Koers Euro t.o.v. Pond

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 15 Mar 2009 10:43:50 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Mar/15/t1237135474rlzonlkc8eludpw.htm/, Retrieved Sun, 15 Mar 2009 17:44:34 +0100

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/2009/Mar/15/t1237135474rlzonlkc8eludpw.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

WesleyDeBondt

Dataseries X:

» Textbox « » Textfile « » CSV «

0,63709 0,64218 0,65711 0,66977 0,68255 0,68902 0,71322 0,70224 0,70045 0,69919 0,69693 0,69763 0,69278 0,70196 0,69215 0,6769 0,67124 0,66533 0,67157 0,66428 0,66576 0,66942 0,68130 0,69144 0,69862 0,695 0,69867 0,68968 0,69233 0,68293 0,68399 0,66895 0,68756 0,68527 0,6776 0,68137 0,67933 0,67922 0,68598 0,68297 0,68935 0,69463 0,6833 0,68666 0,68782 0,67669 0,67511 0,67254 0,67397 0,67286 0,66341 0,668 0,68021 0,67934 0,68136 0,67562 0,6744 0,67766 0,68887 0,69614 0,70896 0,72064 0,74725 0,75094 0,77494 0,79487 0,79209 0,79152 0,79308 0,79279 0,79924 0,78668

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.696554444444444 0.00447398373633177 155.689981344356 Geometric Mean 0.695588142695841 Harmonic Mean 0.694672845412761 Quadratic Mean 0.69757384393259 Winsorized Mean ( 1 / 24 ) 0.696564444444445 0.00444199887723836 156.813286922194 Winsorized Mean ( 2 / 24 ) 0.696929444444444 0.00436404790076369 159.697936478306 Winsorized Mean ( 3 / 24 ) 0.697179861111111 0.00432899591290744 161.048861014718 Winsorized Mean ( 4 / 24 ) 0.697189305555555 0.00431166615547212 161.698350571675 Winsorized Mean ( 5 / 24 ) 0.697222638888889 0.00429167025841071 162.459508048758 Winsorized Mean ( 6 / 24 ) 0.696855138888889 0.00416421558889268 167.343674700135 Winsorized Mean ( 7 / 24 ) 0.695931527777778 0.00380072251727928 183.105060844051 Winsorized Mean ( 8 / 24 ) 0.693370416666667 0.00303940255586782 228.127207213160 Winsorized Mean ( 9 / 24 ) 0.692967916666667 0.00291060711886226 238.083632853047 Winsorized Mean ( 10 / 24 ) 0.689320694444444 0.00199655499784125 345.255049417503 Winsorized Mean ( 11 / 24 ) 0.688411666666667 0.00172450571267585 399.193613338911 Winsorized Mean ( 12 / 24 ) 0.687756666666667 0.00157732758929262 436.026524442588 Winsorized Mean ( 13 / 24 ) 0.686718472222222 0.00133621132556265 513.929540249226 Winsorized Mean ( 14 / 24 ) 0.68672625 0.00131806650548872 521.010318629843 Winsorized Mean ( 15 / 24 ) 0.686642916666667 0.00123376959733474 556.54063623386 Winsorized Mean ( 16 / 24 ) 0.686458472222222 0.00117653869317853 583.455925591098 Winsorized Mean ( 17 / 24 ) 0.686503333333333 0.00113393801184654 605.415222138474 Winsorized Mean ( 18 / 24 ) 0.686618333333333 0.00111415889312236 616.266079795074 Winsorized Mean ( 19 / 24 ) 0.686639444444444 0.00103606988258501 662.734682269953 Winsorized Mean ( 20 / 24 ) 0.686503333333333 0.000999360769870829 686.942447642873 Winsorized Mean ( 21 / 24 ) 0.686477083333333 0.000938287310254437 731.627802945752 Winsorized Mean ( 22 / 24 ) 0.686147083333333 0.000886035428642587 774.401407835933 Winsorized Mean ( 23 / 24 ) 0.686527222222222 0.000803726142986208 854.180529292554 Winsorized Mean ( 24 / 24 ) 0.685947222222222 0.00071348631652899 961.402070833339 Trimmed Mean ( 1 / 24 ) 0.695937 0.00427369714676618 162.841908563081 Trimmed Mean ( 2 / 24 ) 0.695272647058824 0.00407108444531861 170.783155298664 Trimmed Mean ( 3 / 24 ) 0.69436893939394 0.00387549049533484 179.169305209184 Trimmed Mean ( 4 / 24 ) 0.69331484375 0.00365002539260701 189.947950815434 Trimmed Mean ( 5 / 24 ) 0.69219 0.00337342190615908 205.189276424696 Trimmed Mean ( 6 / 24 ) 0.690982166666667 0.00302361826398586 228.528242105465 Trimmed Mean ( 7 / 24 ) 0.689767068965517 0.00260785256089141 264.496190969378 Trimmed Mean ( 8 / 24 ) 0.688634821428571 0.00218344822889195 315.388664735155 Trimmed Mean ( 9 / 24 ) 0.687845555555556 0.00190448621981682 361.171190633091 Trimmed Mean ( 10 / 24 ) 0.6870575 0.00156314852906129 439.534367481121 Trimmed Mean ( 11 / 24 ) 0.6867316 0.00143541683798662 478.419635207317 Trimmed Mean ( 12 / 24 ) 0.6865025 0.00134873993926141 508.995455696181 Trimmed Mean ( 13 / 24 ) 0.686338913043478 0.00127694881766019 537.483494679989 Trimmed Mean ( 14 / 24 ) 0.686291136363636 0.00124485907809008 551.300262369115 Trimmed Mean ( 15 / 24 ) 0.686237857142857 0.00120634104421154 568.858914678957 Trimmed Mean ( 16 / 24 ) 0.68618925 0.00117489106900957 584.04499625523 Trimmed Mean ( 17 / 24 ) 0.686157368421053 0.00114563030811641 598.934371376051 Trimmed Mean ( 18 / 24 ) 0.686116666666667 0.00111507035865989 615.312443145965 Trimmed Mean ( 19 / 24 ) 0.686057647058824 0.00107641603945053 637.35360856294 Trimmed Mean ( 20 / 24 ) 0.68598875 0.00104254522896394 657.994234630683 Trimmed Mean ( 21 / 24 ) 0.685927 0.00100331326401435 683.661847801697 Trimmed Mean ( 22 / 24 ) 0.685859642857143 0.00096362637413402 711.748517129892 Trimmed Mean ( 23 / 24 ) 0.685823461538462 0.000920859956329732 744.76412707959 Trimmed Mean ( 24 / 24 ) 0.685731666666667 0.000882422896961612 777.100944487955 Median 0.685625 Midrange 0.718165 Midmean - Weighted Average at Xnp 0.685819189189189 Midmean - Weighted Average at X(n+1)p 0.686116666666667 Midmean - Empirical Distribution Function 0.685819189189189 Midmean - Empirical Distribution Function - Averaging 0.686116666666667 Midmean - Empirical Distribution Function - Interpolation 0.686116666666667 Midmean - Closest Observation 0.685819189189189 Midmean - True Basic - Statistics Graphics Toolkit 0.686116666666667 Midmean - MS Excel (old versions) 0.686157368421053 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237135474rlzonlkc8eludpw/1rpy21237135425.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237135474rlzonlkc8eludpw/1rpy21237135425.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237135474rlzonlkc8eludpw/25llg1237135425.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237135474rlzonlkc8eludpw/25llg1237135425.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')

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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