*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: Sat, 19 Dec 2009 09:23:34 -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/19/t1261239858zeo9m2xsw3b1aur.htm/, Retrieved Sat, 19 Dec 2009 17:24:20 +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/19/t1261239858zeo9m2xsw3b1aur.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:

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Dataseries X:

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2.70074404761903 1.14360119047618 -0.184970238095229 3.31502976190477 0.557886904761897 -2.54211309523811 4.35788690476192 -2.25639880952378 1.9721726190476 0.898297371031753 -4.60170262896828 0.331630704365086 -1.80182663690476 -1.05896949404762 4.91245907738096 1.31245907738096 -2.3446837797619 2.1553162202381 2.15531622023809 2.44103050595237 4.06960193452381 -2.70427331349207 -1.50427331349206 2.82906001984126 -4.50439732142857 -4.36154017857142 -5.29011160714285 -0.99011160714286 -3.84725446428572 2.45274553571429 -6.54725446428571 -0.861540178571431 0.967031250000007 -9.30684399801587 1.19315600198413 1.32648933531746 -2.30696800595238 -1.76411086309523 3.30731770833333 -5.29268229166666 5.75017485119048 0.950174851190468 -4.24982514880952 1.73588913690476 0.364460565476192 -0.909414682539687 3.09058531746033 -1.17608134920635 2.49046130952381 0.633318452380951 4.40474702380952 -2.09525297619048 2.94760416666667 1.34760416666667 0.647604166666663 3. 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 1.29572867781623e-16 0.374823582958701 3.45690275832775e-16 Geometric Mean NaN Harmonic Mean 17.1740145159679 Quadratic Mean 3.35252404426275 Winsorized Mean ( 1 / 27 ) 0.00218489736429542 0.358398940783877 0.00609627182356259 Winsorized Mean ( 2 / 27 ) -0.0156140995492846 0.351521182494525 -0.0444186590363662 Winsorized Mean ( 3 / 27 ) 0.0209795861503040 0.340787366716646 0.0615621005920323 Winsorized Mean ( 4 / 27 ) -0.0124186599794229 0.332446308274983 -0.0373553854270834 Winsorized Mean ( 5 / 27 ) -0.0169162441211045 0.331544376497468 -0.0510225638564968 Winsorized Mean ( 6 / 27 ) -0.00353128674309481 0.315023559827715 -0.0112095957046072 Winsorized Mean ( 7 / 27 ) 0.000828173990791233 0.312792655377897 0.00264767722819669 Winsorized Mean ( 8 / 27 ) -0.013535068219674 0.305407761941900 -0.0443180230050894 Winsorized Mean ( 9 / 27 ) -0.084963639648245 0.290018274434321 -0.292959606817764 Winsorized Mean ( 10 / 27 ) -0.0721237660444834 0.287421153173544 -0.250934091830518 Winsorized Mean ( 11 / 27 ) -0.0426741316382536 0.279085837127531 -0.152906833530048 Winsorized Mean ( 12 / 27 ) -0.0284874399862818 0.270068518254584 -0.105482268612396 Winsorized Mean ( 13 / 27 ) -0.0129953275034297 0.260499720180808 -0.0498861476488724 Winsorized Mean ( 14 / 27 ) 0.00413130144032673 0.251627553494777 0.0164183189914951 Winsorized Mean ( 15 / 27 ) 0.0793719686948842 0.237992227578591 0.333506558186542 Winsorized Mean ( 16 / 27 ) 0.094164982608263 0.230921734326581 0.40777877787411 Winsorized Mean ( 17 / 27 ) 0.0914673507005695 0.218943334310929 0.417767231820236 Winsorized Mean ( 18 / 27 ) 0.0914673507005695 0.21663556566686 0.422217609647841 Winsorized Mean ( 19 / 27 ) 0.100581291029791 0.214626097781042 0.468634951991728 Winsorized Mean ( 20 / 27 ) 0.0417969362384895 0.203615457920797 0.205273885712291 Winsorized Mean ( 21 / 27 ) 0.0557436954977454 0.201696558635393 0.276374053552958 Winsorized Mean ( 22 / 27 ) 0.0481253521213002 0.196396265479534 0.245042093869729 Winsorized Mean ( 23 / 27 ) 0.0365377443415578 0.190827190326566 0.191470326000346 Winsorized Mean ( 24 / 27 ) 0.0992681235302747 0.180320638541804 0.550508939703323 Winsorized Mean ( 25 / 27 ) 0.0463580706202253 0.170654313596322 0.271648982339141 Winsorized Mean ( 26 / 27 ) 0.0956478266460867 0.160540175599561 0.595787479918193 Winsorized Mean ( 27 / 27 ) 0.00164650389477002 0.144041716901772 0.0114307433303703 Trimmed Mean ( 1 / 27 ) 0.00091929123970265 0.346190982047175 0.00265544536794832 Trimmed Mean ( 2 / 27 ) -0.000412060657596243 0.331903052918593 -0.00124150909120233 Trimmed Mean ( 3 / 27 ) 0.00779704034391546 0.319518031309741 0.0244025049602193 Trimmed Mean ( 4 / 27 ) 0.00292130422374437 0.309851828043862 0.00942806838412727 Trimmed Mean ( 5 / 27 ) 0.00729643485915477 0.301479974155258 0.0242020548117641 Trimmed Mean ( 6 / 27 ) 0.0129811507936504 0.291832112321780 0.0444815708949026 Trimmed Mean ( 7 / 27 ) 0.0163082837301588 0.284935792625338 0.0572349425809151 Trimmed Mean ( 8 / 27 ) 0.0190640834859583 0.27723243911782 0.0687657026956225 Trimmed Mean ( 9 / 27 ) 0.0243032328672206 0.269707258851573 0.0901096728753426 Trimmed Mean ( 10 / 27 ) 0.0404245747137647 0.26396377728226 0.153144401591656 Trimmed Mean ( 11 / 27 ) 0.055876126580575 0.257483287726237 0.217008750641649 Trimmed Mean ( 12 / 27 ) 0.068607499651907 0.251269164884080 0.273043847953084 Trimmed Mean ( 13 / 27 ) 0.080523696789321 0.245407329092046 0.328122624076637 Trimmed Mean ( 14 / 27 ) 0.0915179507337518 0.239995780471096 0.381331499054309 Trimmed Mean ( 15 / 27 ) 0.101431562208216 0.234915868553257 0.431778248242182 Trimmed Mean ( 16 / 27 ) 0.103862619452542 0.231117643197057 0.449392863373855 Trimmed Mean ( 17 / 27 ) 0.104907178740291 0.227490743075714 0.461149220060244 Trimmed Mean ( 18 / 27 ) 0.106330219356261 0.224953924636333 0.472675546906583 Trimmed Mean ( 19 / 27 ) 0.107885635843485 0.221825050863853 0.486354608838568 Trimmed Mean ( 20 / 27 ) 0.108645137679055 0.21785154417128 0.498711808963059 Trimmed Mean ( 21 / 27 ) 0.115587066290190 0.214633558342987 0.538532125090528 Trimmed Mean ( 22 / 27 ) 0.121825564403689 0.210381431434171 0.57906994725344 Trimmed Mean ( 23 / 27 ) 0.129578443877550 0.205494656899369 0.63056843342163 Trimmed Mean ( 24 / 27 ) 0.139507688492063 0.199770114839235 0.698341133779355 Trimmed Mean ( 25 / 27 ) 0.143888608870968 0.194310623160349 0.740508195232474 Trimmed Mean ( 26 / 27 ) 0.154785124178982 0.188771253787373 0.819961308056616 Trimmed Mean ( 27 / 27 ) 0.161608658509700 0.183401563687717 0.881173831128702 Median 0.534219990079373 Midrange -0.0363120039682494 Midmean - Weighted Average at Xnp 0.0574783606150787 Midmean - Weighted Average at X(n+1)p 0.108645137679055 Midmean - Empirical Distribution Function 0.108645137679055 Midmean - Empirical Distribution Function - Averaging 0.108645137679055 Midmean - Empirical Distribution Function - Interpolation 0.108645137679055 Midmean - Closest Observation 0.0523345675075588 Midmean - True Basic - Statistics Graphics Toolkit 0.108645137679055 Midmean - MS Excel (old versions) 0.108645137679055 Number of observations 81

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239858zeo9m2xsw3b1aur/1fuu01261239812.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239858zeo9m2xsw3b1aur/1fuu01261239812.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239858zeo9m2xsw3b1aur/2uv5u1261239812.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239858zeo9m2xsw3b1aur/2uv5u1261239812.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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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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