Q9: Investeringsgoederen

*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: Mon, 20 Oct 2008 17:08:44 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/21/t1224544278nb32pa13wz9xwd7.htm/, Retrieved Mon, 20 Oct 2008 23:11:18 +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/Oct/21/t1224544278nb32pa13wz9xwd7.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}, }

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Dataseries X:

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117,7 124,6 144,4 109,6 117,9 122,2 89,3 78,4 119,1 110,3 118,3 105,5 97,7 101,5 119,6 108,1 117,8 125,5 89,1 92,3 104,5 122,8 96 94,5 93,4 101,1 114,2 104,8 113,3 118,2 83,6 73,9 99,5 97,7 103 106,3 92,2 101,8 122,8 111,8 106,3 121,5 81,9 85,4 110,9 117,3 106,3 105,6 101,2 105,9 126,3 111,9 108,9 127,2 94,2 85,7 116,2 107,2 110,5 112 104,4 112 132,8 110,8 128,7 136,8 94,8 88,8 123,2 125,3 122,7 125,8 116,3 118,6 142,1 127,9 132 152,4 110,8 99,1 134,9 133,2 131 133,9 119,9 137 148,9 145,1 142,4 159,6 120,7

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 113.391208791209 1.81934969956522 62.3251312368956 Geometric Mean 112.065511471777 Harmonic Mean 110.722812605261 Quadratic Mean 114.697293912146 Winsorized Mean ( 1 / 30 ) 113.361538461538 1.78722762586195 63.4287075810315 Winsorized Mean ( 2 / 30 ) 113.361538461538 1.75318845710645 64.6602126554243 Winsorized Mean ( 3 / 30 ) 113.292307692308 1.71518124913526 66.0526738788838 Winsorized Mean ( 4 / 30 ) 113.340659340659 1.69401516227484 66.9065200033145 Winsorized Mean ( 5 / 30 ) 113.247252747253 1.66913322293214 67.8479411896872 Winsorized Mean ( 6 / 30 ) 113.431868131868 1.62935441129577 69.617676391019 Winsorized Mean ( 7 / 30 ) 113.062637362637 1.55339295295955 72.7843120101894 Winsorized Mean ( 8 / 30 ) 113.062637362637 1.54738240382493 73.0670305434266 Winsorized Mean ( 9 / 30 ) 113.161538461538 1.46864399613273 77.0517148876909 Winsorized Mean ( 10 / 30 ) 113.062637362637 1.44908092496943 78.0236875763324 Winsorized Mean ( 11 / 30 ) 113.110989010989 1.41476554234378 79.9503420358986 Winsorized Mean ( 12 / 30 ) 113.163736263736 1.39030439695739 81.3949351749077 Winsorized Mean ( 13 / 30 ) 113.092307692308 1.36605921528177 82.7872660476002 Winsorized Mean ( 14 / 30 ) 112.984615384615 1.33571757804384 84.5872040930102 Winsorized Mean ( 15 / 30 ) 112.803296703297 1.25075649933693 90.1880555992293 Winsorized Mean ( 16 / 30 ) 112.961538461538 1.18731160112684 95.1406002891999 Winsorized Mean ( 17 / 30 ) 112.830769230769 1.16924121195774 96.499138139212 Winsorized Mean ( 18 / 30 ) 112.929670329670 1.10595954118084 102.110128015257 Winsorized Mean ( 19 / 30 ) 112.908791208791 1.08046664764948 104.500024553669 Winsorized Mean ( 20 / 30 ) 113.194505494506 1.02435466165919 110.503236555940 Winsorized Mean ( 21 / 30 ) 113.171428571429 1.01518541671742 111.478579880872 Winsorized Mean ( 22 / 30 ) 113.074725274725 0.983437435858576 114.979073555408 Winsorized Mean ( 23 / 30 ) 112.796703296703 0.928395428769353 121.496400996095 Winsorized Mean ( 24 / 30 ) 113.007692307692 0.874290545483834 129.256450148564 Winsorized Mean ( 25 / 30 ) 113.392307692308 0.826551496717439 137.187226860798 Winsorized Mean ( 26 / 30 ) 113.392307692308 0.819492726695479 138.368900660718 Winsorized Mean ( 27 / 30 ) 113.332967032967 0.790174792404837 143.427717667438 Winsorized Mean ( 28 / 30 ) 113.332967032967 0.737864878294395 153.595828134469 Winsorized Mean ( 29 / 30 ) 113.109890109890 0.703118910677296 160.868792450674 Winsorized Mean ( 30 / 30 ) 112.945054945055 0.660120357058349 171.097669898206 Trimmed Mean ( 1 / 30 ) 113.315730337079 1.72902053173861 65.5375273208205 Trimmed Mean ( 2 / 30 ) 113.267816091954 1.66199438189647 68.1517442692595 Trimmed Mean ( 3 / 30 ) 113.217647058824 1.60588743188780 70.501608525406 Trimmed Mean ( 4 / 30 ) 113.190361445783 1.5579421375522 72.6537646793642 Trimmed Mean ( 5 / 30 ) 113.148148148148 1.50989136956067 74.9379395294315 Trimmed Mean ( 6 / 30 ) 113.125316455696 1.46160474820279 77.3980219993105 Trimmed Mean ( 7 / 30 ) 113.064935064935 1.41592080885815 79.8525838151323 Trimmed Mean ( 8 / 30 ) 113.065333333333 1.38102128723485 81.8708113904012 Trimmed Mean ( 9 / 30 ) 113.065753424658 1.34136737519168 84.2914145041737 Trimmed Mean ( 10 / 30 ) 113.052112676056 1.31121283981184 86.2194978904256 Trimmed Mean ( 11 / 30 ) 113.050724637681 1.27934709875704 88.3659522482336 Trimmed Mean ( 12 / 30 ) 113.043283582090 1.24800922228490 90.5788848059355 Trimmed Mean ( 13 / 30 ) 113.029230769231 1.21508689756702 93.0215205147467 Trimmed Mean ( 14 / 30 ) 113.022222222222 1.18000374140113 95.78124056456 Trimmed Mean ( 15 / 30 ) 113.026229508197 1.14322643235049 98.8660044150773 Trimmed Mean ( 16 / 30 ) 113.049152542373 1.11415989291766 101.465824843443 Trimmed Mean ( 17 / 30 ) 113.057894736842 1.08990568723643 103.73181465225 Trimmed Mean ( 18 / 30 ) 113.08 1.06297783867863 106.38039278464 Trimmed Mean ( 19 / 30 ) 113.094339622642 1.04082979865598 108.657861034225 Trimmed Mean ( 20 / 30 ) 113.111764705882 1.01737704680385 111.179788320593 Trimmed Mean ( 21 / 30 ) 113.104081632653 0.99779501452835 113.354025612281 Trimmed Mean ( 22 / 30 ) 113.097872340426 0.974036155683242 116.112601858288 Trimmed Mean ( 23 / 30 ) 113.1 0.949316606934704 119.138335065257 Trimmed Mean ( 24 / 30 ) 113.127906976744 0.92780552711195 121.930624113532 Trimmed Mean ( 25 / 30 ) 113.139024390244 0.910145244699187 124.308757365027 Trimmed Mean ( 26 / 30 ) 113.115384615385 0.89562995465498 126.297009191658 Trimmed Mean ( 27 / 30 ) 113.089189189189 0.876227442670021 129.063738114143 Trimmed Mean ( 28 / 30 ) 113.065714285714 0.855500667771231 132.163209854968 Trimmed Mean ( 29 / 30 ) 113.065714285714 0.838547393380852 134.835210482089 Trimmed Mean ( 30 / 30 ) 113.032258064516 0.822079543763688 137.495524517039 Median 112 Midrange 116.75 Midmean - Weighted Average at Xnp 112.847826086957 Midmean - Weighted Average at X(n+1)p 113.097872340426 Midmean - Empirical Distribution Function 113.097872340426 Midmean - Empirical Distribution Function - Averaging 113.097872340426 Midmean - Empirical Distribution Function - Interpolation 113.1 Midmean - Closest Observation 112.847826086957 Midmean - True Basic - Statistics Graphics Toolkit 113.097872340426 Midmean - MS Excel (old versions) 113.097872340426 Number of observations 91

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224544278nb32pa13wz9xwd7/15i0i1224544117.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224544278nb32pa13wz9xwd7/15i0i1224544117.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224544278nb32pa13wz9xwd7/2ddkh1224544117.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224544278nb32pa13wz9xwd7/2ddkh1224544117.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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Software written by Ed van Stee & Patrick Wessa

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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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