niet-duurzame consumptiegoederen

*The author of this computation has been verified*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Fri, 05 Dec 2008 08:52:13 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228493959rg7n8n0vxfn9bzv.htm/, Retrieved Fri, 05 Dec 2008 16:19:21 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228493959rg7n8n0vxfn9bzv.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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98,6 98 106,8 96,7 100,2 107,7 92 98,4 107,4 117,7 105,7 97,5 99,9 98,2 104,5 100,8 101,5 103,9 99,6 98,4 112,7 118,4 108,1 105,4 114,6 106,9 115,9 109,8 101,8 114,2 110,8 108,4 127,5 128,6 116,6 127,4 105 108,3 125 111,6 106,5 130,3 115 116,1 134 126,5 125,8 136,4 114,9 110,9 125,5 116,8 116,8 125,5 104,2 115,1 132,8 123,3 124,8 122 117,4 117,9 137,4 114,6 124,7 129,6 109,4 120,9 134,9 136,3 133,2 127,2 122,7 120,5 137,8 119,1 124,3 134,4 121,1 122,2 127,7 137,4 132,2 129,2 124,9

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 116.361176470588 1.30397162558452 89.235972767757 Geometric Mean 115.742518417325 Harmonic Mean 115.120659156622 Quadratic Mean 116.973296600750 Winsorized Mean ( 1 / 28 ) 116.411764705882 1.29187984516940 90.1103652488808 Winsorized Mean ( 2 / 28 ) 116.430588235294 1.28852403297563 90.359655897467 Winsorized Mean ( 3 / 28 ) 116.412941176471 1.27876514778129 91.0354347539516 Winsorized Mean ( 4 / 28 ) 116.417647058824 1.27628462934397 91.216053521434 Winsorized Mean ( 5 / 28 ) 116.347058823529 1.25942673837844 92.3809660999658 Winsorized Mean ( 6 / 28 ) 116.311764705882 1.25329974748421 92.8044268255527 Winsorized Mean ( 7 / 28 ) 116.295294117647 1.24488635356160 93.4184022380259 Winsorized Mean ( 8 / 28 ) 116.314117647059 1.21662751129332 95.6037214080522 Winsorized Mean ( 9 / 28 ) 116.303529411765 1.20450304391389 96.5572731421668 Winsorized Mean ( 10 / 28 ) 116.268235294118 1.18740615051788 97.9178314373797 Winsorized Mean ( 11 / 28 ) 116.1 1.13698579352509 102.112093802022 Winsorized Mean ( 12 / 28 ) 116.1 1.10678452681428 104.898466853505 Winsorized Mean ( 13 / 28 ) 116.084705882353 1.09078455290077 106.423129639711 Winsorized Mean ( 14 / 28 ) 116.331764705882 1.02466529585450 113.531477231177 Winsorized Mean ( 15 / 28 ) 116.225882352941 0.994803237644483 116.833035875661 Winsorized Mean ( 16 / 28 ) 116.244705882353 0.981563244539954 118.428136474115 Winsorized Mean ( 17 / 28 ) 116.324705882353 0.964720690601657 120.578636921124 Winsorized Mean ( 18 / 28 ) 116.367058823529 0.947185700567406 122.855590782061 Winsorized Mean ( 19 / 28 ) 116.277647058824 0.916919053318112 126.813426592067 Winsorized Mean ( 20 / 28 ) 116.301176470588 0.869715324360553 133.723269227315 Winsorized Mean ( 21 / 28 ) 116.301176470588 0.85022075584102 136.789387546233 Winsorized Mean ( 22 / 28 ) 116.327058823529 0.846783977352278 137.375129826217 Winsorized Mean ( 23 / 28 ) 116.327058823529 0.811626627318062 143.325828537588 Winsorized Mean ( 24 / 28 ) 116.383529411765 0.796995139424082 146.027903627950 Winsorized Mean ( 25 / 28 ) 116.471764705882 0.778085007857726 149.690282590793 Winsorized Mean ( 26 / 28 ) 116.502352941176 0.766373058753843 152.017808573040 Winsorized Mean ( 27 / 28 ) 116.407058823529 0.746230092397206 155.993519973954 Winsorized Mean ( 28 / 28 ) 116.407058823529 0.663322399517085 175.490921018613 Trimmed Mean ( 1 / 28 ) 116.396385542169 1.27633866709934 91.195533397649 Trimmed Mean ( 2 / 28 ) 116.380246913580 1.25819096539864 92.4980786813287 Trimmed Mean ( 3 / 28 ) 116.353164556962 1.23902364877226 93.9071378276396 Trimmed Mean ( 4 / 28 ) 116.331168831169 1.22076371407088 95.29376364181 Trimmed Mean ( 5 / 28 ) 116.306666666667 1.20011160642161 96.9132087751901 Trimmed Mean ( 6 / 28 ) 116.297260273973 1.18069835351334 98.4987062342494 Trimmed Mean ( 7 / 28 ) 116.294366197183 1.15925961129249 100.317793412576 Trimmed Mean ( 8 / 28 ) 116.294202898551 1.13576643954278 102.392709319150 Trimmed Mean ( 9 / 28 ) 116.291044776119 1.11403352645691 104.387383336633 Trimmed Mean ( 10 / 28 ) 116.289230769231 1.09047476224835 106.640918978689 Trimmed Mean ( 11 / 28 ) 116.292063492063 1.06554112464599 109.138972492216 Trimmed Mean ( 12 / 28 ) 116.316393442623 1.04522379836898 111.283720887459 Trimmed Mean ( 13 / 28 ) 116.342372881356 1.02603514576158 113.390241418095 Trimmed Mean ( 14 / 28 ) 116.371929824561 1.00525796383162 115.763250838621 Trimmed Mean ( 15 / 28 ) 116.376363636364 0.991645110151458 117.356867335925 Trimmed Mean ( 16 / 28 ) 116.392452830189 0.979484214022677 118.830350876379 Trimmed Mean ( 17 / 28 ) 116.407843137255 0.965940943825688 120.512381094658 Trimmed Mean ( 18 / 28 ) 116.416326530612 0.951253858094992 122.381975683916 Trimmed Mean ( 19 / 28 ) 116.421276595745 0.935139559650948 124.496151824868 Trimmed Mean ( 20 / 28 ) 116.435555555556 0.91951434016729 126.627231864999 Trimmed Mean ( 21 / 28 ) 116.448837209302 0.907605200105358 128.303404603438 Trimmed Mean ( 22 / 28 ) 116.463414634146 0.89465047063331 130.1775592335 Trimmed Mean ( 23 / 28 ) 116.476923076923 0.876876907655982 132.831554873856 Trimmed Mean ( 24 / 28 ) 116.491891891892 0.859712033448487 135.501060075451 Trimmed Mean ( 25 / 28 ) 116.502857142857 0.838410718570084 138.956784022935 Trimmed Mean ( 26 / 28 ) 116.506060606061 0.812449758282751 143.400941926939 Trimmed Mean ( 27 / 28 ) 116.506451612903 0.777754356055186 149.798520195799 Trimmed Mean ( 28 / 28 ) 116.517241379310 0.732851051834752 158.991709280624 Median 116.6 Midrange 114.9 Midmean - Weighted Average at Xnp 116.448837209302 Midmean - Weighted Average at X(n+1)p 116.448837209302 Midmean - Empirical Distribution Function 116.448837209302 Midmean - Empirical Distribution Function - Averaging 116.448837209302 Midmean - Empirical Distribution Function - Interpolation 116.448837209302 Midmean - Closest Observation 116.222727272727 Midmean - True Basic - Statistics Graphics Toolkit 116.448837209302 Midmean - MS Excel (old versions) 116.448837209302 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228493959rg7n8n0vxfn9bzv/14r2z1228492331.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228493959rg7n8n0vxfn9bzv/14r2z1228492331.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228493959rg7n8n0vxfn9bzv/2gdxv1228492331.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228493959rg7n8n0vxfn9bzv/2gdxv1228492331.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

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)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') 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() bitmap(file='test2.png') 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() load(file='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='mytable.tab')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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