Central Tendency 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: Wed, 10 Dec 2008 05:50:14 -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/10/t1228913451oy4bkl8ypti5bk5.htm/, Retrieved Wed, 10 Dec 2008 12:50:53 +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/10/t1228913451oy4bkl8ypti5bk5.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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85,0 95,9 108,9 96,2 100,1 105,7 64,5 66,8 110,3 96,1 102,5 97,6 83,6 86,5 96,0 91,1 87,2 84,5 59,2 61,5 98,8 97,9 92,7 84,2 74,5 79,7 86,8 79,8 87,0 91,4 58,7 62,8 87,9 90,4 80,6 73,5 71,4 70,6 78,3 76,0 77,4 80,9 63,4 58,1 88,2 81,2 84,9 76,4 71,5 76,1 82,9 78,0 82,0 84,7 55,7 59,5 83,2 87,6 76,2 76,4 68,3 70,0 76,3 70,9 72,4 80,1 57,4 62,7 82,6 88,9 80,4 72,0 69,4 69,2 77,3 79,4 78,6 76,1 61,8 59,4 78,1

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 79.725925925926 1.40766286667927 56.6370881928584 Geometric Mean 78.724280702201 Harmonic Mean 77.7148889543859 Quadratic Mean 80.7139668486467 Winsorized Mean ( 1 / 27 ) 79.7296296296296 1.39873007266826 57.0014409410208 Winsorized Mean ( 2 / 27 ) 79.6679012345679 1.37566014137556 57.9124878583062 Winsorized Mean ( 3 / 27 ) 79.5716049382716 1.34466278595253 59.1758809491443 Winsorized Mean ( 4 / 27 ) 79.4777777777778 1.31563602419064 60.4101562411013 Winsorized Mean ( 5 / 27 ) 79.4098765432099 1.29790025694195 61.1833429560386 Winsorized Mean ( 6 / 27 ) 79.3506172839506 1.28422662928335 61.7886403182838 Winsorized Mean ( 7 / 27 ) 79.4975308641975 1.2472327088258 63.7391324823737 Winsorized Mean ( 8 / 27 ) 79.3888888888889 1.21740084393548 65.2117905818508 Winsorized Mean ( 9 / 27 ) 79.4777777777778 1.19769067916677 66.35918535583 Winsorized Mean ( 10 / 27 ) 79.4777777777778 1.1933923014605 66.598198832447 Winsorized Mean ( 11 / 27 ) 79.5456790123457 1.17693372452401 67.5872203802439 Winsorized Mean ( 12 / 27 ) 79.2345679012346 1.07030796377801 74.0296910634485 Winsorized Mean ( 13 / 27 ) 79.395061728395 0.976231259971836 81.3281288807384 Winsorized Mean ( 14 / 27 ) 79.6024691358025 0.927549831127257 85.8201537690553 Winsorized Mean ( 15 / 27 ) 79.6395061728395 0.882602211428428 90.2326157147836 Winsorized Mean ( 16 / 27 ) 79.3827160493827 0.832945817534935 95.3035772294436 Winsorized Mean ( 17 / 27 ) 79.3617283950617 0.7934989865592 100.014908322937 Winsorized Mean ( 18 / 27 ) 79.4283950617284 0.764786814820413 103.856909562935 Winsorized Mean ( 19 / 27 ) 79.4283950617284 0.744977492757831 106.618516443621 Winsorized Mean ( 20 / 27 ) 79.453086419753 0.713967973180613 111.283824211053 Winsorized Mean ( 21 / 27 ) 79.4271604938272 0.70330790796961 112.933694607710 Winsorized Mean ( 22 / 27 ) 79.5086419753086 0.677012768473023 117.440387652714 Winsorized Mean ( 23 / 27 ) 79.537037037037 0.649903707123013 122.382802506437 Winsorized Mean ( 24 / 27 ) 79.4185185185185 0.547260605284194 145.120108686201 Winsorized Mean ( 25 / 27 ) 79.6962962962963 0.502446006080318 158.616638070273 Winsorized Mean ( 26 / 27 ) 80.1135802469136 0.434239625939254 184.491638858681 Winsorized Mean ( 27 / 27 ) 80.0802469135803 0.421528742459399 189.975768784719 Trimmed Mean ( 1 / 27 ) 79.6430379746836 1.35584216023378 58.7406412859675 Trimmed Mean ( 2 / 27 ) 79.551948051948 1.30566698253197 60.9282068982704 Trimmed Mean ( 3 / 27 ) 79.4893333333333 1.26149428529496 63.0120439386276 Trimmed Mean ( 4 / 27 ) 79.458904109589 1.2236831452385 64.9342147260697 Trimmed Mean ( 5 / 27 ) 79.4535211267606 1.18964822588519 66.7874077378136 Trimmed Mean ( 6 / 27 ) 79.463768115942 1.15483152562471 68.809836199229 Trimmed Mean ( 7 / 27 ) 79.4865671641791 1.11716773664357 71.1500740282647 Trimmed Mean ( 8 / 27 ) 79.4846153846154 1.08167922954141 73.4826122327537 Trimmed Mean ( 9 / 27 ) 79.5 1.0461888016532 75.9901079751315 Trimmed Mean ( 10 / 27 ) 79.5032786885246 1.00780551297571 78.8875211188101 Trimmed Mean ( 11 / 27 ) 79.506779661017 0.961900953741478 82.6558902470798 Trimmed Mean ( 12 / 27 ) 79.5017543859649 0.909096646102782 87.4513779440085 Trimmed Mean ( 13 / 27 ) 79.5345454545455 0.868208489374727 91.6076569486498 Trimmed Mean ( 14 / 27 ) 79.5509433962264 0.838083993220041 94.9200128385462 Trimmed Mean ( 15 / 27 ) 79.5450980392157 0.810665733320655 98.1231779877786 Trimmed Mean ( 16 / 27 ) 79.534693877551 0.785430419611496 101.262558581436 Trimmed Mean ( 17 / 27 ) 79.5510638297872 0.763566006725963 104.183611016012 Trimmed Mean ( 18 / 27 ) 79.5711111111111 0.743480908181594 107.025089999589 Trimmed Mean ( 19 / 27 ) 79.586046511628 0.723215575397663 110.044707579572 Trimmed Mean ( 20 / 27 ) 79.6024390243903 0.7005789226695 113.623799472972 Trimmed Mean ( 21 / 27 ) 79.6179487179487 0.677335732807255 117.545767721375 Trimmed Mean ( 22 / 27 ) 79.6378378378378 0.648112891856705 122.876490868269 Trimmed Mean ( 23 / 27 ) 79.6514285714286 0.614849457950787 129.546228823062 Trimmed Mean ( 24 / 27 ) 79.6636363636364 0.576017186287069 138.300797719488 Trimmed Mean ( 25 / 27 ) 79.6903225806452 0.552498816983304 144.236186813507 Trimmed Mean ( 26 / 27 ) 79.6896551724138 0.531990055732882 149.795384920553 Trimmed Mean ( 27 / 27 ) 79.6407407407407 0.521647053487264 152.671696712047 Median 79.7 Midrange 83 Midmean - Weighted Average at Xnp 79.4125 Midmean - Weighted Average at X(n+1)p 79.6024390243902 Midmean - Empirical Distribution Function 79.6024390243902 Midmean - Empirical Distribution Function - Averaging 79.6024390243902 Midmean - Empirical Distribution Function - Interpolation 79.6024390243902 Midmean - Closest Observation 79.395238095238 Midmean - True Basic - Statistics Graphics Toolkit 79.6024390243902 Midmean - MS Excel (old versions) 79.6024390243902 Number of observations 81

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913451oy4bkl8ypti5bk5/15s6q1228913412.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913451oy4bkl8ypti5bk5/15s6q1228913412.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913451oy4bkl8ypti5bk5/2nvue1228913412.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913451oy4bkl8ypti5bk5/2nvue1228913412.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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