Opgave 5 Oefening 2 Central Tendency

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 14 May 2009 02:42:05 -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/May/14/t1242290576bkv08v1p21u83jv.htm/, Retrieved Thu, 14 May 2009 10:42:59 +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/May/14/t1242290576bkv08v1p21u83jv.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:

» Textbox « » Textfile « » CSV «

5,29 5,29 5,29 5,31 5,33 5,34 5,34 5,37 5,41 5,41 5,38 5,44 5,44 5,46 5,46 5,45 5,46 5,46 5,48 5,47 5,48 5,51 5,55 5,58 5,59 5,6 5,6 5,67 5,71 5,7 5,73 5,72 5,75 5,75 5,77 5,83 5,85 5,87 5,86 5,87 5,93 5,97 5,98 5,99 5,99 6,03 6,06 6,07 6,08 6,08 6,1 6,13 6,14 6,14 6,16 6,2 6,19 6,32 6,32 6,33 6,32 6,33 6,38 6,42 6,46 6,47 6,42 6,48 6,47 6,49 6,48 6,51 6,51 6,52 6,57 6,59 6,62 6,63 6,61 6,64

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 5.925 0.0481910097188419 122.948243553474 Geometric Mean 5.90955852796622 Harmonic Mean 5.89419258614842 Quadratic Mean 5.94046231365876 Winsorized Mean ( 1 / 26 ) 5.924875 0.0481676902549175 123.005171488270 Winsorized Mean ( 2 / 26 ) 5.924625 0.0481216627151261 123.117628646230 Winsorized Mean ( 3 / 26 ) 5.925 0.0479299330378487 123.617948627661 Winsorized Mean ( 4 / 26 ) 5.925 0.0475906862497434 124.499150293970 Winsorized Mean ( 5 / 26 ) 5.924375 0.0472737261273324 125.320669329992 Winsorized Mean ( 6 / 26 ) 5.920625 0.0466444753502084 126.930894935525 Winsorized Mean ( 7 / 26 ) 5.922375 0.0460967762093916 128.476988783294 Winsorized Mean ( 8 / 26 ) 5.923375 0.0459460827898764 128.920130734304 Winsorized Mean ( 9 / 26 ) 5.9245 0.0450891872861619 131.395138315528 Winsorized Mean ( 10 / 26 ) 5.92325 0.0448918443581172 131.944901901296 Winsorized Mean ( 11 / 26 ) 5.927375 0.0443060928711428 133.782390093363 Winsorized Mean ( 12 / 26 ) 5.925875 0.0440704606104556 134.463650207325 Winsorized Mean ( 13 / 26 ) 5.9275 0.043845059476597 135.191970788953 Winsorized Mean ( 14 / 26 ) 5.9275 0.0433317713123211 136.793392480463 Winsorized Mean ( 15 / 26 ) 5.92 0.0421855455477887 140.332427212389 Winsorized Mean ( 16 / 26 ) 5.92 0.0421855455477887 140.332427212389 Winsorized Mean ( 17 / 26 ) 5.9115 0.0409318281654023 144.423063052842 Winsorized Mean ( 18 / 26 ) 5.9025 0.0390210507939406 151.264506718937 Winsorized Mean ( 19 / 26 ) 5.904875 0.038689364052964 152.622694751883 Winsorized Mean ( 20 / 26 ) 5.902375 0.0383431556738007 153.935556327540 Winsorized Mean ( 21 / 26 ) 5.91025 0.0372584944863907 158.628255958083 Winsorized Mean ( 22 / 26 ) 5.92125 0.0357878661107294 165.454122961100 Winsorized Mean ( 23 / 26 ) 5.895375 0.0299772824058993 196.661422479038 Winsorized Mean ( 24 / 26 ) 5.895375 0.0291943204496866 201.935681639176 Winsorized Mean ( 25 / 26 ) 5.889125 0.0275986113150461 213.384830590712 Winsorized Mean ( 26 / 26 ) 5.882625 0.0267996219921858 219.504028889484 Trimmed Mean ( 1 / 26 ) 5.92397435897436 0.0478698214429649 123.751753827462 Trimmed Mean ( 2 / 26 ) 5.92302631578947 0.0475032851077644 124.686667508420 Trimmed Mean ( 3 / 26 ) 5.92216216216216 0.0470842825759232 125.777899506331 Trimmed Mean ( 4 / 26 ) 5.92111111111111 0.0466564188763061 126.908820987932 Trimmed Mean ( 5 / 26 ) 5.92 0.0462484961425248 128.004162162511 Trimmed Mean ( 6 / 26 ) 5.91897058823529 0.0458363599369404 129.132649197675 Trimmed Mean ( 7 / 26 ) 5.91863636363636 0.0454851528652137 130.122380399052 Trimmed Mean ( 8 / 26 ) 5.91796875 0.0451651399361431 131.029567457715 Trimmed Mean ( 9 / 26 ) 5.91709677419355 0.0447830348019146 132.128088245162 Trimmed Mean ( 10 / 26 ) 5.916 0.0444661999484227 133.044874688237 Trimmed Mean ( 11 / 26 ) 5.915 0.0440852786849898 134.171772901006 Trimmed Mean ( 12 / 26 ) 5.91339285714286 0.0436940936197809 135.336206046526 Trimmed Mean ( 13 / 26 ) 5.91185185185185 0.0432203607792574 136.783954258177 Trimmed Mean ( 14 / 26 ) 5.91 0.042637409840992 138.610671287027 Trimmed Mean ( 15 / 26 ) 5.908 0.0419718078364660 140.761151461935 Trimmed Mean ( 16 / 26 ) 5.90666666666667 0.0413269841840584 142.925180321896 Trimmed Mean ( 17 / 26 ) 5.90521739130435 0.0404679620765783 145.923270861275 Trimmed Mean ( 18 / 26 ) 5.90454545454545 0.0395955431128710 149.121466466919 Trimmed Mean ( 19 / 26 ) 5.9047619047619 0.0388305202461005 152.064970217721 Trimmed Mean ( 20 / 26 ) 5.90475 0.0378525944983486 155.993270164284 Trimmed Mean ( 21 / 26 ) 5.905 0.0365895887997508 161.384705149794 Trimmed Mean ( 22 / 26 ) 5.90444444444444 0.0351198502284755 168.122711402029 Trimmed Mean ( 23 / 26 ) 5.90264705882353 0.0334533725136411 176.444005949374 Trimmed Mean ( 24 / 26 ) 5.9034375 0.0327367597435676 180.330538093648 Trimmed Mean ( 25 / 26 ) 5.90433333333333 0.0318534118540431 185.359526332307 Trimmed Mean ( 26 / 26 ) 5.90607142857143 0.0309605453212808 190.761221008336 Median 5.9 Midrange 5.965 Midmean - Weighted Average at Xnp 5.89439024390244 Midmean - Weighted Average at X(n+1)p 5.89439024390244 Midmean - Empirical Distribution Function 5.89439024390244 Midmean - Empirical Distribution Function - Averaging 5.89439024390244 Midmean - Empirical Distribution Function - Interpolation 5.89439024390244 Midmean - Closest Observation 5.89439024390244 Midmean - True Basic - Statistics Graphics Toolkit 5.89439024390244 Midmean - MS Excel (old versions) 5.9146511627907 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242290576bkv08v1p21u83jv/17jdw1242290523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242290576bkv08v1p21u83jv/17jdw1242290523.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242290576bkv08v1p21u83jv/20qug1242290523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242290576bkv08v1p21u83jv/20qug1242290523.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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