Prijsindexcijfers van de grondstoffen , Algemeen

*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 12:57:54 -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/20/t1224529111okgpmumbk3z943s.htm/, Retrieved Mon, 20 Oct 2008 18:58:33 +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/20/t1224529111okgpmumbk3z943s.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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98,5 96,8 91,2 97,1 104,9 110,9 104,8 94,1 95,8 99,3 101,1 104 99 105,4 107,1 110,7 117,1 118,7 126,5 127,5 134,6 131,8 135,9 142,7 141,7 153,4 145 137,7 148,3 152,2 169,4 168,6 161,1 174,1 179 190,6 190 181,6 174,8 180,5 196,8 193,8 197 216,3 221,4 217,9 229,7 227,4 204,2 196,6 198,8 207,5 190,7 201,6 210,5 223,5 223,8 231,2 244 234,7 250,2 265,7 287,6 283,3 295,4 312,3 333,8 347,7 383,2 407,1 413,6 362,7 321,9

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 189.526027397260 9.42513358944226 20.1085773054253 Geometric Mean 174.391440371510 Harmonic Mean 161.141015700804 Quadratic Mean 205.708778057386 Winsorized Mean ( 1 / 24 ) 189.476712328767 9.39042217458839 20.1776564254495 Winsorized Mean ( 2 / 24 ) 188.868493150685 9.1821380183041 20.5691193896439 Winsorized Mean ( 3 / 24 ) 188.067123287671 8.93807719550435 21.0411164699120 Winsorized Mean ( 4 / 24 ) 187.261643835616 8.71910475828278 21.4771641156996 Winsorized Mean ( 5 / 24 ) 186.405479452055 8.46848079709084 22.0116788262767 Winsorized Mean ( 6 / 24 ) 185.468493150685 8.23164691579965 22.5311526414842 Winsorized Mean ( 7 / 24 ) 184.576712328767 8.01960533398569 23.0156852665259 Winsorized Mean ( 8 / 24 ) 182.921917808219 7.59457500005188 24.0858662672986 Winsorized Mean ( 9 / 24 ) 182.317808219178 7.34669401997125 24.8163061811974 Winsorized Mean ( 10 / 24 ) 181.838356164384 7.21429501934126 25.2052841860337 Winsorized Mean ( 11 / 24 ) 179.201369863014 6.71498570951272 26.6867835041182 Winsorized Mean ( 12 / 24 ) 176.735616438356 6.2660984057732 28.2050496167636 Winsorized Mean ( 13 / 24 ) 175.934246575342 6.04187638407173 29.1191403781713 Winsorized Mean ( 14 / 24 ) 174.841095890411 5.66217752470013 30.8787732506975 Winsorized Mean ( 15 / 24 ) 174.16301369863 5.55156830134057 31.3718582290654 Winsorized Mean ( 16 / 24 ) 175.193150684931 5.29340552409249 33.0964914529134 Winsorized Mean ( 17 / 24 ) 175.030136986301 5.16071010481005 33.9159017715729 Winsorized Mean ( 18 / 24 ) 176.065753424658 4.75079390112183 37.0602802582284 Winsorized Mean ( 19 / 24 ) 176.247945205479 4.70230120709763 37.4812113140374 Winsorized Mean ( 20 / 24 ) 176.850684931507 4.45458271516415 39.7008420854948 Winsorized Mean ( 21 / 24 ) 176.649315068493 4.20345952834352 42.0247450647173 Winsorized Mean ( 22 / 24 ) 176.558904109589 4.08370086670264 43.2350237866836 Winsorized Mean ( 23 / 24 ) 175.298630136986 3.76272801568966 46.5881746982597 Winsorized Mean ( 24 / 24 ) 175.627397260274 3.4544014124363 50.8416296461645 Trimmed Mean ( 1 / 24 ) 187.754929577465 9.04723949110367 20.7527312349903 Trimmed Mean ( 2 / 24 ) 185.933333333333 8.6330748594486 21.5373243439255 Trimmed Mean ( 3 / 24 ) 184.334328358209 8.27070830067404 22.2876108861421 Trimmed Mean ( 4 / 24 ) 182.936923076923 7.94938482417603 23.0127144581763 Trimmed Mean ( 5 / 24 ) 181.684126984127 7.64462844869072 23.7662468756403 Trimmed Mean ( 6 / 24 ) 180.554098360656 7.3575961913245 24.5398216571808 Trimmed Mean ( 7 / 24 ) 179.540677966102 7.07810897367061 25.3656278299703 Trimmed Mean ( 8 / 24 ) 178.619298245614 6.79379712972264 26.2915266433495 Trimmed Mean ( 9 / 24 ) 177.905454545455 6.55599883016745 27.1362852791892 Trimmed Mean ( 10 / 24 ) 177.230188679245 6.3215383804646 28.0359270184831 Trimmed Mean ( 11 / 24 ) 176.570588235294 6.05904690241201 29.1416440702917 Trimmed Mean ( 12 / 24 ) 176.214285714286 5.85136111265988 30.1150932785591 Trimmed Mean ( 13 / 24 ) 176.146808510638 5.69174292880994 30.9477800936923 Trimmed Mean ( 14 / 24 ) 176.173333333333 5.53539884778327 31.8266737732701 Trimmed Mean ( 15 / 24 ) 176.334883720930 5.41496315359833 32.5643737028483 Trimmed Mean ( 16 / 24 ) 176.592682926829 5.27653502141725 33.4675468295096 Trimmed Mean ( 17 / 24 ) 176.756410256410 5.14956963320011 34.3245014334466 Trimmed Mean ( 18 / 24 ) 176.956756756757 5.00472530549796 35.3579359415312 Trimmed Mean ( 19 / 24 ) 177.06 4.9043304479671 36.1027875014812 Trimmed Mean ( 20 / 24 ) 177.154545454545 4.76823273220066 37.1530827885543 Trimmed Mean ( 21 / 24 ) 177.190322580645 4.63675441466418 38.2142996446531 Trimmed Mean ( 22 / 24 ) 177.255172413793 4.51095979598112 39.2943365559835 Trimmed Mean ( 23 / 24 ) 177.340740740741 4.35076133514819 40.7608524301415 Trimmed Mean ( 24 / 24 ) 177.6 4.20627309305201 42.2226508053798 Median 180.5 Midrange 252.4 Midmean - Weighted Average at Xnp 175.655555555556 Midmean - Weighted Average at X(n+1)p 176.956756756757 Midmean - Empirical Distribution Function 176.956756756757 Midmean - Empirical Distribution Function - Averaging 176.956756756757 Midmean - Empirical Distribution Function - Interpolation 176.956756756757 Midmean - Closest Observation 175.423684210526 Midmean - True Basic - Statistics Graphics Toolkit 176.956756756757 Midmean - MS Excel (old versions) 176.956756756757 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224529111okgpmumbk3z943s/1vluz1224529072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224529111okgpmumbk3z943s/1vluz1224529072.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224529111okgpmumbk3z943s/2ulje1224529072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224529111okgpmumbk3z943s/2ulje1224529072.ps (open in new window)

Parameters (Session):

par1 = Investeringen ; par3 = Investeringen ;

Parameters (R input):

par1 = Investeringen ; par3 = Investeringen ;

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')

Copyright

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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