Central Tendency Prijs kleurentelevisie - Tjitse Voortman

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 29 May 2009 07:45:51 -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/29/t1243604818adphdas9qwapr3z.htm/, Retrieved Fri, 29 May 2009 15:46:58 +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/29/t1243604818adphdas9qwapr3z.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 «

666,27 664,45 660,76 660,40 660,69 660,69 662,23 661,41 659,02 655,43 652,59 652,59 648,20 645,84 644,67 642,71 640,14 640,14 639,64 630,28 614,57 614,70 615,08 615,08 614,43 604,55 598,98 594,05 593,05 593,05 593,34 584,72 580,70 577,08 569,92 569,92 568,86 559,38 548,22 545,61 545,33 530,30 527,76 521,41 1601,93 1577,49 1551,43 1551,43 1516,88 1485,95 1438,22 1385,06 1329,49 1329,49 1276,16 1242,34 1181,59 1160,21 1135,18 1135,18 1084,96 1077,35 1061,13 1029,98 1013,08 1013,08 996,04 975,02 951,89 944,40 932,47 932,47 920,44 900,18 886,90

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 847.275466666667 37.0391656013334 22.875122938411 Geometric Mean 795.873757474623 Harmonic Mean 753.953088724831 Quadratic Mean 905.20511529708 Winsorized Mean ( 1 / 25 ) 847.034266666667 36.9407880082831 22.9295126697552 Winsorized Mean ( 2 / 25 ) 846.407066666667 36.7499615942795 23.0315088764179 Winsorized Mean ( 3 / 25 ) 847.008266666667 36.6816110438215 23.0908142408138 Winsorized Mean ( 4 / 25 ) 845.180533333333 36.2098411768156 23.3411831111395 Winsorized Mean ( 5 / 25 ) 843.292533333333 35.6809473660706 23.6342528880057 Winsorized Mean ( 6 / 25 ) 840.366933333333 34.6723172257183 24.2374032246679 Winsorized Mean ( 7 / 25 ) 836.290133333333 33.4474628954709 25.0030962272649 Winsorized Mean ( 8 / 25 ) 830.475733333333 32.1558330130476 25.8265967793886 Winsorized Mean ( 9 / 25 ) 830.475733333333 32.1558330130476 25.8265967793886 Winsorized Mean ( 10 / 25 ) 824.319733333333 30.5954061911104 26.9425981202643 Winsorized Mean ( 11 / 25 ) 819.8904 29.5632314240523 27.7334499818226 Winsorized Mean ( 12 / 25 ) 810.8136 27.6721727910552 29.3006843417112 Winsorized Mean ( 13 / 25 ) 808.5516 26.8505838787925 30.1129987954795 Winsorized Mean ( 14 / 25 ) 803.879333333333 26.0352200020002 30.8766099641783 Winsorized Mean ( 15 / 25 ) 803.937333333333 26.0288757568429 30.886364084395 Winsorized Mean ( 16 / 25 ) 793.3752 24.2175839812077 32.7602951894641 Winsorized Mean ( 17 / 25 ) 792.767733333333 23.8143782623158 33.2894575118016 Winsorized Mean ( 18 / 25 ) 790.211733333333 23.0444695734869 34.290732134815 Winsorized Mean ( 19 / 25 ) 784.823333333333 21.5399752024863 36.4356655917944 Winsorized Mean ( 20 / 25 ) 780.354 20.8493991237114 37.4281290012106 Winsorized Mean ( 21 / 25 ) 780.3904 20.8454885826668 37.4368965690208 Winsorized Mean ( 22 / 25 ) 775.503466666667 20.0855564765513 38.6100065274278 Winsorized Mean ( 23 / 25 ) 769.057333333333 19.1383717197698 40.1840524676874 Winsorized Mean ( 24 / 25 ) 766.519733333333 17.5516275069631 43.6722881128397 Winsorized Mean ( 25 / 25 ) 767.143066666667 16.8732058921866 45.4651636190788 Trimmed Mean ( 1 / 25 ) 841.401643835616 36.326340462232 23.1623013254090 Trimmed Mean ( 2 / 25 ) 835.451690140845 35.5840115697459 23.4782885145856 Trimmed Mean ( 3 / 25 ) 829.49768115942 34.8083725665366 23.83040688196 Trimmed Mean ( 4 / 25 ) 822.963880597015 33.8944285442165 24.2802111126739 Trimmed Mean ( 5 / 25 ) 816.55523076923 32.9591166214557 24.7747911495198 Trimmed Mean ( 6 / 25 ) 810.189206349206 31.9865231191913 25.3290801044615 Trimmed Mean ( 7 / 25 ) 804.00524590164 31.08561703204 25.8642202621537 Trimmed Mean ( 8 / 25 ) 798.142372881356 30.3003140614615 26.3410594115426 Trimmed Mean ( 9 / 25 ) 792.824385964912 29.6477933041924 26.7414298875593 Trimmed Mean ( 10 / 25 ) 787.119636363636 28.8164694304362 27.3149227480406 Trimmed Mean ( 11 / 25 ) 781.855471698113 28.1344818373447 27.7899367835631 Trimmed Mean ( 12 / 25 ) 776.770588235294 27.4946058843944 28.2517447786432 Trimmed Mean ( 13 / 25 ) 772.428367346939 27.0895072162632 28.5139320246922 Trimmed Mean ( 14 / 25 ) 767.994255319149 26.7108380798732 28.7521586938838 Trimmed Mean ( 15 / 25 ) 763.722222222222 26.3644577607634 28.9678714105329 Trimmed Mean ( 16 / 25 ) 759.046046511628 25.8661295742456 29.3451729735165 Trimmed Mean ( 17 / 25 ) 755.121219512195 25.5934579941235 29.5044624171371 Trimmed Mean ( 18 / 25 ) 750.862564102564 25.2560754698760 29.7299778422878 Trimmed Mean ( 19 / 25 ) 746.431351351351 24.9161146227139 29.9577748238040 Trimmed Mean ( 20 / 25 ) 742.101428571429 24.7413888903936 29.9943318404234 Trimmed Mean ( 21 / 25 ) 737.754545454545 24.5822102931369 30.0117254167547 Trimmed Mean ( 22 / 25 ) 732.842580645161 24.2396314158417 30.2332394446483 Trimmed Mean ( 23 / 25 ) 727.827586206897 23.8674574945671 30.4945588097337 Trimmed Mean ( 24 / 25 ) 722.848148148148 23.5119755146849 30.743828722375 Trimmed Mean ( 25 / 25 ) 717.3892 23.3202589316671 30.762488619963 Median 660.69 Midrange 1061.67 Midmean - Weighted Average at Xnp 742.697631578948 Midmean - Weighted Average at X(n+1)p 750.862564102564 Midmean - Empirical Distribution Function 750.862564102564 Midmean - Empirical Distribution Function - Averaging 750.862564102564 Midmean - Empirical Distribution Function - Interpolation 746.431351351352 Midmean - Closest Observation 742.697631578948 Midmean - True Basic - Statistics Graphics Toolkit 750.862564102564 Midmean - MS Excel (old versions) 750.862564102564 Number of observations 75

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243604818adphdas9qwapr3z/195fs1243604747.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243604818adphdas9qwapr3z/195fs1243604747.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243604818adphdas9qwapr3z/25mh61243604747.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243604818adphdas9qwapr3z/25mh61243604747.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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