Opgave 5-Oefening 2- Stap1-Van Muylder Jurgen

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 05 Nov 2008 12:14:28 -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/05/t1225912582pev6o7bvumxx1up.htm/, Retrieved Wed, 05 Nov 2008 19:16:24 +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/05/t1225912582pev6o7bvumxx1up.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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101,6 101,8 102,1 102,1 101,9 102,1 102 102,1 102,2 102,3 102,7 102,8 103,1 103,1 103,3 103,5 103,3 103,5 103,8 103,9 103,9 104,2 104,6 104,9 105,2 105,2 105,6 105,6 106,2 106,3 106,4 106,9 107,2 107,3 107,3 107,4 107,55 107,87 108,37 108,38 107,92 108,03 108,14 108,3 108,64 108,66 109,04 109,03 109,03 109,54 109,75 109,83 109,65 109,82 109,95 110,12 110,15 110,2 109,99 110,14 110,14 110,81 110,97 110,99 109,73 109,81 110,02 110,18 110,21 110,25 110,36 110,51 110,64 110,95 111,18 111,19 111,69 111,7 111,83 111,77 111,73 112,01 111,86 112,04

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 107.477023809524 0.362286666597169 296.662929439324 Geometric Mean 107.425891537061 Harmonic Mean 107.374325180122 Quadratic Mean 107.527691931627 Winsorized Mean ( 1 / 28 ) 107.479047619048 0.361774790201353 297.088272953536 Winsorized Mean ( 2 / 28 ) 107.477857142857 0.360797113920451 297.890013517553 Winsorized Mean ( 3 / 28 ) 107.480357142857 0.359980574411696 298.572658590005 Winsorized Mean ( 4 / 28 ) 107.482261904762 0.358699696015623 299.644139927235 Winsorized Mean ( 5 / 28 ) 107.479880952381 0.358358135769781 299.923094313195 Winsorized Mean ( 6 / 28 ) 107.477738095238 0.358052813566975 300.172862836991 Winsorized Mean ( 7 / 28 ) 107.476904761905 0.357934526083242 300.269733512407 Winsorized Mean ( 8 / 28 ) 107.438809523810 0.349756673255239 307.181585768929 Winsorized Mean ( 9 / 28 ) 107.448452380952 0.347695655574749 309.030183892685 Winsorized Mean ( 10 / 28 ) 107.473452380952 0.336488630153863 319.396980313448 Winsorized Mean ( 11 / 28 ) 107.483928571429 0.333933382080516 321.872368380088 Winsorized Mean ( 12 / 28 ) 107.523928571429 0.326451699228768 329.371630858257 Winsorized Mean ( 13 / 28 ) 107.502261904762 0.323748189440662 332.055175630458 Winsorized Mean ( 14 / 28 ) 107.507261904762 0.314891559036887 341.410427874214 Winsorized Mean ( 15 / 28 ) 107.484047619048 0.312144467590535 344.340710084418 Winsorized Mean ( 16 / 28 ) 107.493571428571 0.302741567621361 355.067103183577 Winsorized Mean ( 17 / 28 ) 107.471309523810 0.300230489950415 357.962675748086 Winsorized Mean ( 18 / 28 ) 107.527023809524 0.289156972963216 371.863845120561 Winsorized Mean ( 19 / 28 ) 107.547380952381 0.285406179494052 376.822187743213 Winsorized Mean ( 20 / 28 ) 107.542619047619 0.284873985439620 377.509441171535 Winsorized Mean ( 21 / 28 ) 107.610119047619 0.272603020157859 394.750281876203 Winsorized Mean ( 22 / 28 ) 107.712261904762 0.256755058014707 419.513690353832 Winsorized Mean ( 23 / 28 ) 107.794404761905 0.244905132919944 440.147592974873 Winsorized Mean ( 24 / 28 ) 107.874404761905 0.232188529496592 464.598337376042 Winsorized Mean ( 25 / 28 ) 107.844642857143 0.22874934022826 471.453350420722 Winsorized Mean ( 26 / 28 ) 107.959166666667 0.210693143997425 512.399998492529 Winsorized Mean ( 27 / 28 ) 107.946309523810 0.209204760133954 515.984002728672 Winsorized Mean ( 28 / 28 ) 108.106309523810 0.178109597381340 606.965099653497 Trimmed Mean ( 1 / 28 ) 107.493048780488 0.359770314204728 298.782430168262 Trimmed Mean ( 2 / 28 ) 107.50775 0.357309344354848 300.881439846233 Trimmed Mean ( 3 / 28 ) 107.523846153846 0.354896542863088 302.972368472259 Trimmed Mean ( 4 / 28 ) 107.539868421053 0.352283204126326 305.265386375019 Trimmed Mean ( 5 / 28 ) 107.556216216216 0.349507439024491 307.736557815239 Trimmed Mean ( 6 / 28 ) 107.574027777778 0.346192720652295 310.734516817937 Trimmed Mean ( 7 / 28 ) 107.593285714286 0.342217692598552 314.400126122354 Trimmed Mean ( 8 / 28 ) 107.613823529412 0.337405924807696 318.944676477587 Trimmed Mean ( 9 / 28 ) 107.641666666667 0.333281318785553 322.975398257853 Trimmed Mean ( 10 / 28 ) 107.66984375 0.328617647341437 327.644740387694 Trimmed Mean ( 11 / 28 ) 107.696451612903 0.325070557103238 331.301772060212 Trimmed Mean ( 12 / 28 ) 107.7235 0.321064597843955 335.519707633279 Trimmed Mean ( 13 / 28 ) 107.747586206897 0.317417009302598 339.451204721608 Trimmed Mean ( 14 / 28 ) 107.775892857143 0.313167705039316 344.147532209978 Trimmed Mean ( 15 / 28 ) 107.805740740741 0.309291880971116 348.556646240606 Trimmed Mean ( 16 / 28 ) 107.840384615385 0.304631167034816 354.003123400238 Trimmed Mean ( 17 / 28 ) 107.8768 0.300239556055507 359.302423095963 Trimmed Mean ( 18 / 28 ) 107.918541666667 0.294738282387791 366.150405683225 Trimmed Mean ( 19 / 28 ) 107.958260869565 0.289672863019369 372.690281527498 Trimmed Mean ( 20 / 28 ) 107.999545454545 0.283556198691978 380.875276057229 Trimmed Mean ( 21 / 28 ) 108.045238095238 0.275263834603389 392.515196378463 Trimmed Mean ( 22 / 28 ) 108.08875 0.266968544075217 404.874478281406 Trimmed Mean ( 23 / 28 ) 108.126578947368 0.259597093530588 416.516908863727 Trimmed Mean ( 24 / 28 ) 108.160277777778 0.252362955457963 428.590153342828 Trimmed Mean ( 25 / 28 ) 108.189705882353 0.24548053398548 440.726212078194 Trimmed Mean ( 26 / 28 ) 108.2259375 0.236067778067516 458.452815483556 Trimmed Mean ( 27 / 28 ) 108.254666666667 0.228060152043691 474.675938328443 Trimmed Mean ( 28 / 28 ) 108.288928571429 0.216072652932820 501.169060969029 Median 108.335 Midrange 106.82 Midmean - Weighted Average at Xnp 107.856818181818 Midmean - Weighted Average at X(n+1)p 108.045238095238 Midmean - Empirical Distribution Function 107.856818181818 Midmean - Empirical Distribution Function - Averaging 108.045238095238 Midmean - Empirical Distribution Function - Interpolation 108.045238095238 Midmean - Closest Observation 107.856818181818 Midmean - True Basic - Statistics Graphics Toolkit 108.045238095238 Midmean - MS Excel (old versions) 107.908444444444 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/05/t1225912582pev6o7bvumxx1up/1p3yh1225912466.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/05/t1225912582pev6o7bvumxx1up/1p3yh1225912466.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/05/t1225912582pev6o7bvumxx1up/2cwat1225912466.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/05/t1225912582pev6o7bvumxx1up/2cwat1225912466.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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