Centrummaten Goudkoers Brussel

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 18 May 2011 14:30:36 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t1305728800ex5r3q3vcpwsdxg.htm/, Retrieved Wed, 18 May 2011 16:26:42 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KEYWORD: KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

32819 32700 32242 32810 33865 32226 31077 31293 30236 30160 32436 30695 27525 26434 25739 25204 24977 24320 22680 22052 21467 21383 21777 21928 21814 22937 23595 20830 19650 19195 19644 18483 18079 19178 18391 18441 18584 20108 20148 19394 17745 17696 17032 16438 15683 15594 15713 15937 16171 15928 16348 15579 15305 15648 14954 15137 15839 16050 15168 17064 16005 14886 14931 14544 13812 13031 12574 11964 11451 11346 11353 10702 10646 10556 10463 10407 10625 10872 10805 10653 10574 10431 10383 10296 10872 10635 10297 10570 10662 10709 10413 10846 10371 9924 9828

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' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17957.7052631579 716.532540742285 25.0619535639718 Geometric Mean 16733.8711176108 Harmonic Mean 15661.3112154365 Quadratic Mean 19254.6242035791 Winsorized Mean ( 1 / 31 ) 17947.7052631579 713.89077019851 25.1406882010356 Winsorized Mean ( 2 / 31 ) 17955.3473684211 712.933016139978 25.1851814433233 Winsorized Mean ( 3 / 31 ) 17951.9052631579 712.161778126845 25.2076225016957 Winsorized Mean ( 4 / 31 ) 17943.9052631579 709.37430469382 25.295397851918 Winsorized Mean ( 5 / 31 ) 17934.3263157895 707.094038491592 25.36342457935 Winsorized Mean ( 6 / 31 ) 17934.8315789474 706.704588889895 25.3781167702897 Winsorized Mean ( 7 / 31 ) 17866.5263157895 692.162899358202 25.8126032648614 Winsorized Mean ( 8 / 31 ) 17849.8526315789 688.252893859213 25.9350200933993 Winsorized Mean ( 9 / 31 ) 17816.6947368421 680.562389314885 26.1793702040719 Winsorized Mean ( 10 / 31 ) 17778.1684210526 669.794348383987 26.5427268294306 Winsorized Mean ( 11 / 31 ) 17770.9894736842 667.869486464735 26.6084764071978 Winsorized Mean ( 12 / 31 ) 17438.6526315789 605.302938929315 28.809793427445 Winsorized Mean ( 13 / 31 ) 17296.3368421053 578.665967197401 29.8900191519384 Winsorized Mean ( 14 / 31 ) 17195.3894736842 561.588460481686 30.6192001504721 Winsorized Mean ( 15 / 31 ) 17112.6526315789 547.897608519894 31.2333041164526 Winsorized Mean ( 16 / 31 ) 17075.6 541.780010230059 31.517589570625 Winsorized Mean ( 17 / 31 ) 16959.6421052632 523.659559385365 32.3867707584087 Winsorized Mean ( 18 / 31 ) 16829.8526315789 502.56837032013 33.4876876968173 Winsorized Mean ( 19 / 31 ) 16699.6526315789 483.93283194922 34.5082034717811 Winsorized Mean ( 20 / 31 ) 16665.7578947368 473.910328531062 35.1664795878035 Winsorized Mean ( 21 / 31 ) 16536 454.366841003838 36.3935008185606 Winsorized Mean ( 22 / 31 ) 16513.3052631579 449.871345071196 36.706728365961 Winsorized Mean ( 23 / 31 ) 16485.7052631579 446.351769960978 36.9343337982039 Winsorized Mean ( 24 / 31 ) 16596.1052631579 429.354597933669 38.6536101931342 Winsorized Mean ( 25 / 31 ) 16516.3684210526 418.74639262109 39.442413623364 Winsorized Mean ( 26 / 31 ) 16520.2 412.345509459401 40.0639745577891 Winsorized Mean ( 27 / 31 ) 16508.8315789474 373.84650084386 44.1593850462235 Winsorized Mean ( 28 / 31 ) 16487.6105263158 326.366804714306 50.5186504514412 Winsorized Mean ( 29 / 31 ) 16614.9052631579 307.341840560949 54.0600174477806 Winsorized Mean ( 30 / 31 ) 16716.9052631579 259.897097852727 64.3212463750969 Winsorized Mean ( 31 / 31 ) 16953.8105263158 232.215773261777 73.0088670901945 Trimmed Mean ( 1 / 31 ) 17874.0752688172 706.035395514057 25.3161178354285 Trimmed Mean ( 2 / 31 ) 17797.2087912088 696.928014234456 25.5366528934243 Trimmed Mean ( 3 / 31 ) 17712.808988764 686.926275770793 25.78560409396 Trimmed Mean ( 4 / 31 ) 17625.7816091954 675.634569288506 26.0877438935025 Trimmed Mean ( 5 / 31 ) 17536.8941176471 663.446654458302 26.4330131138664 Trimmed Mean ( 6 / 31 ) 17445.9156626506 649.89968601478 26.8440130655085 Trimmed Mean ( 7 / 31 ) 17445.9156626506 634.150357545796 27.5106927798124 Trimmed Mean ( 8 / 31 ) 17261.6708860759 619.226319872487 27.8761905495725 Trimmed Mean ( 9 / 31 ) 17170.961038961 602.542166734934 28.4975259607263 Trimmed Mean ( 10 / 31 ) 17080.08 584.498569657387 29.2217652645613 Trimmed Mean ( 11 / 31 ) 16989.2328767123 565.337174792746 30.0515048969504 Trimmed Mean ( 12 / 31 ) 16894.1408450704 542.83926397914 31.1218107570782 Trimmed Mean ( 13 / 31 ) 16831.6666666667 528.655310384817 31.8386410502802 Trimmed Mean ( 14 / 31 ) 16831.6666666667 516.661303932953 32.5777574951712 Trimmed Mean ( 15 / 31 ) 16737.7230769231 505.323347313615 33.1227978400437 Trimmed Mean ( 16 / 31 ) 16700.0317460317 494.047148281587 33.8025061051732 Trimmed Mean ( 17 / 31 ) 16663.4754098361 481.411364604946 34.6137973363183 Trimmed Mean ( 18 / 31 ) 16635.4237288136 469.260755917908 35.4502768855526 Trimmed Mean ( 19 / 31 ) 16617.4210526316 458.108534263462 36.2739827131768 Trimmed Mean ( 20 / 31 ) 16609.9454545455 447.602846311003 37.10866807805 Trimmed Mean ( 21 / 31 ) 16604.9433962264 436.243611632536 38.063464893128 Trimmed Mean ( 22 / 31 ) 16611.0588235294 425.488154635023 39.0400029767647 Trimmed Mean ( 23 / 31 ) 16619.6734693878 412.620904140599 40.2783118901913 Trimmed Mean ( 24 / 31 ) 16631.4468085106 396.806658635157 41.9132251099708 Trimmed Mean ( 25 / 31 ) 16634.5555555556 380.062290954538 43.7679715969121 Trimmed Mean ( 26 / 31 ) 16645 360.534935402418 46.1675093466916 Trimmed Mean ( 27 / 31 ) 16656.1219512195 336.156859790627 49.5486599963888 Trimmed Mean ( 28 / 31 ) 16656.1219512195 313.740869114461 53.0887862911571 Trimmed Mean ( 29 / 31 ) 16686.0810810811 296.368086355764 56.3018821839369 Trimmed Mean ( 30 / 31 ) 16692.7428571429 277.933920998817 60.0601135592006 Trimmed Mean ( 31 / 31 ) 16690.4242424242 266.287641493062 62.6781781867226 Median 16050 Midrange 21846.5 Midmean - Weighted Average at Xnp 16396.3673469388 Midmean - Weighted Average at X(n+1)p 16504.72 Midmean - Empirical Distribution Function 16504.72 Midmean - Empirical Distribution Function - Averaging 16504.72 Midmean - Empirical Distribution Function - Interpolation 16631.4468085106 Midmean - Closest Observation 16396.3673469388 Midmean - True Basic - Statistics Graphics Toolkit 16504.72 Midmean - MS Excel (old versions) 16504.72 Number of observations 95

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305728800ex5r3q3vcpwsdxg/1nnhy1305729034.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728800ex5r3q3vcpwsdxg/1nnhy1305729034.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728800ex5r3q3vcpwsdxg/28ypg1305729034.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728800ex5r3q3vcpwsdxg/28ypg1305729034.ps (open in new window)

Parameters (Session):

par1 = Goudkoers Brussel 2003-2011 ; par2 = http://www.nbb.be/belgostat/PresentationLinker?TableId=751000059&Lang=N ; par3 = Goudkoers Brussel (EUR/kg) ; par4 = 12 ;

Parameters (R input):

par1 = Goudkoers Brussel 2003-2011 ; par2 = http://www.nbb.be/belgostat/PresentationLinker?TableId=751000059&Lang=N ; par3 = Goudkoers Brussel (EUR/kg) ; par4 = 12 ;

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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