Opgave 5 IKO2

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 20 Oct 2010 15:06:40 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Oct/20/t1287587125dhql2aovd40c0pm.htm/, Retrieved Wed, 20 Oct 2010 17:05:27 +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/2010/Oct/20/t1287587125dhql2aovd40c0pm.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

101,02 101,15 101,51 101,75 101,8 101,8 101,8 101,82 101,99 102,25 102,34 102,35 102,35 102,39 102,49 102,67 102,68 102,7 102,71 102,72 102,83 102,92 103,04 103,08 103,09 103,11 103,18 103,18 103,22 103,25 103,25 103,25 103,47 103,57 103,66 103,7 103,7 103,75 103,85 104,02 104,13 104,17 104,18 104,2 104,5 104,78 104,88 104,89 104,9 104,95 105,24 105,35 105,44 105,46 105,47 105,48 105,75 106,1 106,19 106,23 106,24 106,25 106,35 106,48 106,52 106,55 106,55 106,56 106,89 107,09 107,24 107,28 107,3 107,31 107,47 107,35 107,31 107,32 107,32 107,34 107,53 107,72 107,75 107,79 107,81 107,9 107,8 107,86 107,8 107,74 107,75 107,83 107,8 107,81 107,86 107,83

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 104.947916666667 0.219484239766431 478.156959143625 Geometric Mean 104.926095515109 Harmonic Mean 104.904260899049 Quadratic Mean 104.969717915057 Winsorized Mean ( 1 / 32 ) 104.948854166667 0.21917453140073 478.836904525108 Winsorized Mean ( 2 / 32 ) 104.956354166667 0.217865750137902 481.747838291392 Winsorized Mean ( 3 / 32 ) 104.962916666667 0.216524375510145 484.762588135249 Winsorized Mean ( 4 / 32 ) 104.965 0.216201153087793 485.496948100813 Winsorized Mean ( 5 / 32 ) 104.963958333333 0.216056283235607 485.817661775063 Winsorized Mean ( 6 / 32 ) 104.963958333333 0.216056283235607 485.817661775063 Winsorized Mean ( 7 / 32 ) 104.9646875 0.215731007027483 486.553550860808 Winsorized Mean ( 8 / 32 ) 104.978854166667 0.213600600286609 491.472655160174 Winsorized Mean ( 9 / 32 ) 105.003229166667 0.210123579698784 499.721303611859 Winsorized Mean ( 10 / 32 ) 105.0115625 0.208699414930217 503.171331530147 Winsorized Mean ( 11 / 32 ) 105.008125 0.207905823426074 505.075438819242 Winsorized Mean ( 12 / 32 ) 105.008125 0.207905823426074 505.075438819242 Winsorized Mean ( 13 / 32 ) 105.0121875 0.206992255720304 507.324233626868 Winsorized Mean ( 14 / 32 ) 105.023854166667 0.204665022090637 513.149990623 Winsorized Mean ( 15 / 32 ) 105.022291666667 0.197015254505942 533.066802009991 Winsorized Mean ( 16 / 32 ) 105.013958333333 0.195474539507733 537.225761461273 Winsorized Mean ( 17 / 32 ) 104.99625 0.192254528498213 546.131479035492 Winsorized Mean ( 18 / 32 ) 104.99625 0.191777594711513 547.489659352249 Winsorized Mean ( 19 / 32 ) 104.994270833333 0.191021133256754 549.647408343083 Winsorized Mean ( 20 / 32 ) 105.0171875 0.188183007646217 558.058821641493 Winsorized Mean ( 21 / 32 ) 105.0346875 0.185515282455843 566.178085759597 Winsorized Mean ( 22 / 32 ) 105.0621875 0.182259165962381 576.443916799693 Winsorized Mean ( 23 / 32 ) 105.069375 0.180833584717668 581.027994130862 Winsorized Mean ( 24 / 32 ) 105.066875 0.179895883173837 584.04268706067 Winsorized Mean ( 25 / 32 ) 105.061666666667 0.177948387615541 590.405274666795 Winsorized Mean ( 26 / 32 ) 105.04 0.170577836325866 615.789262324415 Winsorized Mean ( 27 / 32 ) 104.98375 0.163567361653374 641.838010583541 Winsorized Mean ( 28 / 32 ) 104.899166666667 0.150706789992049 696.048045825943 Winsorized Mean ( 29 / 32 ) 104.905208333333 0.149296154164773 702.66517527004 Winsorized Mean ( 30 / 32 ) 104.905208333333 0.149296154164773 702.66517527004 Winsorized Mean ( 31 / 32 ) 104.895520833333 0.148175443501394 707.914336914717 Winsorized Mean ( 32 / 32 ) 104.955520833333 0.138192107401483 759.489979615198 Trimmed Mean ( 1 / 32 ) 104.958297872340 0.217929811736931 481.615144967126 Trimmed Mean ( 2 / 32 ) 104.968152173913 0.216456109262750 484.939660661161 Trimmed Mean ( 3 / 32 ) 104.974444444444 0.215483726143037 487.157180374555 Trimmed Mean ( 4 / 32 ) 104.978636363636 0.214841633359825 488.632648718576 Trimmed Mean ( 5 / 32 ) 104.982441860465 0.214119322886929 490.298775678006 Trimmed Mean ( 6 / 32 ) 104.986666666667 0.213237235419887 492.346782023959 Trimmed Mean ( 7 / 32 ) 104.991097560976 0.212132034788728 494.932779320865 Trimmed Mean ( 8 / 32 ) 104.995625 0.210838654172698 497.990396552229 Trimmed Mean ( 9 / 32 ) 104.998205128205 0.209674338260233 500.768029122805 Trimmed Mean ( 10 / 32 ) 104.9975 0.208856966501336 502.724432700827 Trimmed Mean ( 11 / 32 ) 104.995675675676 0.208030385482527 504.713171742377 Trimmed Mean ( 12 / 32 ) 104.994166666667 0.207070987767386 507.044312671229 Trimmed Mean ( 13 / 32 ) 104.992571428571 0.205820047002238 510.118294878388 Trimmed Mean ( 14 / 32 ) 104.990441176471 0.204367311409966 513.734023568266 Trimmed Mean ( 15 / 32 ) 104.986969696970 0.202882717816649 517.476159757726 Trimmed Mean ( 16 / 32 ) 104.9834375 0.202137783379907 519.365730367635 Trimmed Mean ( 17 / 32 ) 104.980483870968 0.201302531062401 521.506030336129 Trimmed Mean ( 18 / 32 ) 104.979 0.200593427519054 523.342171766961 Trimmed Mean ( 19 / 32 ) 104.977413793103 0.199605412376568 525.924685824937 Trimmed Mean ( 20 / 32 ) 104.975892857143 0.198316744023573 529.334491517595 Trimmed Mean ( 21 / 32 ) 104.972222222222 0.196967340541924 532.942273238842 Trimmed Mean ( 22 / 32 ) 104.966730769231 0.195496182191421 536.924709181544 Trimmed Mean ( 23 / 32 ) 104.9584 0.193938210231391 541.195053180972 Trimmed Mean ( 24 / 32 ) 104.94875 0.191963451613371 546.712142951954 Trimmed Mean ( 25 / 32 ) 104.938478260870 0.18937858394531 554.120091483916 Trimmed Mean ( 26 / 32 ) 104.927727272727 0.18619588438292 563.534084657525 Trimmed Mean ( 27 / 32 ) 104.917857142857 0.183303514325363 572.372316641068 Trimmed Mean ( 28 / 32 ) 104.912 0.180719076512095 580.525321536702 Trimmed Mean ( 29 / 32 ) 104.913157894737 0.179634964639613 584.035285698502 Trimmed Mean ( 30 / 32 ) 104.913888888889 0.178005830909390 589.384563151152 Trimmed Mean ( 31 / 32 ) 104.914705882353 0.175299710399004 598.48761668547 Trimmed Mean ( 32 / 32 ) 104.9165625 0.171364077482450 612.243616289678 Median 104.895 Midrange 104.46 Midmean - Weighted Average at Xnp 104.910612244898 Midmean - Weighted Average at X(n+1)p 104.94875 Midmean - Empirical Distribution Function 104.910612244898 Midmean - Empirical Distribution Function - Averaging 104.94875 Midmean - Empirical Distribution Function - Interpolation 104.94875 Midmean - Closest Observation 104.910612244898 Midmean - True Basic - Statistics Graphics Toolkit 104.94875 Midmean - MS Excel (old versions) 104.9584 Number of observations 96

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/20/t1287587125dhql2aovd40c0pm/1eynz1287587197.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287587125dhql2aovd40c0pm/1eynz1287587197.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287587125dhql2aovd40c0pm/2eynz1287587197.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287587125dhql2aovd40c0pm/2eynz1287587197.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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