Jurgen Leemans - Opgave 5 - oef 2

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 05 Jun 2009 08:17:56 -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/Jun/05/t124421168529xs4cbc0xkcnq4.htm/, Retrieved Fri, 05 Jun 2009 16:21:27 +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/2009/Jun/05/t124421168529xs4cbc0xkcnq4.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:

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163,40 162,89 162,29 161,26 161,43 161,44 161,44 161,44 161,92 162,23 161,89 161,40 161,40 159,55 158,93 158,59 158,29 158,03 158,03 163,94 164,36 164,39 163,22 163,22 163,56 162,82 162,80 162,44 161,98 161,53 161,53 161,52 162,07 161,84 161,54 161,47 161,47 161,54 161,57 160,75 160,31 160,57 160,57 159,65 158,76 158,95 159,25 158,72 158,72 158,72 158,53 157,92 157,89 157,81 157,81 157,88 157,52 156,11 155,61 155,31 155,31 155,31 153,09 151,94 151,73 151,65 151,65 151,09 149,94 149,47 149,15 149,22

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 159.049583333333 0.469385667059117 338.846271829817 Geometric Mean 158.999500394690 Harmonic Mean 158.948497995282 Quadratic Mean 159.098751989832 Winsorized Mean ( 1 / 24 ) 159.050138888889 0.469031169947643 339.103558739269 Winsorized Mean ( 2 / 24 ) 159.045416666667 0.465204699315536 341.882652734749 Winsorized Mean ( 3 / 24 ) 159.049166666667 0.457344890199452 347.766357676597 Winsorized Mean ( 4 / 24 ) 159.104166666667 0.438923082352959 362.487581682304 Winsorized Mean ( 5 / 24 ) 159.130555555556 0.427422804572817 372.302445852408 Winsorized Mean ( 6 / 24 ) 159.130555555556 0.427422804572817 372.302445852408 Winsorized Mean ( 7 / 24 ) 159.10625 0.421313452124798 377.643412992355 Winsorized Mean ( 8 / 24 ) 159.121805555556 0.414609538129004 383.787132041437 Winsorized Mean ( 9 / 24 ) 159.263055555556 0.380272822276126 418.812616169321 Winsorized Mean ( 10 / 24 ) 159.521388888889 0.308163086202406 517.652489967967 Winsorized Mean ( 11 / 24 ) 159.498472222222 0.30515803518293 522.674987491675 Winsorized Mean ( 12 / 24 ) 159.488472222222 0.303878467215649 524.842953446386 Winsorized Mean ( 13 / 24 ) 159.51375 0.289862929501274 550.307520435444 Winsorized Mean ( 14 / 24 ) 159.593472222222 0.269604718457382 591.953557546695 Winsorized Mean ( 15 / 24 ) 159.874722222222 0.218522207326317 731.617734317881 Winsorized Mean ( 16 / 24 ) 159.9325 0.208116013413489 768.477626381604 Winsorized Mean ( 17 / 24 ) 159.920694444444 0.206561510274668 774.203743145542 Winsorized Mean ( 18 / 24 ) 159.870694444444 0.195490467649096 817.79278737729 Winsorized Mean ( 19 / 24 ) 159.865416666667 0.194146635761791 823.426149206183 Winsorized Mean ( 20 / 24 ) 159.87375 0.192955296328098 828.553312826164 Winsorized Mean ( 21 / 24 ) 159.902916666667 0.188061879810118 850.267565272225 Winsorized Mean ( 22 / 24 ) 159.902916666667 0.188061879810118 850.267565272225 Winsorized Mean ( 23 / 24 ) 159.982777777778 0.176220783571873 907.854195941237 Winsorized Mean ( 24 / 24 ) 160.046111111111 0.163532928199369 978.678195720884 Trimmed Mean ( 1 / 24 ) 159.114714285714 0.454895602494556 349.782924726380 Trimmed Mean ( 2 / 24 ) 159.183088235294 0.437923418952581 363.49526274714 Trimmed Mean ( 3 / 24 ) 159.258181818182 0.419898750649224 379.277579587807 Trimmed Mean ( 4 / 24 ) 159.3365625 0.401715024921299 396.640784175837 Trimmed Mean ( 5 / 24 ) 159.404032258065 0.386807941886915 412.101239391478 Trimmed Mean ( 6 / 24 ) 159.469666666667 0.372394600161918 428.227655818126 Trimmed Mean ( 7 / 24 ) 159.539827586207 0.354481079232924 450.065848172889 Trimmed Mean ( 8 / 24 ) 159.619464285714 0.333638580763993 478.420283170503 Trimmed Mean ( 9 / 24 ) 159.702407407407 0.308996361767041 516.842355340775 Trimmed Mean ( 10 / 24 ) 159.77 0.287827195937016 555.090006279191 Trimmed Mean ( 11 / 24 ) 159.8058 0.280392595028718 569.935878597766 Trimmed Mean ( 12 / 24 ) 159.847708333333 0.271382760690396 589.012020979821 Trimmed Mean ( 13 / 24 ) 159.894565217391 0.259862599614544 615.304262539373 Trimmed Mean ( 14 / 24 ) 159.9425 0.248242261514214 644.30004393447 Trimmed Mean ( 15 / 24 ) 159.985238095238 0.238165715469290 671.739161868860 Trimmed Mean ( 16 / 24 ) 159.9985 0.237304724039118 674.232258324639 Trimmed Mean ( 17 / 24 ) 160.006315789474 0.237757847169854 672.980167401857 Trimmed Mean ( 18 / 24 ) 160.016388888889 0.237863557253919 672.723433283524 Trimmed Mean ( 19 / 24 ) 160.033529411765 0.239394989930309 668.491556395363 Trimmed Mean ( 20 / 24 ) 160.0534375 0.240599306074788 665.228175887793 Trimmed Mean ( 21 / 24 ) 160.075 0.241283802944206 663.430358966181 Trimmed Mean ( 22 / 24 ) 160.096071428571 0.242173982719601 661.078740295307 Trimmed Mean ( 23 / 24 ) 160.120384615385 0.241781516611895 662.252379169282 Trimmed Mean ( 24 / 24 ) 160.138333333333 0.243319932130479 658.138985701592 Median 160.44 Midrange 156.77 Midmean - Weighted Average at Xnp 159.900263157895 Midmean - Weighted Average at X(n+1)p 160.016388888889 Midmean - Empirical Distribution Function 159.900263157895 Midmean - Empirical Distribution Function - Averaging 160.016388888889 Midmean - Empirical Distribution Function - Interpolation 160.016388888889 Midmean - Closest Observation 159.900263157895 Midmean - True Basic - Statistics Graphics Toolkit 160.016388888889 Midmean - MS Excel (old versions) 159.95 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124421168529xs4cbc0xkcnq4/18slf1244211474.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124421168529xs4cbc0xkcnq4/18slf1244211474.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124421168529xs4cbc0xkcnq4/2ozza1244211474.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124421168529xs4cbc0xkcnq4/2ozza1244211474.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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