*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, 29 Dec 2009 15:16:53 -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/29/t1262125058cu2mh3nhzeee1q1.htm/, Retrieved Tue, 29 Dec 2009 23:17:41 +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/29/t1262125058cu2mh3nhzeee1q1.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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-0.357487876856165 1.03213322243711 4.69825491312001 0.474482569950477 -2.62579843861073 1.65688504751995 -0.254966692995566 3.19914260597389 -0.539355714404328 -2.91247481025789 -0.339403100442276 2.45177061301795 -1.71128871238477 -4.1065766358034 -5.30195185290025 2.32936026002719 2.44309617725562 6.22114147701846 -5.95778641803127 -0.160348177380264 0.154044602743691 -0.857210205336665 4.33657892258829 2.63195760000889 2.30463277484981 -1.43427032431387 5.09383487829321 -5.61906233899656 4.99928693817776 -1.38048337807612 -1.34407614361804 -1.71801644720189 -0.0431838313728479 3.79444564624234 1.73516060338679 -1.964361621547 0.471717645931308 -0.716355767477998 1.70195590809979 -3.97017217819589 0.700753376028875 0.61044654955841 0.696412596531601 0.730219893737894 -6.1045219371015 3.65945261733721 1.79296060841843 -2.71630722407563 2.8757768775632 6.25180067953198 -6.2419699091405 0.877172525362433 -0 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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.220557322699471 0.398796659471378 -0.55305709679672 Geometric Mean NaN Harmonic Mean -1.83387701306634 Quadratic Mean 3.29594937366648 Winsorized Mean ( 1 / 23 ) -0.203158858384054 0.389100147375002 -0.522124855913397 Winsorized Mean ( 2 / 23 ) -0.190725330202633 0.38570987344445 -0.494478734753211 Winsorized Mean ( 3 / 23 ) -0.233762661797687 0.373179248742583 -0.626408522406709 Winsorized Mean ( 4 / 23 ) -0.230737294901758 0.370082357494116 -0.623475532484487 Winsorized Mean ( 5 / 23 ) -0.228005986642558 0.360124569371221 -0.633130883129293 Winsorized Mean ( 6 / 23 ) -0.253790831259726 0.352700360553624 -0.719564989560423 Winsorized Mean ( 7 / 23 ) -0.283228678705921 0.336909334333816 -0.840667354218489 Winsorized Mean ( 8 / 23 ) -0.160285816306881 0.305643792123986 -0.524420323386973 Winsorized Mean ( 9 / 23 ) -0.202534366796770 0.291588207132138 -0.694590390978974 Winsorized Mean ( 10 / 23 ) -0.153232044590048 0.266090020297379 -0.5758654323781 Winsorized Mean ( 11 / 23 ) -0.12926697609421 0.249014982112620 -0.519113247715142 Winsorized Mean ( 12 / 23 ) -0.126487741452241 0.238436881331341 -0.530487317003903 Winsorized Mean ( 13 / 23 ) -0.111069675566250 0.235475528432779 -0.471682455945553 Winsorized Mean ( 14 / 23 ) -0.12861130947578 0.230958930057679 -0.556857920339608 Winsorized Mean ( 15 / 23 ) -0.104316260000993 0.225501307803821 -0.462597139754705 Winsorized Mean ( 16 / 23 ) -0.192258553181744 0.211835367248435 -0.907584770565098 Winsorized Mean ( 17 / 23 ) -0.211641479623982 0.205321210467470 -1.03078234899415 Winsorized Mean ( 18 / 23 ) -0.167918295553196 0.194032024862980 -0.865415364663519 Winsorized Mean ( 19 / 23 ) -0.116890355083466 0.183657885590542 -0.636457044616472 Winsorized Mean ( 20 / 23 ) -0.0585499742819389 0.171373010597085 -0.341652247795282 Winsorized Mean ( 21 / 23 ) -0.162980109024947 0.155833866350091 -1.04585808490949 Winsorized Mean ( 22 / 23 ) -0.162303566495009 0.131097816751013 -1.23803409177488 Winsorized Mean ( 23 / 23 ) -0.153053408016113 0.127386243876532 -1.20149086242356 Trimmed Mean ( 1 / 23 ) -0.202510090658488 0.376391634791230 -0.538030264064749 Trimmed Mean ( 2 / 23 ) -0.201821398765194 0.361145189338936 -0.55883728960815 Trimmed Mean ( 3 / 23 ) -0.207897817263739 0.344970206014229 -0.602654413741352 Trimmed Mean ( 4 / 23 ) -0.198145498832906 0.331393401725391 -0.597916246374449 Trimmed Mean ( 5 / 23 ) -0.188616541507690 0.31602203212782 -0.596846176317864 Trimmed Mean ( 6 / 23 ) -0.17908014952767 0.300572993274313 -0.595795874994781 Trimmed Mean ( 7 / 23 ) -0.163458825165513 0.283725236012601 -0.57611662417739 Trimmed Mean ( 8 / 23 ) -0.141183569385760 0.267351149565667 -0.528082896277514 Trimmed Mean ( 9 / 23 ) -0.137953042332924 0.25577249557416 -0.539358393572560 Trimmed Mean ( 10 / 23 ) -0.12784848136239 0.244838545586631 -0.522174648015761 Trimmed Mean ( 11 / 23 ) -0.12784848136239 0.237417670879924 -0.538496064292749 Trimmed Mean ( 12 / 23 ) -0.123404773944722 0.231916553653325 -0.532108519209848 Trimmed Mean ( 13 / 23 ) -0.122992516661740 0.22709610717676 -0.541587956705963 Trimmed Mean ( 14 / 23 ) -0.124535998904871 0.221264719667788 -0.562837126008395 Trimmed Mean ( 15 / 23 ) -0.124020987129426 0.214439989029801 -0.578348225489746 Trimmed Mean ( 16 / 23 ) -0.126470764015664 0.206472156435631 -0.612531811547635 Trimmed Mean ( 17 / 23 ) -0.118364768564843 0.199058372968201 -0.594623410208177 Trimmed Mean ( 18 / 23 ) -0.106892231910511 0.190323695334325 -0.56163386131581 Trimmed Mean ( 19 / 23 ) -0.0993459982342645 0.181235191299519 -0.548160638791613 Trimmed Mean ( 20 / 23 ) -0.0971489735108617 0.171288399140388 -0.567166101139391 Trimmed Mean ( 21 / 23 ) -0.102081067856780 0.160658126648429 -0.635393116964232 Trimmed Mean ( 22 / 23 ) -0.102081067856780 0.150236489144906 -0.679469205103164 Trimmed Mean ( 23 / 23 ) -0.0847735976082687 0.143888291547437 -0.589162583672214 Median -0.195635680452197 Midrange -0.825139596072404 Midmean - Weighted Average at Xnp -0.174580220829057 Midmean - Weighted Average at X(n+1)p -0.118364768564843 Midmean - Empirical Distribution Function -0.118364768564843 Midmean - Empirical Distribution Function - Averaging -0.118364768564843 Midmean - Empirical Distribution Function - Interpolation -0.118364768564843 Midmean - Closest Observation -0.183352820669628 Midmean - True Basic - Statistics Graphics Toolkit -0.118364768564843 Midmean - MS Excel (old versions) -0.118364768564843 Number of observations 69

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262125058cu2mh3nhzeee1q1/1rdbn1262125011.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262125058cu2mh3nhzeee1q1/1rdbn1262125011.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262125058cu2mh3nhzeee1q1/2i8f81262125011.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262125058cu2mh3nhzeee1q1/2i8f81262125011.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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