*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: Fri, 17 Dec 2010 14:34:21 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596318y0ha2y1ldddng11.htm/, Retrieved Fri, 17 Dec 2010 15:31:58 +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/2010/Dec/17/t1292596318y0ha2y1ldddng11.htm/}, year = {2010}, } @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 = {2010}, 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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2.26 2.57 3.07 2.76 2.51 2.87 3.14 3.11 3.16 2.47 2.57 2.89 2.63 2.38 1.69 1.96 2.19 1.87 1.60 1.63 1.22 1.21 1.49 1.64 1.66 1.77 1.82 1.78 1.28 1.29 1.37 1.12 1.51 2.24 2.94 3.09 3.46 3.64 4.39 4.15 5.21 5.80 5.91 5.39 5.46 4.72 3.14 2.63 2.32 1.93 0.62 0.60 -0.37 -1.10 -1.68 -0.78 -1.19 -0.79 -0.12 0.26 0.62 0.70 1.66 1.80 2.27 2.46 2.57

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.12597014925373 0.19765999475838 10.7556926319487 Geometric Mean NaN Harmonic Mean 3.5115989873212 Quadratic Mean 2.66426994284705 Winsorized Mean ( 1 / 22 ) 2.13164179104478 0.195177567857567 10.9215511518227 Winsorized Mean ( 2 / 22 ) 2.12417910447761 0.191704859143332 11.0804656385336 Winsorized Mean ( 3 / 22 ) 2.13492537313433 0.187468721725125 11.3881684021116 Winsorized Mean ( 4 / 22 ) 2.12477611940299 0.184552015224261 11.5131558808558 Winsorized Mean ( 5 / 22 ) 2.11880597014925 0.168548157326684 12.5709233714287 Winsorized Mean ( 6 / 22 ) 2.11164179104478 0.156915167633119 13.4572191005905 Winsorized Mean ( 7 / 22 ) 2.12626865671642 0.143258082308052 14.842224762888 Winsorized Mean ( 8 / 22 ) 2.10597014925373 0.123150277875522 17.1008152444642 Winsorized Mean ( 9 / 22 ) 2.0844776119403 0.118233508498989 17.6301764060239 Winsorized Mean ( 10 / 22 ) 2.03970149253731 0.110841926257303 18.4018950356605 Winsorized Mean ( 11 / 22 ) 2.04955223880597 0.107818597514345 19.0092645059058 Winsorized Mean ( 12 / 22 ) 2.12477611940299 0.0945594556201081 22.4702659873515 Winsorized Mean ( 13 / 22 ) 2.13641791044776 0.0908576904987915 23.5138918755169 Winsorized Mean ( 14 / 22 ) 2.13432835820896 0.0898592355845354 23.7519086861258 Winsorized Mean ( 15 / 22 ) 2.14328358208955 0.0870929539916593 24.6091501534649 Winsorized Mean ( 16 / 22 ) 2.11462686567164 0.0818533421597073 25.8343374855203 Winsorized Mean ( 17 / 22 ) 2.12223880597015 0.0768684994627661 27.6086930381427 Winsorized Mean ( 18 / 22 ) 2.14910447761194 0.0714015315868515 30.098856843117 Winsorized Mean ( 19 / 22 ) 2.12358208955224 0.0659340231517805 32.2076825899694 Winsorized Mean ( 20 / 22 ) 2.11164179104478 0.0566594550769082 37.2690098797894 Winsorized Mean ( 21 / 22 ) 2.1210447761194 0.0553844890288091 38.2967291621325 Winsorized Mean ( 22 / 22 ) 2.10462686567164 0.0522403243301985 40.2874004450815 Trimmed Mean ( 1 / 22 ) 2.12630769230769 0.186026849958078 11.4301117972317 Trimmed Mean ( 2 / 22 ) 2.12063492063492 0.174885651034705 12.1258371289368 Trimmed Mean ( 3 / 22 ) 2.11868852459016 0.163584251685315 12.9516655959392 Trimmed Mean ( 4 / 22 ) 2.11254237288136 0.151725626974454 13.9234380836471 Trimmed Mean ( 5 / 22 ) 2.10894736842105 0.138030063788406 15.2788987452326 Trimmed Mean ( 6 / 22 ) 2.10654545454545 0.126931997006647 16.5958584456458 Trimmed Mean ( 7 / 22 ) 2.10547169811321 0.116927453858058 18.0066496673151 Trimmed Mean ( 8 / 22 ) 2.10156862745098 0.108634076388877 19.3453904825224 Trimmed Mean ( 9 / 22 ) 2.10081632653061 0.104066892380261 20.1871726778793 Trimmed Mean ( 10 / 22 ) 2.10340425531915 0.0995630028899903 21.1263641539946 Trimmed Mean ( 11 / 22 ) 2.11288888888889 0.095638535734275 22.0924428910058 Trimmed Mean ( 12 / 22 ) 2.12186046511628 0.0913048365632392 23.2392997456016 Trimmed Mean ( 13 / 22 ) 2.12146341463415 0.089085845810964 23.8136978475323 Trimmed Mean ( 14 / 22 ) 2.11948717948718 0.0869617229445401 24.3726447420882 Trimmed Mean ( 15 / 22 ) 2.11756756756757 0.0842574039531942 25.132124516249 Trimmed Mean ( 16 / 22 ) 2.11428571428571 0.0812055030985794 26.0362368757087 Trimmed Mean ( 17 / 22 ) 2.11424242424242 0.0783712395828708 26.9772742589684 Trimmed Mean ( 18 / 22 ) 2.11322580645161 0.0757065459262307 27.9133829261048 Trimmed Mean ( 19 / 22 ) 2.10862068965517 0.0733483559104179 28.7480293659272 Trimmed Mean ( 20 / 22 ) 2.10666666666667 0.0714701140895774 29.4761900621324 Trimmed Mean ( 21 / 22 ) 2.106 0.0713582510996451 29.5130551484392 Trimmed Mean ( 22 / 22 ) 2.10391304347826 0.0710445474300417 29.6139974084571 Median 2.19 Midrange 2.115 Midmean - Weighted Average at Xnp 2.09 Midmean - Weighted Average at X(n+1)p 2.11428571428571 Midmean - Empirical Distribution Function 2.11428571428571 Midmean - Empirical Distribution Function - Averaging 2.11428571428571 Midmean - Empirical Distribution Function - Interpolation 2.11424242424243 Midmean - Closest Observation 2.09 Midmean - True Basic - Statistics Graphics Toolkit 2.11428571428571 Midmean - MS Excel (old versions) 2.11428571428571 Number of observations 67

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596318y0ha2y1ldddng11/1km5l1292596458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596318y0ha2y1ldddng11/1km5l1292596458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596318y0ha2y1ldddng11/2km5l1292596458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596318y0ha2y1ldddng11/2km5l1292596458.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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