Opgave, oefening 2 (eigen reeks) - centrummaten - Ines S'Jongers

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 07 Nov 2008 14:34:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/07/t1226093858t7lblogve3i69w1.htm/, Retrieved Fri, 07 Nov 2008 21:37:38 +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/Nov/07/t1226093858t7lblogve3i69w1.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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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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0,7200 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7400 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7500 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7600 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,7800 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8000 0,8100 0,8100 0,8100 0,8100 0,8100 0,8100 0,8100 0,8100 0,8100 0,8100 0,8100

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.773214285714286 0.00265733116131764 290.974003153933 Geometric Mean 0.772835152982095 Harmonic Mean 0.772456010242095 Quadratic Mean 0.773593193203914 Winsorized Mean ( 1 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 2 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 3 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 4 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 5 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 6 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 7 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 8 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 9 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840279 Winsorized Mean ( 10 / 28 ) 0.773452380952381 0.00261013321485403 296.326783840278 Winsorized Mean ( 11 / 28 ) 0.772142857142857 0.00240762455789982 320.707335622294 Winsorized Mean ( 12 / 28 ) 0.772142857142857 0.00240762455789982 320.707335622295 Winsorized Mean ( 13 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 14 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 15 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 16 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 17 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 18 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 19 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 20 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 21 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 22 / 28 ) 0.773690476190476 0.00218073083477657 354.78494817071 Winsorized Mean ( 23 / 28 ) 0.768214285714286 0.00149737496722632 513.040689559072 Winsorized Mean ( 24 / 28 ) 0.768214285714286 0.00149737496722632 513.040689559072 Winsorized Mean ( 25 / 28 ) 0.771190476190476 0.00108983676482986 707.62016943966 Winsorized Mean ( 26 / 28 ) 0.771190476190476 0.00108983676482986 707.62016943966 Winsorized Mean ( 27 / 28 ) 0.771190476190476 0.00108983676482986 707.62016943966 Winsorized Mean ( 28 / 28 ) 0.771190476190476 0.00108983676482986 707.62016943966 Trimmed Mean ( 1 / 28 ) 0.773414634146341 0.00260416542732471 296.991360852555 Trimmed Mean ( 2 / 28 ) 0.773375 0.00259590567352182 297.921071589159 Trimmed Mean ( 3 / 28 ) 0.773333333333333 0.00258499645690409 299.162241119476 Trimmed Mean ( 4 / 28 ) 0.77328947368421 0.00257101357509526 300.772225076859 Trimmed Mean ( 5 / 28 ) 0.773243243243243 0.00255345014986209 302.822925007956 Trimmed Mean ( 6 / 28 ) 0.773194444444445 0.00253169570315394 305.405757682968 Trimmed Mean ( 7 / 28 ) 0.773142857142857 0.0025050082930718 308.638841348817 Trimmed Mean ( 8 / 28 ) 0.773088235294118 0.0024724767020528 312.677662302036 Trimmed Mean ( 9 / 28 ) 0.773030303030303 0.00243296798007300 317.731392012446 Trimmed Mean ( 10 / 28 ) 0.77296875 0.00238505273788653 324.088745595183 Trimmed Mean ( 11 / 28 ) 0.772903225806452 0.00232689534004922 332.160717546541 Trimmed Mean ( 12 / 28 ) 0.773 0.00229590645294576 336.686191638254 Trimmed Mean ( 13 / 28 ) 0.773103448275862 0.00225703037624255 342.531255411329 Trimmed Mean ( 14 / 28 ) 0.773035714285714 0.00224938148579685 343.665900678410 Trimmed Mean ( 15 / 28 ) 0.772962962962963 0.00223731191706250 345.487348933371 Trimmed Mean ( 16 / 28 ) 0.772884615384615 0.00221976141933964 348.183642012547 Trimmed Mean ( 17 / 28 ) 0.7728 0.00219535688140555 352.015659296918 Trimmed Mean ( 18 / 28 ) 0.772708333333333 0.0021622892906268 357.356592701499 Trimmed Mean ( 19 / 28 ) 0.772608695652174 0.00211812474277625 364.76071500846 Trimmed Mean ( 20 / 28 ) 0.7725 0.00205950075027434 375.09090486959 Trimmed Mean ( 21 / 28 ) 0.772380952380952 0.00198160893256393 389.774662239535 Trimmed Mean ( 22 / 28 ) 0.77225 0.00187724224902874 411.374717567513 Trimmed Mean ( 23 / 28 ) 0.772105263157895 0.00173483655060161 445.05937051542 Trimmed Mean ( 24 / 28 ) 0.7725 0.00170782512765993 452.329683811645 Trimmed Mean ( 25 / 28 ) 0.772941176470588 0.00166378066161541 464.569155239561 Trimmed Mean ( 26 / 28 ) 0.773125 0.00170610266113226 453.152683958017 Trimmed Mean ( 27 / 28 ) 0.773333333333333 0.00175075243812964 441.714840140106 Trimmed Mean ( 28 / 28 ) 0.773571428571429 0.00179757962744542 430.340562810432 Median 0.78 Midrange 0.765 Midmean - Weighted Average at Xnp 0.774 Midmean - Weighted Average at X(n+1)p 0.774 Midmean - Empirical Distribution Function 0.774 Midmean - Empirical Distribution Function - Averaging 0.774 Midmean - Empirical Distribution Function - Interpolation 0.774 Midmean - Closest Observation 0.774 Midmean - True Basic - Statistics Graphics Toolkit 0.774 Midmean - MS Excel (old versions) 0.774 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226093858t7lblogve3i69w1/1jn5n1226093666.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226093858t7lblogve3i69w1/1jn5n1226093666.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226093858t7lblogve3i69w1/2e2ut1226093666.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226093858t7lblogve3i69w1/2e2ut1226093666.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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