centrumaten, stof voor jurk: birgit teugels

*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 05:10:03 -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/t1243595430cg4f4xvl8ay5ug6.htm/, Retrieved Fri, 29 May 2009 13:10:33 +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/t1243595430cg4f4xvl8ay5ug6.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 «

20,73 20,73 20,74 20,74 20,75 20,75 20,77 20,78 20,78 20,8 20,84 20,85 20,86 20,86 20,86 20,86 20,9 20,92 20,95 20,95 20,95 20,96 21,1 21,18 21,19 21,19 21,19 21,19 21,19 21,21 21,22 21,22 21,22 21,23 21,41 21,42 21,43 21,44 21,44 21,44 21,48 21,53 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,57 21,6 21,61 21,6 21,6 21,71 21,75 21,84 21,85 21,92 21,92 21,93 22 22 21,99 22,01 22,01 22,06 22,03 22,05 22,05 22,06 22,06 22,13 22,06 22,25 22,28 22,18

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 21.422125 0.0518263573985528 413.344214706438 Geometric Mean 21.4171751650371 Harmonic Mean 21.4122289246844 Quadratic Mean 21.4270770580124 Winsorized Mean ( 1 / 26 ) 21.42175 0.0517490827289831 413.954197259661 Winsorized Mean ( 2 / 26 ) 21.42025 0.051365830821173 417.01359946018 Winsorized Mean ( 3 / 26 ) 21.418375 0.0510247655648644 419.764300000012 Winsorized Mean ( 4 / 26 ) 21.415375 0.0503481372922322 425.345924432124 Winsorized Mean ( 5 / 26 ) 21.415375 0.0503481372922322 425.345924432124 Winsorized Mean ( 6 / 26 ) 21.416875 0.0501000877200526 427.481786452599 Winsorized Mean ( 7 / 26 ) 21.41775 0.0499578857449078 428.716101184949 Winsorized Mean ( 8 / 26 ) 21.41675 0.0497960317543578 430.089491982978 Winsorized Mean ( 9 / 26 ) 21.419 0.0494356121316955 433.270654016384 Winsorized Mean ( 10 / 26 ) 21.4215 0.0482563368961312 443.910611079089 Winsorized Mean ( 11 / 26 ) 21.420125 0.0476121240775626 449.888036188125 Winsorized Mean ( 12 / 26 ) 21.421625 0.0473859202203206 452.067299746428 Winsorized Mean ( 13 / 26 ) 21.42 0.0471316497171836 454.47167940295 Winsorized Mean ( 14 / 26 ) 21.42 0.0471316497171836 454.47167940295 Winsorized Mean ( 15 / 26 ) 21.418125 0.0468407258663179 457.254335919702 Winsorized Mean ( 16 / 26 ) 21.414125 0.0438205827562947 488.677321319374 Winsorized Mean ( 17 / 26 ) 21.41625 0.0428772810959046 499.477799259188 Winsorized Mean ( 18 / 26 ) 21.423 0.0419004244563257 511.28360339953 Winsorized Mean ( 19 / 26 ) 21.406375 0.0394676777506015 542.377363453409 Winsorized Mean ( 20 / 26 ) 21.403875 0.0391133915322093 547.226260918188 Winsorized Mean ( 21 / 26 ) 21.382875 0.0355036964335129 602.271795559184 Winsorized Mean ( 22 / 26 ) 21.410375 0.0284663046147146 752.130467575083 Winsorized Mean ( 23 / 26 ) 21.404625 0.0216976809631171 986.493673512148 Winsorized Mean ( 24 / 26 ) 21.404625 0.0209497165851951 1021.71429923431 Winsorized Mean ( 25 / 26 ) 21.404625 0.0209497165851951 1021.71429923431 Winsorized Mean ( 26 / 26 ) 21.404625 0.0209497165851951 1021.71429923431 Trimmed Mean ( 1 / 26 ) 21.42 0.0512254099450910 418.1518512582 Trimmed Mean ( 2 / 26 ) 21.4181578947368 0.0506011963405886 423.273745359193 Trimmed Mean ( 3 / 26 ) 21.4170270270270 0.0500912642573092 427.560121401845 Trimmed Mean ( 4 / 26 ) 21.4165277777778 0.0496222663348408 431.591085204845 Trimmed Mean ( 5 / 26 ) 21.4168571428571 0.0492790855805796 434.60337972053 Trimmed Mean ( 6 / 26 ) 21.4172058823529 0.0488474923211855 438.450468276427 Trimmed Mean ( 7 / 26 ) 21.4172727272727 0.048374291200626 442.740807063145 Trimmed Mean ( 8 / 26 ) 21.4171875 0.047818724306962 447.882870369292 Trimmed Mean ( 9 / 26 ) 21.4172580645161 0.0471650955442305 454.091268498151 Trimmed Mean ( 10 / 26 ) 21.417 0.0464315911354245 461.259230542718 Trimmed Mean ( 11 / 26 ) 21.4163793103448 0.045761486299112 468.000081342646 Trimmed Mean ( 12 / 26 ) 21.4158928571429 0.0450467122528009 475.41522535446 Trimmed Mean ( 13 / 26 ) 21.4151851851852 0.0441866797272754 484.652508795906 Trimmed Mean ( 14 / 26 ) 21.4146153846154 0.0431494487506595 496.289431375137 Trimmed Mean ( 15 / 26 ) 21.414 0.0418325134754472 511.8984785021 Trimmed Mean ( 16 / 26 ) 21.4135416666667 0.0402160494929615 532.462584879561 Trimmed Mean ( 17 / 26 ) 21.4134782608696 0.0388123410217029 551.718285915701 Trimmed Mean ( 18 / 26 ) 21.4131818181818 0.0371994974949476 575.63094289352 Trimmed Mean ( 19 / 26 ) 21.4121428571429 0.0353077324599266 606.443443555745 Trimmed Mean ( 20 / 26 ) 21.41275 0.0334107834196977 640.893382565099 Trimmed Mean ( 21 / 26 ) 21.4136842105263 0.0309255542862768 692.426852314451 Trimmed Mean ( 22 / 26 ) 21.4169444444444 0.0285268446239245 750.764577253062 Trimmed Mean ( 23 / 26 ) 21.4176470588235 0.0273456088153974 783.22070660076 Trimmed Mean ( 24 / 26 ) 21.4190625 0.0274132038433977 781.341087395687 Trimmed Mean ( 25 / 26 ) 21.4206666666667 0.0275469644251802 777.605341047539 Trimmed Mean ( 26 / 26 ) 21.4225 0.0275720556717894 776.964193566411 Median 21.46 Midrange 21.505 Midmean - Weighted Average at Xnp 21.3907142857143 Midmean - Weighted Average at X(n+1)p 21.3907142857143 Midmean - Empirical Distribution Function 21.3907142857143 Midmean - Empirical Distribution Function - Averaging 21.3907142857143 Midmean - Empirical Distribution Function - Interpolation 21.3907142857143 Midmean - Closest Observation 21.3907142857143 Midmean - True Basic - Statistics Graphics Toolkit 21.3907142857143 Midmean - MS Excel (old versions) 21.4013953488372 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243595430cg4f4xvl8ay5ug6/15iu01243595401.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243595430cg4f4xvl8ay5ug6/15iu01243595401.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243595430cg4f4xvl8ay5ug6/2hzgb1243595401.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243595430cg4f4xvl8ay5ug6/2hzgb1243595401.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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