opdracht5oef2- MerelBoels-2MAR04A

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 18 May 2009 05:41:14 -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/18/t1242646927xs05iq5ziy59ty2.htm/, Retrieved Mon, 18 May 2009 13:42:10 +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/18/t1242646927xs05iq5ziy59ty2.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 «

672,1 674,4 676,6 678,7 680,8 682,9 684 684,1 684,1 684,2 685,9 689,2 692,4 695,7 697,2 696,8 696,4 695,9 696,2 697,2 705,2 706,2 707,4 708,7 710 711,3 711,5 710,7 710 709,2 707,9 706,1 704,4 702,7 701,5 700,8 700 699,3 698,8 698,4 696,8 695,1 694,3 693,4 692,4 691 689,7 688,3 686 683,6 682,6 681,9 681 679,9 678,5 677,5 678 679 679,8 681,3 684,2 687 688,4 689,5 691,1 693,3 695,9 698 699,6 701,6 703,5 705,5 708,1 709,6 710,3

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 693.741333333333 1.25497509875635 552.792907222475 Geometric Mean 693.657290094253 Harmonic Mean 693.573209055894 Quadratic Mean 693.825327297873 Winsorized Mean ( 1 / 25 ) 693.769333333333 1.24767599936819 556.049273757493 Winsorized Mean ( 2 / 25 ) 693.812 1.23298503969355 562.709179482373 Winsorized Mean ( 3 / 25 ) 693.832 1.22340561438032 567.13161346038 Winsorized Mean ( 4 / 25 ) 693.842666666667 1.21576013123342 570.706876168695 Winsorized Mean ( 5 / 25 ) 693.876 1.20996290613979 573.468819977063 Winsorized Mean ( 6 / 25 ) 693.86 1.20151106063524 577.489481980427 Winsorized Mean ( 7 / 25 ) 693.850666666667 1.19020533217287 582.967197264991 Winsorized Mean ( 8 / 25 ) 693.882666666667 1.16682579095014 594.675462308421 Winsorized Mean ( 9 / 25 ) 693.822666666667 1.15266330586893 601.930037274527 Winsorized Mean ( 10 / 25 ) 693.916 1.12898270400655 614.638291213337 Winsorized Mean ( 11 / 25 ) 693.872 1.11222131442094 623.861448259739 Winsorized Mean ( 12 / 25 ) 693.728 1.07385566161472 646.016056717404 Winsorized Mean ( 13 / 25 ) 693.814666666667 1.05506191839705 657.60563865368 Winsorized Mean ( 14 / 25 ) 693.833333333333 1.01785560372286 681.661849476096 Winsorized Mean ( 15 / 25 ) 693.833333333333 0.999690642839766 694.048042064692 Winsorized Mean ( 16 / 25 ) 693.812 0.95187999849326 728.885995186622 Winsorized Mean ( 17 / 25 ) 693.698666666667 0.908554922967262 763.518692299973 Winsorized Mean ( 18 / 25 ) 693.530666666667 0.877523077047408 790.327553550137 Winsorized Mean ( 19 / 25 ) 693.252 0.839095093881841 826.190029061976 Winsorized Mean ( 20 / 25 ) 693.252 0.831588862380944 833.647528677972 Winsorized Mean ( 21 / 25 ) 693.056 0.805718838582567 860.171025936584 Winsorized Mean ( 22 / 25 ) 693.32 0.702682120280688 986.676592429948 Winsorized Mean ( 23 / 25 ) 693.228 0.682682995300215 1015.446414767 Winsorized Mean ( 24 / 25 ) 693.452 0.625336983027823 1108.92529759294 Winsorized Mean ( 25 / 25 ) 693.718666666667 0.544901655176247 1273.10801880806 Trimmed Mean ( 1 / 25 ) 693.794520547945 1.23041103007639 563.872156205291 Trimmed Mean ( 2 / 25 ) 693.821126760563 1.20982549499582 573.488597843576 Trimmed Mean ( 3 / 25 ) 693.826086956522 1.19435060521408 580.923293317338 Trimmed Mean ( 4 / 25 ) 693.823880597015 1.17979769968269 588.087161708843 Trimmed Mean ( 5 / 25 ) 693.818461538462 1.16468651342592 595.712626136282 Trimmed Mean ( 6 / 25 ) 693.804761904762 1.14786345881337 604.431438754916 Trimmed Mean ( 7 / 25 ) 693.793442622951 1.12944415182422 614.27866220952 Trimmed Mean ( 8 / 25 ) 693.783050847458 1.10952560284503 625.297017994418 Trimmed Mean ( 9 / 25 ) 693.766666666667 1.09031201224395 636.30103940508 Trimmed Mean ( 10 / 25 ) 693.758181818182 1.06944930889858 648.705998541139 Trimmed Mean ( 11 / 25 ) 693.735849056604 1.04834548733232 661.743535351047 Trimmed Mean ( 12 / 25 ) 693.717647058824 1.02517222228842 676.684006820125 Trimmed Mean ( 13 / 25 ) 693.716326530612 1.00381647126493 691.078843980756 Trimmed Mean ( 14 / 25 ) 693.704255319149 0.980144967693455 707.756789234578 Trimmed Mean ( 15 / 25 ) 693.688888888889 0.957306945604832 724.625358745947 Trimmed Mean ( 16 / 25 ) 693.672093023256 0.931076167861014 745.021854245123 Trimmed Mean ( 17 / 25 ) 693.656097560976 0.906978693785889 764.798668715726 Trimmed Mean ( 18 / 25 ) 693.651282051282 0.884312764839255 784.395871722342 Trimmed Mean ( 19 / 25 ) 693.664864864865 0.86029550248437 806.309997973594 Trimmed Mean ( 20 / 25 ) 693.711428571429 0.835803557682552 829.993390426448 Trimmed Mean ( 21 / 25 ) 693.763636363636 0.802503400608981 864.499310329617 Trimmed Mean ( 22 / 25 ) 693.845161290323 0.761221976155648 911.488610450273 Trimmed Mean ( 23 / 25 ) 693.906896551724 0.734258968196114 945.043815067694 Trimmed Mean ( 24 / 25 ) 693.988888888889 0.698662404023445 993.310767678863 Trimmed Mean ( 25 / 25 ) 694.056 0.665208739168891 1043.36572737627 Median 695.1 Midrange 691.8 Midmean - Weighted Average at Xnp 693.413157894737 Midmean - Weighted Average at X(n+1)p 693.651282051282 Midmean - Empirical Distribution Function 693.651282051282 Midmean - Empirical Distribution Function - Averaging 693.651282051282 Midmean - Empirical Distribution Function - Interpolation 693.413157894737 Midmean - Closest Observation 693.413157894737 Midmean - True Basic - Statistics Graphics Toolkit 693.651282051282 Midmean - MS Excel (old versions) 693.651282051282 Number of observations 75

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/18/t1242646927xs05iq5ziy59ty2/1ndio1242646871.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/18/t1242646927xs05iq5ziy59ty2/1ndio1242646871.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/18/t1242646927xs05iq5ziy59ty2/2gyyj1242646871.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/18/t1242646927xs05iq5ziy59ty2/2gyyj1242646871.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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