Opgave 5 - Sofie Loopmans - Eigen reeks

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 31 May 2009 02:01:53 -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/31/t1243757039xv82xkpt3mt4hjd.htm/, Retrieved Sun, 31 May 2009 10:03:59 +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/31/t1243757039xv82xkpt3mt4hjd.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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30,06 30,46 30,46 30,49 30,49 30,5 30,5 30,5 30,51 30,51 30,61 30,88 30,95 31,09 31,28 31,31 31,32 31,34 31,34 31,34 31,34 31,36 31,36 31,36 31,72 32,07 32,13 32,19 32,26 32,27 32,28 32,28 32,28 32,29 32,61 32,68 32,69 32,74 32,86 32,86 32,9 32,95 32,95 32,96 32,99 33 33,06 33,42 33,48 33,5 33,51 33,52 33,55 33,56 33,56 33,56 33,6 33,61 33,62 33,72 33,83 33,96 34,06 34,11 34,11 34,21 34,19 34,17 34,12 34,15 34,15 34,15

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 32.4416666666667 0.149925646673664 216.385037426457 Geometric Mean 32.4168913330953 Harmonic Mean 32.3919517424162 Quadratic Mean 32.4662540613755 Winsorized Mean ( 1 / 24 ) 32.4469444444444 0.148735099579700 218.152571492096 Winsorized Mean ( 2 / 24 ) 32.4463888888889 0.148643883593361 218.282704303200 Winsorized Mean ( 3 / 24 ) 32.4468055555555 0.148274613369354 218.829136143017 Winsorized Mean ( 4 / 24 ) 32.4468055555556 0.148274613369354 218.829136143017 Winsorized Mean ( 5 / 24 ) 32.4475 0.148145784002394 219.024120183371 Winsorized Mean ( 6 / 24 ) 32.445 0.147743856932686 219.603039162450 Winsorized Mean ( 7 / 24 ) 32.4440277777778 0.147588950887887 219.826942210757 Winsorized Mean ( 8 / 24 ) 32.4451388888889 0.147383145544506 220.141446764626 Winsorized Mean ( 9 / 24 ) 32.4388888888889 0.146398543272942 221.579314682186 Winsorized Mean ( 10 / 24 ) 32.4388888888889 0.141713683934275 228.904421847742 Winsorized Mean ( 11 / 24 ) 32.4602777777778 0.131504471951639 246.837824570065 Winsorized Mean ( 12 / 24 ) 32.4536111111111 0.126909408122234 255.722657534209 Winsorized Mean ( 13 / 24 ) 32.4608333333333 0.120273838243752 269.891057002329 Winsorized Mean ( 14 / 24 ) 32.4958333333333 0.114269769420625 284.378217424389 Winsorized Mean ( 15 / 24 ) 32.5 0.113052330453513 287.477488253672 Winsorized Mean ( 16 / 24 ) 32.4933333333333 0.111515032636467 291.380745403714 Winsorized Mean ( 17 / 24 ) 32.4980555555556 0.110817604321596 293.257156699085 Winsorized Mean ( 18 / 24 ) 32.4980555555556 0.110817604321596 293.257156699085 Winsorized Mean ( 19 / 24 ) 32.4954166666667 0.110462099785607 294.177068240928 Winsorized Mean ( 20 / 24 ) 32.4870833333333 0.109347445109414 297.099610336818 Winsorized Mean ( 21 / 24 ) 32.49 0.108099241483878 300.557150577654 Winsorized Mean ( 22 / 24 ) 32.4869444444444 0.107693785536712 301.660344490072 Winsorized Mean ( 23 / 24 ) 32.4805555555556 0.106849697883288 303.983597511282 Winsorized Mean ( 24 / 24 ) 32.5805555555556 0.0868936376274391 374.947538682249 Trimmed Mean ( 1 / 24 ) 32.4504285714286 0.148213157969218 218.944316523962 Trimmed Mean ( 2 / 24 ) 32.4541176470588 0.147493282728865 220.037936959603 Trimmed Mean ( 3 / 24 ) 32.4583333333333 0.146593420468420 221.417395334777 Trimmed Mean ( 4 / 24 ) 32.46265625 0.145580774875218 222.987247305318 Trimmed Mean ( 5 / 24 ) 32.4672580645161 0.144265892612483 225.051517559507 Trimmed Mean ( 6 / 24 ) 32.472 0.142625066536425 227.673863988746 Trimmed Mean ( 7 / 24 ) 32.4775862068966 0.140653412173359 230.905071587364 Trimmed Mean ( 8 / 24 ) 32.48375 0.138200532471205 235.047936640679 Trimmed Mean ( 9 / 24 ) 32.4901851851852 0.135159788640929 240.383515777018 Trimmed Mean ( 10 / 24 ) 32.4980769230769 0.131551261582499 247.037364234600 Trimmed Mean ( 11 / 24 ) 32.5066 0.128077020832412 253.805091567008 Trimmed Mean ( 12 / 24 ) 32.5129166666667 0.125953793147623 258.133684219896 Trimmed Mean ( 13 / 24 ) 32.5206521739130 0.124115188112434 262.019924140574 Trimmed Mean ( 14 / 24 ) 32.5281818181818 0.123012002339548 264.430959577383 Trimmed Mean ( 15 / 24 ) 32.5321428571429 0.122642003647078 265.261018979757 Trimmed Mean ( 16 / 24 ) 32.536 0.122123728768021 266.418331050172 Trimmed Mean ( 17 / 24 ) 32.5410526315789 0.121447990655996 267.942289170943 Trimmed Mean ( 18 / 24 ) 32.5461111111111 0.120370643060334 270.382464392068 Trimmed Mean ( 19 / 24 ) 32.5517647058824 0.118564250043077 274.549577077877 Trimmed Mean ( 20 / 24 ) 32.5584375 0.115816795482898 281.120172288032 Trimmed Mean ( 21 / 24 ) 32.567 0.111905286306985 291.022891542946 Trimmed Mean ( 22 / 24 ) 32.5764285714286 0.106322876389984 306.391528121764 Trimmed Mean ( 23 / 24 ) 32.5876923076923 0.0977458363343936 333.392127273924 Trimmed Mean ( 24 / 24 ) 32.6016666666667 0.0840778337351997 387.755787920804 Median 32.685 Midrange 32.135 Midmean - Weighted Average at Xnp 32.5671794871795 Midmean - Weighted Average at X(n+1)p 32.5671794871795 Midmean - Empirical Distribution Function 32.5671794871795 Midmean - Empirical Distribution Function - Averaging 32.5671794871795 Midmean - Empirical Distribution Function - Interpolation 32.5671794871795 Midmean - Closest Observation 32.5671794871795 Midmean - True Basic - Statistics Graphics Toolkit 32.5671794871795 Midmean - MS Excel (old versions) 32.5671794871795 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t1243757039xv82xkpt3mt4hjd/1qx3d1243756908.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t1243757039xv82xkpt3mt4hjd/1qx3d1243756908.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t1243757039xv82xkpt3mt4hjd/2xl221243756908.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t1243757039xv82xkpt3mt4hjd/2xl221243756908.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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