dennis volkaerts - opg5 oef2 centrum

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 18 Aug 2009 06:58:43 -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/Aug/18/t1250600357rivyfgqawsxcdy5.htm/, Retrieved Tue, 18 Aug 2009 14:59:19 +0200

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/Aug/18/t1250600357rivyfgqawsxcdy5.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

17,23 17,36 17,39 17,29 17,28 17,4 17,51 17,54 17,64 17,65 17,5 17,37 17,56 17,49 17,61 17,79 17,83 17,56 17,95 18,09 18,38 18,38 18,44 18,84 19,01 19,06 19,06 18,97 18,98 19,41 19,55 19,64 19,71 19,48 19,48 19,41 19,25 19,14 19,21 19,3 19,53 19,14 19,16 19,24 19,38 19,27 19,27 19,07 19,15 19,24 19,36 19,57 19,59 19,36 19,46 19,65 19,46 19,51 19,64 19,64 19,69 19,28 19,67 19,65 19,6 19,53 19,64 19,67 19,81 19,73 19,87 19,97 20,12 19,94 20,31 20,13 20,22 20,38 20,44 20,34 20,14 19,97 19,82 19,98 20,12

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 19.0523529411765 0.101095352147056 188.459237111735 Geometric Mean 19.0292511283716 Harmonic Mean 19.0055848843898 Quadratic Mean 19.0748697320353 Winsorized Mean ( 1 / 28 ) 19.0522352941176 0.100857718856603 188.902103974863 Winsorized Mean ( 2 / 28 ) 19.0515294117647 0.100663138196971 189.260237193141 Winsorized Mean ( 3 / 28 ) 19.0529411764706 0.0999968940035023 190.535329785376 Winsorized Mean ( 4 / 28 ) 19.0491764705882 0.0992878298618478 191.858120950915 Winsorized Mean ( 5 / 28 ) 19.0456470588235 0.0984096860281991 193.534273174757 Winsorized Mean ( 6 / 28 ) 19.0456470588235 0.0981754342185491 193.996056247899 Winsorized Mean ( 7 / 28 ) 19.0522352941176 0.0966140168323203 197.199494636311 Winsorized Mean ( 8 / 28 ) 19.0531764705882 0.0964331979874224 197.579017062913 Winsorized Mean ( 9 / 28 ) 19.0394117647059 0.0943729642689415 201.746463218511 Winsorized Mean ( 10 / 28 ) 19.0417647058824 0.0935559834002533 203.533371290829 Winsorized Mean ( 11 / 28 ) 19.0443529411765 0.0930629507525319 204.639470242226 Winsorized Mean ( 12 / 28 ) 19.0401176470588 0.0925671070252028 205.689885521375 Winsorized Mean ( 13 / 28 ) 19.0370588235294 0.0899063975640929 211.743094366096 Winsorized Mean ( 14 / 28 ) 19.0337647058824 0.0880822725403405 216.090754211242 Winsorized Mean ( 15 / 28 ) 19.0337647058824 0.087563178707049 217.371787855734 Winsorized Mean ( 16 / 28 ) 19.0450588235294 0.0811017660560268 234.829150457373 Winsorized Mean ( 17 / 28 ) 19.0490588235294 0.0792324212014963 240.420001492642 Winsorized Mean ( 18 / 28 ) 19.0702352941176 0.074199174848483 257.014115494676 Winsorized Mean ( 19 / 28 ) 19.0970588235294 0.0681873805507301 280.067347789105 Winsorized Mean ( 20 / 28 ) 19.1652941176471 0.0565114668801282 339.139915767899 Winsorized Mean ( 21 / 28 ) 19.1603529411765 0.0559915577517079 342.200747943863 Winsorized Mean ( 22 / 28 ) 19.1758823529412 0.0534297869371287 358.89872395534 Winsorized Mean ( 23 / 28 ) 19.2814117647059 0.0362071355539064 532.530714449893 Winsorized Mean ( 24 / 28 ) 19.3181176470588 0.0310797718167395 621.565620267975 Winsorized Mean ( 25 / 28 ) 19.3210588235294 0.0306891086116635 629.573803136998 Winsorized Mean ( 26 / 28 ) 19.3302352941176 0.0294886278562704 655.514911997077 Winsorized Mean ( 27 / 28 ) 19.3334117647059 0.0258873626422387 746.828173726776 Winsorized Mean ( 28 / 28 ) 19.3301176470588 0.0254854789860772 758.475744466838 Trimmed Mean ( 1 / 28 ) 19.0575903614458 0.0997527932335892 191.048187661462 Trimmed Mean ( 2 / 28 ) 19.0632098765432 0.0984547002371176 193.624172646217 Trimmed Mean ( 3 / 28 ) 19.0694936708861 0.0970476045253813 196.496284108679 Trimmed Mean ( 4 / 28 ) 19.0755844155844 0.0956782268143925 199.372261074501 Trimmed Mean ( 5 / 28 ) 19.0830666666667 0.0942951038315702 202.376007780349 Trimmed Mean ( 6 / 28 ) 19.0917808219178 0.092897576712048 205.514304007047 Trimmed Mean ( 7 / 28 ) 19.1009859154930 0.0912830861005 209.250001631883 Trimmed Mean ( 8 / 28 ) 19.1095652173913 0.089726171189682 212.976492410375 Trimmed Mean ( 9 / 28 ) 19.1185074626866 0.0878885065598244 217.531372542698 Trimmed Mean ( 10 / 28 ) 19.13 0.0860724203125574 222.254700524659 Trimmed Mean ( 11 / 28 ) 19.1419047619048 0.084024128255987 227.814380931001 Trimmed Mean ( 12 / 28 ) 19.1542622950820 0.0816146680726674 234.691419415289 Trimmed Mean ( 13 / 28 ) 19.1679661016949 0.0787262640046334 243.476130158632 Trimmed Mean ( 14 / 28 ) 19.1829824561404 0.0756674415537871 253.516995714787 Trimmed Mean ( 15 / 28 ) 19.1994545454545 0.0721821574256928 265.986155445953 Trimmed Mean ( 16 / 28 ) 19.2171698113208 0.0678411538783218 283.267142622429 Trimmed Mean ( 17 / 28 ) 19.2350980392157 0.0637645008799734 301.658411400768 Trimmed Mean ( 18 / 28 ) 19.2540816326531 0.0588675140880814 327.074820992846 Trimmed Mean ( 19 / 28 ) 19.2725531914894 0.0537402772525159 358.624000038762 Trimmed Mean ( 20 / 28 ) 19.29 0.048585029077948 397.035884635406 Trimmed Mean ( 21 / 28 ) 19.3023255813953 0.0452308428875362 426.751401237192 Trimmed Mean ( 22 / 28 ) 19.3163414634146 0.0406888192492444 474.733398998137 Trimmed Mean ( 23 / 28 ) 19.3302564102564 0.0351236243159215 550.349139268467 Trimmed Mean ( 24 / 28 ) 19.3351351351351 0.0334583727331321 577.886297380762 Trimmed Mean ( 25 / 28 ) 19.3368571428571 0.0326009007159465 593.138739059399 Trimmed Mean ( 26 / 28 ) 19.3384848484848 0.0314640283189115 614.622026540112 Trimmed Mean ( 27 / 28 ) 19.3393548387097 0.0301713225797083 640.984656460382 Trimmed Mean ( 28 / 28 ) 19.34 0.029373591570889 658.414547411597 Median 19.36 Midrange 18.835 Midmean - Weighted Average at Xnp 19.2813636363636 Midmean - Weighted Average at X(n+1)p 19.2813636363636 Midmean - Empirical Distribution Function 19.2813636363636 Midmean - Empirical Distribution Function - Averaging 19.2813636363636 Midmean - Empirical Distribution Function - Interpolation 19.2813636363636 Midmean - Closest Observation 19.2813636363636 Midmean - True Basic - Statistics Graphics Toolkit 19.2813636363636 Midmean - MS Excel (old versions) 19.2813636363636 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600357rivyfgqawsxcdy5/14ash1250600321.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600357rivyfgqawsxcdy5/14ash1250600321.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600357rivyfgqawsxcdy5/2u6gw1250600321.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600357rivyfgqawsxcdy5/2u6gw1250600321.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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