9744 0.4131905
 [15,] 123.9811 0.4126307
 [16,] 123.9811 0.4120963
 [17,] 123.9949 0.4115583
 [18,] 124.0021 0.4110440
 [19,] 124.0093 0.4105205
 [20,] 124.0166 0.4100157
 [21,] 124.0236 0.4095585
 [22,] 124.0302 0.4091245
 [23,] 124.0363 0.4087415
 [24,] 124.0423 0.4083843
 [25,] 124.0485 0.4080268
 [26,] 124.0547 0.4076654
 [27,] 124.0611 0.4073013
 [28,] 124.0677 0.4069437
 [29,] 124.0743 0.4065910
 [30,] 124.0807 0.4062453
 [31,] 124.0871 0.4058929
 [32,] 124.0871 0.4055329
 [33,] 124.1001 0.4051667
 [34,] 124.1068 0.4047909
 [35,] 124.1135 0.4044161
 [36,] 124.1206 0.4040449
 [37,] 124.1278 0.4036862
 [38,] 124.1354 0.4033248
 [39,] 124.1424 0.4030026
 [40,] 124.1491 0.4027098
 [41,] 124.1557 0.4024279
 [42,] 124.1623 0.4021633
 [43,] 124.1689 0.4019061
 [44,] 124.1756 0.4016446
 [45,] 124.1824 0.4013818
 [46,] 124.1890 0.4011354
 [47,] 124.1956 0.4008847
 [48,] 124.2022 0.4006406
 [49,] 124.2087 0.4003912
 [50,] 124.2152 0.4001362
 [51,] 124.2216 0.3999127
 [52,] 124.2282 0.3997113
 [53,] 124.2350 0.3994978
 [54,] 124.2418 0.3992703
 [55,] 124.2485 0.3990682
 [56,] 124.2554 0.3988632
 [57,] 124.2623 0.3986466
 [58,] 124.2693 0.3984321
 [59,] 124.2762 0.3982185
 [60,] 124.2830 0.3980112
 [61,] 124.2897 0.3977965
 [62,] 124.2963 0.3975873
 [63,] 124.3030 0.3973658
 [64,] 124.3030 0.3971544
 [65,] 124.3165 0.3969257
 [66,] 124.3235 0.3966891
 [67,] 124.3305 0.3964480
 [68,] 124.3375 0.3962135
 [69,] 124.3445 0.3959674
 [70,] 124.3516 0.3957067
 [71,] 124.3587 0.3954386
 [72,] 124.3659 0.3951624
 [73,] 124.3727 0.3949094
 [74,] 124.3796 0.3946577
 [75,] 124.3864 0.3944065
 [76,] 124.3935 0.3941588
 [77,] 124.4007 0.3939079
 [78,] 124.4080 0.3936454
 [79,] 124.4154 0.3933638
 [80,] 124.4232 0.3930779
 [81,] 124.4314 0.3928031
 [82,] 124.4398 0.3925082
 [83,] 124.4482 0.3922040
 [84,] 124.4566 0.3918852
 [85,] 124.4652 0.3915571
 [86,] 124.4739 0.3912045
 [87,] 124.4828 0.3908492
 [88,] 124.4918 0.3904704
 [89,] 124.5005 0.3901167
 [90,] 124.5093 0.3897390
 [91,] 124.5183 0.3893747
 [92,] 124.5273 0.3889959
 [93,] 124.5365 0.3885998
 [94,] 124.5457 0.3881848
 [95,] 124.5549 0.3877743
 [96,] 124.5642 0.3873668
 [97,] 124.5735 0.3869480
 [98,] 124.5829 0.3865021
 [99,] 124.5925 0.3860297
[100,] 124.6022 0.3855403
[101,] 124.6122 0.3850306
[102,] 124.6224 0.3844961
[103,] 124.6328 0.3839495
[104,] 124.6434 0.3833717
[105,] 124.6542 0.3827717
[106,] 124.6652 0.3821421
[107,] 124.6764 0.3814747
[108,] 124.6877 0.3807690
[109,] 124.6992 0.3800233
[110,] 124.7107 0.3792572
[111,] 124.7225 0.3784728
[112,] 124.7343 0.3776604
[113,] 124.7460 0.3768666
[114,] 124.7579 0.3760296
[115,] 124.7701 0.3751733
[116,] 124.7825 0.3742751
[117,] 124.7948 0.3733898
[118,] 124.8075 0.3724672
[119,] 124.8204 0.3714976
[120,] 124.8335 0.3704767
[121,] 124.8471 0.3694157
[122,] 124.8608 0.3682988
[123,] 124.8608 0.3671420
[124,] 124.8888 0.3659295
[125,] 124.9029 0.3646709
[126,] 124.9170 0.3633766
[127,] 124.9309 0.3620702
[128,] 124.9309 0.3607148
[129,] 124.9592 0.3592985
[130,] 124.9736 0.3578456
[131,] 124.9883 0.3563149
[132,] 125.0030 0.3547378
[133,] 125.0179 0.3530983
[134,] 125.0330 0.3513763
[135,] 125.0483 0.3495567
[136,] 125.0640 0.3476534
[137,] 125.0800 0.3456662
[138,] 125.0964 0.3435675
[139,] 125.1128 0.3414550
[140,] 125.1296 0.3392508
[141,] 125.1450 0.3371811
[142,] 125.1605 0.3351796
[143,] 125.1765 0.3330702
[144,] 125.1928 0.3308257
[145,] 125.2093 0.3284732
[146,] 125.2269 0.3260793
[147,] 125.2447 0.3235831
[148,] 125.2632 0.3210346
[149,] 125.2817 0.3185156
[150,] 125.3002 0.3159809
[151,] 125.3187 0.3133645
[152,] 125.3364 0.3108269
[153,] 125.3534 0.3084369
[154,] 125.3703 0.3059596
[155,] 125.3871 0.3037005
[156,] 125.4033 0.3014844
[157,] 125.4192 0.2992258
[158,] 125.4351 0.2968784
[159,] 125.4511 0.2944364
[160,] 125.4674 0.2918370
[161,] 125.4821 0.2893851
[162,] 125.4972 0.2868310
[163,] 125.5114 0.2843051
> (midr <- midrange(x))
[1] 122.14
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 124.8293 124.8608 124.8608 124.8608 124.8747 124.8293 124.8608 124.8608
> postscript(file="/var/www/html/freestat/rcomp/tmp/1rasg1291668731.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/www/html/freestat/rcomp/tmp/2rasg1291668731.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/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/3tdjx1291668731.tab") 
> 
> try(system("convert tmp/1rasg1291668731.ps tmp/1rasg1291668731.png",intern=TRUE))
character(0)
> try(system("convert tmp/2rasg1291668731.ps tmp/2rasg1291668731.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.420   0.580   3.507