Paper

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 31 Dec 2009 04:14:24 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/31/t1262258197hhw6uf8hvonfzec.htm/, Retrieved Thu, 31 Dec 2009 12:16:39 +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/Dec/31/t1262258197hhw6uf8hvonfzec.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}, }

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0.00129909929391305 0.0399953455650052 -0.0388246377373741 -0.00331410653299091 0.0210839113108800 -0.0306161034410643 -0.0177106810085845 -0.046387990142741 0.000293807560611557 0.0283994201318544 -0.0097276499256617 -0.0226399010542774 -0.0154224216079923 0.0180996287729906 0.0174136599175999 -0.0230868312646511 0.0152995239008014 0.0186909303105856 0.0411546583121751 -0.0309853409627296 0.00641105220624505 0.0159182504768269 -0.0129464581053229 -0.0128078454602796 0.0274724628079561 0.0283118917490450 -0.0263638289790966 0.00959383292935723 0.0166833770244468 0.0265094201387677 -0.00109417116631749 -0.0125243883301391 0.0328788388222352 -0.0150708239891775 0.0280916856622302 0.0249707612360408 0.0417384790369306 -0.0189545400438149 0.0134272541571829 0.00114937541706439 0.0792737906675707 0.00631274994392772 -0.0258498505131595 0.00309104687364825 0.0263272745307186 -0.0872423105882159 -0.0367158144235664 -0.08597 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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.0023706320605961 0.00409867380273727 0.578390029236503 Geometric Mean NaN Harmonic Mean 0.0119936098191391 Quadratic Mean 0.031836575080266 Winsorized Mean ( 1 / 20 ) 0.00232891268793520 0.00407104013573768 0.572068220966629 Winsorized Mean ( 2 / 20 ) 0.00262320279668508 0.00339788540890167 0.772010377340242 Winsorized Mean ( 3 / 20 ) 0.00258227173824191 0.00325627955614677 0.793012913577226 Winsorized Mean ( 4 / 20 ) 0.00264052238122783 0.0032277077319055 0.818079764511077 Winsorized Mean ( 5 / 20 ) 0.00271835111619814 0.00317253823169652 0.856837937850318 Winsorized Mean ( 6 / 20 ) 0.00266840807104924 0.00314441999655096 0.848616938569323 Winsorized Mean ( 7 / 20 ) 0.00256762195749019 0.00289391658881593 0.887248087043433 Winsorized Mean ( 8 / 20 ) 0.00202858180421602 0.00278681685212995 0.727920746806735 Winsorized Mean ( 9 / 20 ) 0.00243450788042001 0.00270487010194405 0.90004613481079 Winsorized Mean ( 10 / 20 ) 0.00263012480724421 0.00265646097392651 0.990085995261817 Winsorized Mean ( 11 / 20 ) 0.00261114631098671 0.00262190354667742 0.995897165742677 Winsorized Mean ( 12 / 20 ) 0.00296524006429557 0.00249553577692311 1.18821781347153 Winsorized Mean ( 13 / 20 ) 0.00302166956970901 0.00247291234081019 1.22190727097064 Winsorized Mean ( 14 / 20 ) 0.00375466883047976 0.00231258927082341 1.62357789939192 Winsorized Mean ( 15 / 20 ) 0.00384784692662488 0.00222918188067887 1.72612515828142 Winsorized Mean ( 16 / 20 ) 0.00342854449395115 0.00197638915508794 1.73475172393293 Winsorized Mean ( 17 / 20 ) 0.00298753494598818 0.00188203189509298 1.58739867999983 Winsorized Mean ( 18 / 20 ) 0.0034789728721117 0.00176378961012707 1.97244209407779 Winsorized Mean ( 19 / 20 ) 0.00333797141377592 0.00173075400287794 1.92862267440980 Winsorized Mean ( 20 / 20 ) 0.00320600035631684 0.00168450125041374 1.90323418016424 Trimmed Mean ( 1 / 20 ) 0.00252145015519731 0.00370358965947986 0.680812505441392 Trimmed Mean ( 2 / 20 ) 0.00272749902367081 0.00322569188032648 0.845554728988794 Trimmed Mean ( 3 / 20 ) 0.00278533602227199 0.00310807311406861 0.896161679615657 Trimmed Mean ( 4 / 20 ) 0.00286324118784328 0.00303085332450125 0.94469803757806 Trimmed Mean ( 5 / 20 ) 0.00292983847805672 0.00294475113077977 0.994935852959805 Trimmed Mean ( 6 / 20 ) 0.00298249451509089 0.00285466488874785 1.04477920572986 Trimmed Mean ( 7 / 20 ) 0.00305043519979494 0.00274819277686981 1.10997861047775 Trimmed Mean ( 8 / 20 ) 0.00314393236735237 0.00268554691981703 1.17068606925198 Trimmed Mean ( 9 / 20 ) 0.00334171255442015 0.00263093652514326 1.27016084291057 Trimmed Mean ( 10 / 20 ) 0.00349168405879416 0.00257899521042794 1.35389319246342 Trimmed Mean ( 11 / 20 ) 0.00362644076224172 0.00251993064449365 1.43910340158207 Trimmed Mean ( 12 / 20 ) 0.0037786102008819 0.0024464894107194 1.54450298633044 Trimmed Mean ( 13 / 20 ) 0.00389674253024325 0.0023787404693713 1.63815371219255 Trimmed Mean ( 14 / 20 ) 0.0040211701540022 0.00228749695112398 1.75789093490436 Trimmed Mean ( 15 / 20 ) 0.00405862771329913 0.00220504552840496 1.84060948448306 Trimmed Mean ( 16 / 20 ) 0.00408818547878678 0.00210869199024337 1.93873050104153 Trimmed Mean ( 17 / 20 ) 0.00418132922896034 0.00204677210249459 2.04288949603337 Trimmed Mean ( 18 / 20 ) 0.0043526738201634 0.00197713397751832 2.20150676163425 Trimmed Mean ( 19 / 20 ) 0.0044814075347314 0.00190703323278600 2.34993678017057 Trimmed Mean ( 20 / 20 ) 0.0046562185707672 0.00179628755671803 2.59213429016594 Median 0.00419954182511484 Midrange -0.00207850173013970 Midmean - Weighted Average at Xnp 0.00336155659587441 Midmean - Weighted Average at X(n+1)p 0.00405862771329913 Midmean - Empirical Distribution Function 0.00405862771329913 Midmean - Empirical Distribution Function - Averaging 0.00405862771329913 Midmean - Empirical Distribution Function - Interpolation 0.00405862771329913 Midmean - Closest Observation 0.00333946622088932 Midmean - True Basic - Statistics Graphics Toolkit 0.00405862771329913 Midmean - MS Excel (old versions) 0.00405862771329913 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/31/t1262258197hhw6uf8hvonfzec/1vufy1262258061.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/31/t1262258197hhw6uf8hvonfzec/1vufy1262258061.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/31/t1262258197hhw6uf8hvonfzec/2pzl41262258061.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/31/t1262258197hhw6uf8hvonfzec/2pzl41262258061.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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