ws3 central tendency Et (van Yt/Xt)

*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: Tue, 27 Oct 2009 15:44:43 -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/27/t12566799213acp45ha64jngse.htm/, Retrieved Tue, 27 Oct 2009 22:45:21 +0100

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/27/t12566799213acp45ha64jngse.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:

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-0.023452158 -0.005769231 0.009230769 -0.010180996 0.000000000 0.057109557 0.137651822 0.156730769 0.114909781 0.067932068 -0.004102564 -0.020242915 -0.012820513 0.000000000 -0.012820513 -0.017435898 -0.044102564 0.036836403 0.115897436 0.142564102 0.111336032 0.015984016 -0.035964036 -0.053554041 -0.070275404 -0.084427768 -0.108818011 -0.133208255 -0.091528725 0.002107481 0.189520624 0.284382284 0.231917336 0.117056856 0.054945055 0.036836403 0.033119658 0.050920910 0.088071349 0.083516483 0.063348416 0.066105769 0.022962112 -0.003496504 -0.027644231 0.023199023 0.043424317 0.000000000 -0.069004525 -0.113122172 -0.121394231 -0.116015133 -0.110079576 -0.099621690 -0.091880342 -0.038988409 -0.027870680 0.064312736 0.062334 etc...

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.0147866039016393 0.0112994007843796 1.30861841117102 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 0.0887650333189044 Winsorized Mean ( 1 / 20 ) 0.0141201953114754 0.0109441629537734 1.29020331395989 Winsorized Mean ( 2 / 20 ) 0.0129065030491803 0.0104814052859236 1.23137143322886 Winsorized Mean ( 3 / 20 ) 0.011436164 0.010030297428542 1.14016200232084 Winsorized Mean ( 4 / 20 ) 0.0107067167213115 0.00977240893007823 1.09560670228991 Winsorized Mean ( 5 / 20 ) 0.0104074777868852 0.00966165396286755 1.07719421818294 Winsorized Mean ( 6 / 20 ) 0.00928629959016393 0.00905392744832124 1.02566534171707 Winsorized Mean ( 7 / 20 ) 0.0100416028032787 0.00885315617826451 1.13423988022847 Winsorized Mean ( 8 / 20 ) 0.00995818798360656 0.00881855708914338 1.12923099356767 Winsorized Mean ( 9 / 20 ) 0.0104785957213115 0.00851639729240068 1.23040240626887 Winsorized Mean ( 10 / 20 ) 0.00898477293442623 0.00737267397333536 1.21865865314556 Winsorized Mean ( 11 / 20 ) 0.00839257855737705 0.00718657732980586 1.16781301755001 Winsorized Mean ( 12 / 20 ) 0.0067528993442623 0.00641984045672518 1.05187962065135 Winsorized Mean ( 13 / 20 ) 0.00811146455737705 0.00605387363801775 1.33988005736324 Winsorized Mean ( 14 / 20 ) 0.0098691402295082 0.0056300591270548 1.75293722619765 Winsorized Mean ( 15 / 20 ) 0.0108895914590164 0.0053942951120561 2.01872371325745 Winsorized Mean ( 16 / 20 ) 0.0114168502131148 0.00523012390054549 2.18290243791816 Winsorized Mean ( 17 / 20 ) 0.0122163228688525 0.00466272527460546 2.61999627886851 Winsorized Mean ( 18 / 20 ) 0.0116444383770492 0.0045512389482143 2.55852055001813 Winsorized Mean ( 19 / 20 ) 0.0116967438196721 0.00416771913358887 2.8065096146726 Winsorized Mean ( 20 / 20 ) 0.0102910552950820 0.00364058938298693 2.82675528945224 Trimmed Mean ( 1 / 20 ) 0.0127255730338983 0.0104327870837774 1.21976734804509 Trimmed Mean ( 2 / 20 ) 0.0112330825263158 0.0097958609853531 1.14671722507206 Trimmed Mean ( 3 / 20 ) 0.0103050947818182 0.00932530074643569 1.10506835779607 Trimmed Mean ( 4 / 20 ) 0.00987116256603774 0.00896676084635504 1.10086158593717 Trimmed Mean ( 5 / 20 ) 0.00962131549019608 0.00862261817180998 1.11582297841405 Trimmed Mean ( 6 / 20 ) 0.00942557712244898 0.00822643448221207 1.14576699575373 Trimmed Mean ( 7 / 20 ) 0.0094557045319149 0.00792231985019555 1.19355248345363 Trimmed Mean ( 8 / 20 ) 0.00934224486666667 0.00759101403896342 1.23069787761088 Trimmed Mean ( 9 / 20 ) 0.00923302239534884 0.00716729947162459 1.28821495905152 Trimmed Mean ( 10 / 20 ) 0.0090271146097561 0.00669799030800876 1.34773479725141 Trimmed Mean ( 11 / 20 ) 0.00903373728205128 0.00641767966873598 1.40763293719061 Trimmed Mean ( 12 / 20 ) 0.00912983232432432 0.0060899518492336 1.49916330216524 Trimmed Mean ( 13 / 20 ) 0.00947505354285714 0.00586357605379449 1.61591722456223 Trimmed Mean ( 14 / 20 ) 0.00966894381818182 0.00565191946221771 1.71073630521761 Trimmed Mean ( 15 / 20 ) 0.00964080561290323 0.00547287787987295 1.76156052163310 Trimmed Mean ( 16 / 20 ) 0.00946568851724138 0.00527629791500504 1.79400190620820 Trimmed Mean ( 17 / 20 ) 0.00919017725925926 0.0050276354428567 1.82793230808267 Trimmed Mean ( 18 / 20 ) 0.00875583636 0.00484252801450045 1.80811269109472 Trimmed Mean ( 19 / 20 ) 0.00833022108695652 0.00457857860385983 1.81939020986426 Trimmed Mean ( 20 / 20 ) 0.00781553966666667 0.00430332708197831 1.81616212706605 Median 0 Midrange 0.0755870145 Midmean - Weighted Average at Xnp 0.00785055193333333 Midmean - Weighted Average at X(n+1)p 0.00964080561290322 Midmean - Empirical Distribution Function 0.00964080561290322 Midmean - Empirical Distribution Function - Averaging 0.00964080561290322 Midmean - Empirical Distribution Function - Interpolation 0.00964080561290322 Midmean - Closest Observation 0.0079613253125 Midmean - True Basic - Statistics Graphics Toolkit 0.00964080561290322 Midmean - MS Excel (old versions) 0.00964080561290322 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/27/t12566799213acp45ha64jngse/1owkq1256679878.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t12566799213acp45ha64jngse/1owkq1256679878.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t12566799213acp45ha64jngse/2azs71256679878.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t12566799213acp45ha64jngse/2azs71256679878.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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