Q9 Central Tendency versie 2 reeks 1 & 2

*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, 27 Oct 2008 12:16:35 -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/27/t12251314393rcmvgjg0pdfwsc.htm/, Retrieved Mon, 27 Oct 2008 18:17:21 +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/27/t12251314393rcmvgjg0pdfwsc.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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0.533479702 0.527755967 0.528426364 0.526282111 0.524451163 0.523287701 0.52320954 0.523797873 0.525131274 0.530389407 0.532850909 0.532795864 0.532164678 0.537001655 0.534327891 0.533272092 0.530979158 0.529839034 0.529391131 0.528616297 0.529232222 0.534305869 0.537227641 0.536979793 0.534726025 0.529197849 0.527250405 0.526651159 0.527829082 0.524790195 0.522531084 0.520700795 0.521012614 0.526459921 0.532250749 0.535439727 0.528484504 0.526048075 0.523058214 0.522925886 0.520075779 0.518677098 0.52000948 0.518266121 0.518515257 0.527992909 0.534436998 0.537730853 0.529844533 0.524459749 0.522557792 0.519492162 0.519190516 0.51722256 0.518738505 0.516392891 0.519440426 0.52502408 0.530764849 0.534599599 0.523175241

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.527068180622951 0.000748143996262312 704.500982773578 Geometric Mean 0.527036328153348 Harmonic Mean 0.527004482724048 Quadratic Mean 0.527100038125151 Winsorized Mean ( 1 / 20 ) 0.527073532377049 0.000743104529342391 709.285856248894 Winsorized Mean ( 2 / 20 ) 0.527100338114754 0.000734215526708773 717.90954963532 Winsorized Mean ( 3 / 20 ) 0.52711151552459 0.000731545419258625 720.545165956728 Winsorized Mean ( 4 / 20 ) 0.527021140114754 0.000708084152370343 744.29167543226 Winsorized Mean ( 5 / 20 ) 0.526967673311475 0.000695859390807035 757.290453032926 Winsorized Mean ( 6 / 20 ) 0.526999698065574 0.000684947269412279 769.401852667823 Winsorized Mean ( 7 / 20 ) 0.527009717131148 0.000676113213853839 779.4696307253 Winsorized Mean ( 8 / 20 ) 0.527002193065574 0.000672239152230491 783.950460661179 Winsorized Mean ( 9 / 20 ) 0.52707526952459 0.000657704654612583 801.385950104094 Winsorized Mean ( 10 / 20 ) 0.526950701 0.000631657153428048 834.235309677412 Winsorized Mean ( 11 / 20 ) 0.527025970934426 0.000605164140032712 870.881032220346 Winsorized Mean ( 12 / 20 ) 0.527004456704918 0.000580458672045195 907.910385502665 Winsorized Mean ( 13 / 20 ) 0.527316334163935 0.000525920064567402 1002.65490839883 Winsorized Mean ( 14 / 20 ) 0.527197355508197 0.000503653100882197 1046.74696648300 Winsorized Mean ( 15 / 20 ) 0.527266705426229 0.000486424154308845 1083.96489104333 Winsorized Mean ( 16 / 20 ) 0.526990458344262 0.000431006442457397 1222.69740410285 Winsorized Mean ( 17 / 20 ) 0.526963346967213 0.000416911815152705 1263.96836888443 Winsorized Mean ( 18 / 20 ) 0.526862681819672 0.000398784581042113 1321.17114569190 Winsorized Mean ( 19 / 20 ) 0.526717312196721 0.00037058610821247 1421.30884165452 Winsorized Mean ( 20 / 20 ) 0.526882778754098 0.000344949164403772 1527.42152503772 Trimmed Mean ( 1 / 20 ) 0.527068394474576 0.000729466381792922 722.539664102298 Trimmed Mean ( 2 / 20 ) 0.527062896017544 0.000712572004026576 739.662648882128 Trimmed Mean ( 3 / 20 ) 0.527042132672727 0.000697417166638604 755.705706547135 Trimmed Mean ( 4 / 20 ) 0.52701551409434 0.000679654072248024 775.417283017496 Trimmed Mean ( 5 / 20 ) 0.527013831803922 0.000666445486895696 790.78310554514 Trimmed Mean ( 6 / 20 ) 0.52702532432653 0.000653553869601568 806.399210286714 Trimmed Mean ( 7 / 20 ) 0.527030867595745 0.000640110389877516 823.343716849513 Trimmed Mean ( 8 / 20 ) 0.5270349634 0.000624982581087206 843.27944385775 Trimmed Mean ( 9 / 20 ) 0.527040774418605 0.000606038408900716 869.649128962957 Trimmed Mean ( 10 / 20 ) 0.52703507197561 0.000584917263860516 901.042086699788 Trimmed Mean ( 11 / 20 ) 0.527048268461539 0.000563820619790358 934.7800523108 Trimmed Mean ( 12 / 20 ) 0.527051610351351 0.000542552386380654 971.42989982459 Trimmed Mean ( 13 / 20 ) 0.527058458857143 0.000520171800305657 1013.23920010166 Trimmed Mean ( 14 / 20 ) 0.527021791272727 0.0005042709121724 1045.11638199062 Trimmed Mean ( 15 / 20 ) 0.526997115193548 0.000487743521561683 1080.47998978271 Trimmed Mean ( 16 / 20 ) 0.526959310586207 0.000468096872553781 1125.74841124507 Trimmed Mean ( 17 / 20 ) 0.526954912407407 0.000456892251613636 1153.34613477538 Trimmed Mean ( 18 / 20 ) 0.5269537018 0.000442984767122542 1189.55264584579 Trimmed Mean ( 19 / 20 ) 0.526967112956522 0.000426202896104777 1236.42311624972 Trimmed Mean ( 20 / 20 ) 0.527005303047619 0.000408440999933819 1290.28501823522 Median 0.527250405 Midrange 0.527061872 Midmean - Weighted Average at Xnp 0.5268248631 Midmean - Weighted Average at X(n+1)p 0.526997115193548 Midmean - Empirical Distribution Function 0.526997115193548 Midmean - Empirical Distribution Function - Averaging 0.526997115193548 Midmean - Empirical Distribution Function - Interpolation 0.526997115193548 Midmean - Closest Observation 0.52685838634375 Midmean - True Basic - Statistics Graphics Toolkit 0.526997115193548 Midmean - MS Excel (old versions) 0.526997115193548 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/27/t12251314393rcmvgjg0pdfwsc/1voiv1225131393.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/27/t12251314393rcmvgjg0pdfwsc/1voiv1225131393.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/27/t12251314393rcmvgjg0pdfwsc/2m1ff1225131393.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/27/t12251314393rcmvgjg0pdfwsc/2m1ff1225131393.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

Parameters (R input):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

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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