WS 3 - Vraag 2 (3)

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Wed, 21 Oct 2009 10:30:41 -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/Oct/21/t1256142692iqk9kqyrt3p4zqz.htm/, Retrieved Wed, 21 Oct 2009 18:31:32 +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/Oct/21/t1256142692iqk9kqyrt3p4zqz.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:

SHW WS 3 - Vraag 2 (3)

Dataseries X:

» Textbox « » Textfile « » CSV «

-0,07 -0,10 0,03 -0,09 -0,06 -0,05 0,01 -0,02 -0,04 -0,03 -0,05 -0,06 -0,01 -0,08 0,05 -0,06 -0,06 -0,04 0,02 -0,01 0,00 -0,03 -0,04 -0,03 -0,01 -0,06 0,05 -0,05 -0,04 0,00 0,07 0,04 0,01 0,03 0,00 -0,03 -0,03 -0,06 0,05 -0,04 -0,02 -0,02 0,03 -0,01 -0,02 -0,04 -0,02 0,00 -0,03 -0,01 0,02 -0,02 0,00 0,03 0,10 0,07 0,00 0,05 0,03 0,02 0,03 0,03 0,12 0,05 0,05 0,11 0,11 0,09 0,03 0,04 0,00 0,00 0,02

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 -0.000684931506849315 0.00568827724253561 -0.120411062549405 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 0.0482714924805663 Winsorized Mean ( 1 / 24 ) -0.000684931506849315 0.00561759835071516 -0.121926037443050 Winsorized Mean ( 2 / 24 ) -0.000410958904109589 0.00556009905742021 -0.0739121551370825 Winsorized Mean ( 3 / 24 ) -0.000410958904109589 0.00537214175239049 -0.07649814972338 Winsorized Mean ( 4 / 24 ) -0.000410958904109589 0.00514048587036518 -0.0799455371482996 Winsorized Mean ( 5 / 24 ) -0.00178082191780822 0.00483102001699645 -0.368622343013058 Winsorized Mean ( 6 / 24 ) -0.00178082191780822 0.00483102001699645 -0.368622343013058 Winsorized Mean ( 7 / 24 ) -0.0036986301369863 0.00447173964508101 -0.82711213767887 Winsorized Mean ( 8 / 24 ) -0.0036986301369863 0.00447173964508101 -0.82711213767887 Winsorized Mean ( 9 / 24 ) -0.0036986301369863 0.00447173964508101 -0.82711213767887 Winsorized Mean ( 10 / 24 ) -0.00232876712328767 0.00424479512938573 -0.548617083346651 Winsorized Mean ( 11 / 24 ) -0.00232876712328767 0.00424479512938573 -0.548617083346651 Winsorized Mean ( 12 / 24 ) -0.00232876712328767 0.00424479512938573 -0.548617083346651 Winsorized Mean ( 13 / 24 ) -0.00232876712328767 0.00368323647027126 -0.632261094850683 Winsorized Mean ( 14 / 24 ) -0.00232876712328767 0.00368323647027126 -0.632261094850683 Winsorized Mean ( 15 / 24 ) -0.00438356164383562 0.00337297377797697 -1.29961331821108 Winsorized Mean ( 16 / 24 ) -0.00438356164383562 0.00337297377797697 -1.29961331821108 Winsorized Mean ( 17 / 24 ) -0.00438356164383562 0.00337297377797697 -1.29961331821108 Winsorized Mean ( 18 / 24 ) -0.00438356164383562 0.00337297377797697 -1.29961331821108 Winsorized Mean ( 19 / 24 ) -0.00178082191780822 0.0030115358227865 -0.591333466576688 Winsorized Mean ( 20 / 24 ) -0.00178082191780822 0.0030115358227865 -0.591333466576688 Winsorized Mean ( 21 / 24 ) -0.00178082191780822 0.0030115358227865 -0.591333466576688 Winsorized Mean ( 22 / 24 ) -0.00178082191780822 0.0030115358227865 -0.591333466576688 Winsorized Mean ( 23 / 24 ) -0.00493150684931507 0.00256664063077017 -1.92138579518835 Winsorized Mean ( 24 / 24 ) -0.00493150684931507 0.00256664063077017 -1.92138579518835 Trimmed Mean ( 1 / 24 ) -0.000985915492957746 0.00541313303351486 -0.182133985411693 Trimmed Mean ( 2 / 24 ) -0.00130434782608696 0.00516939417382666 -0.252321216418559 Trimmed Mean ( 3 / 24 ) -0.00179104477611940 0.00491412171008835 -0.364468949241227 Trimmed Mean ( 4 / 24 ) -0.00230769230769231 0.00469640426472759 -0.491374289267273 Trimmed Mean ( 5 / 24 ) -0.00285714285714286 0.00452239447510468 -0.631776567230289 Trimmed Mean ( 6 / 24 ) -0.00311475409836066 0.0044139680400159 -0.705658507293912 Trimmed Mean ( 7 / 24 ) -0.00338983050847458 0.00428124482443232 -0.791786185440599 Trimmed Mean ( 8 / 24 ) -0.00333333333333333 0.00421339709986327 -0.791127267221385 Trimmed Mean ( 9 / 24 ) -0.00327272727272727 0.00412803950218735 -0.79280425271927 Trimmed Mean ( 10 / 24 ) -0.00320754716981132 0.00402075154996371 -0.797748164728126 Trimmed Mean ( 11 / 24 ) -0.00333333333333333 0.0039374189482269 -0.846578273016744 Trimmed Mean ( 12 / 24 ) -0.00346938775510204 0.00383049681073104 -0.905727879836014 Trimmed Mean ( 13 / 24 ) -0.00361702127659574 0.00369295065543373 -0.979439373573469 Trimmed Mean ( 14 / 24 ) -0.00377777777777778 0.00364163478786253 -1.0373851299886 Trimmed Mean ( 15 / 24 ) -0.00395348837209302 0.00357082330238987 -1.10716438123585 Trimmed Mean ( 16 / 24 ) -0.00390243902439024 0.00354204792596255 -1.10174653363273 Trimmed Mean ( 17 / 24 ) -0.00384615384615385 0.00349696966589381 -1.09985336266015 Trimmed Mean ( 18 / 24 ) -0.00378378378378378 0.00342993690464891 -1.10316425315441 Trimmed Mean ( 19 / 24 ) -0.00371428571428571 0.0033326930157299 -1.11449980443886 Trimmed Mean ( 20 / 24 ) -0.00393939393939394 0.00328389648510504 -1.19960965799686 Trimmed Mean ( 21 / 24 ) -0.00419354838709677 0.00320531123573557 -1.30831238487654 Trimmed Mean ( 22 / 24 ) -0.00448275862068965 0.00308285449647584 -1.45409347921354 Trimmed Mean ( 23 / 24 ) -0.00481481481481482 0.00289268506515061 -1.66447943912765 Trimmed Mean ( 24 / 24 ) -0.0048 0.00277608837515427 -1.72905158314107 Median 0 Midrange 0.01 Midmean - Weighted Average at Xnp -0.00555555555555556 Midmean - Weighted Average at X(n+1)p -0.00555555555555556 Midmean - Empirical Distribution Function -0.00555555555555556 Midmean - Empirical Distribution Function - Averaging -0.00555555555555556 Midmean - Empirical Distribution Function - Interpolation -0.00555555555555556 Midmean - Closest Observation -0.00555555555555556 Midmean - True Basic - Statistics Graphics Toolkit -0.00555555555555556 Midmean - MS Excel (old versions) -0.00555555555555556 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142692iqk9kqyrt3p4zqz/1c4l51256142636.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142692iqk9kqyrt3p4zqz/1c4l51256142636.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142692iqk9kqyrt3p4zqz/216pw1256142636.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142692iqk9kqyrt3p4zqz/216pw1256142636.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')

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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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