*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: Sun, 18 Oct 2009 11:56:35 -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/18/t1255888899nb7879d7oeir03c.htm/, Retrieved Sun, 18 Oct 2009 20:01:41 +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/18/t1255888899nb7879d7oeir03c.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:

Workshop3,deel2,gemiddeldes

Dataseries X:

» Textbox « » Textfile « » CSV «

0,65 0,57 0,52 0,56 0,55 0,65 0,48 0,59 0,68 0,69 0,78 0,76 0,79 0,89 0,89 0,73 1,60 1,63 1,55 1,07 1,00 0,83 0,75 0,63 0,53 0,47 0,50 0,50 0,49 0,50 0,47 0,46 0,43 0,44 0,45 0,38 0,36 0,32 0,32 0,29 0,29 0,31 0,27 0,29 0,32 0,32 0,34 0,38 0,44 0,50 0,60 0,59 0,81 0,85 1,13 1,28 1,47 1,50 1,80 2,22

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 0.707666666666667 0.0551343334677252 12.8353173450609 Geometric Mean 0.612652145281306 Harmonic Mean 0.5430890291452 Quadratic Mean 0.824706008223537 Winsorized Mean ( 1 / 20 ) 0.701 0.0522032641791723 13.4282790745426 Winsorized Mean ( 2 / 20 ) 0.695333333333333 0.0502976825889919 13.8243612338019 Winsorized Mean ( 3 / 20 ) 0.693833333333333 0.049830272188353 13.9239322376309 Winsorized Mean ( 4 / 20 ) 0.691833333333333 0.048637650006109 14.2242343790548 Winsorized Mean ( 5 / 20 ) 0.6885 0.0472980840739046 14.5566149978549 Winsorized Mean ( 6 / 20 ) 0.6855 0.0464322755708706 14.7634375350333 Winsorized Mean ( 7 / 20 ) 0.663333333333333 0.0403674273419444 16.4323905933953 Winsorized Mean ( 8 / 20 ) 0.643333333333333 0.0354332878910796 18.1561850910057 Winsorized Mean ( 9 / 20 ) 0.637333333333333 0.0329199222447842 19.3601105310725 Winsorized Mean ( 10 / 20 ) 0.629 0.0298798913921139 21.0509466632804 Winsorized Mean ( 11 / 20 ) 0.6125 0.0252978025440812 24.2115890869463 Winsorized Mean ( 12 / 20 ) 0.6125 0.0252978025440812 24.2115890869463 Winsorized Mean ( 13 / 20 ) 0.614666666666667 0.0220918302595882 27.8232568077918 Winsorized Mean ( 14 / 20 ) 0.612333333333333 0.0209308339938016 29.2550852734615 Winsorized Mean ( 15 / 20 ) 0.607333333333333 0.0200618628932990 30.2730278121974 Winsorized Mean ( 16 / 20 ) 0.604666666666667 0.0187843345398622 32.1899434543983 Winsorized Mean ( 17 / 20 ) 0.604666666666667 0.0179208344909277 33.7409882878375 Winsorized Mean ( 18 / 20 ) 0.601666666666667 0.0165279538359643 36.4029735705977 Winsorized Mean ( 19 / 20 ) 0.5985 0.0160169842764090 37.3665847247858 Winsorized Mean ( 20 / 20 ) 0.595166666666667 0.0145059731836153 41.0290753424883 Trimmed Mean ( 1 / 20 ) 0.689137931034483 0.0499917019628224 13.7850463972396 Trimmed Mean ( 2 / 20 ) 0.676428571428571 0.0471935972513363 14.3330581016351 Trimmed Mean ( 3 / 20 ) 0.665925925925926 0.0449990437964396 14.7986683658957 Trimmed Mean ( 4 / 20 ) 0.655192307692308 0.0424348408183676 15.4399614811024 Trimmed Mean ( 5 / 20 ) 0.6442 0.0396392816920441 16.2515558431346 Trimmed Mean ( 6 / 20 ) 0.633125 0.0365040999470369 17.3439422124799 Trimmed Mean ( 7 / 20 ) 0.621739130434783 0.032614427837563 19.0633155832557 Trimmed Mean ( 8 / 20 ) 0.613636363636364 0.0297507100295303 20.6259401213374 Trimmed Mean ( 9 / 20 ) 0.608333333333333 0.027692765770786 21.9672292167756 Trimmed Mean ( 10 / 20 ) 0.6035 0.0257516491879149 23.4353922576431 Trimmed Mean ( 11 / 20 ) 0.599473684210526 0.0241113684678272 24.8626984822711 Trimmed Mean ( 12 / 20 ) 0.5975 0.023310788428169 25.6319086692913 Trimmed Mean ( 13 / 20 ) 0.595294117647059 0.0221734987157477 26.8470991104475 Trimmed Mean ( 14 / 20 ) 0.5925 0.0215151859347404 27.5386883384212 Trimmed Mean ( 15 / 20 ) 0.589666666666667 0.0208799707872552 28.2407802517900 Trimmed Mean ( 16 / 20 ) 0.587142857142857 0.0201899520746589 29.0809435788508 Trimmed Mean ( 17 / 20 ) 0.584615384615385 0.0195348270393065 29.9268267612027 Trimmed Mean ( 18 / 20 ) 0.581666666666667 0.0187534215879673 31.0165621744396 Trimmed Mean ( 19 / 20 ) 0.578636363636364 0.0179982617552405 32.1495693031514 Trimmed Mean ( 20 / 20 ) 0.5755 0.016881553308427 34.0904648692913 Median 0.565 Midrange 1.245 Midmean - Weighted Average at Xnp 0.58483870967742 Midmean - Weighted Average at X(n+1)p 0.58483870967742 Midmean - Empirical Distribution Function 0.58483870967742 Midmean - Empirical Distribution Function - Averaging 0.58483870967742 Midmean - Empirical Distribution Function - Interpolation 0.58483870967742 Midmean - Closest Observation 0.58483870967742 Midmean - True Basic - Statistics Graphics Toolkit 0.58483870967742 Midmean - MS Excel (old versions) 0.5925 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/18/t1255888899nb7879d7oeir03c/1d6jy1255888594.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255888899nb7879d7oeir03c/1d6jy1255888594.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255888899nb7879d7oeir03c/2xkrc1255888594.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255888899nb7879d7oeir03c/2xkrc1255888594.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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