*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, 27 Dec 2008 05:06:00 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/27/t12303796251720xoanjzzxsxk.htm/, Retrieved Sat, 27 Dec 2008 13:07:08 +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/2008/Dec/27/t12303796251720xoanjzzxsxk.htm/}, year = {2008}, } @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 = {2008}, 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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0.09 0.65 -1.53 -3.36 10.51 -1.02 -2.68 -9.75 3.64 9.5 -0.33 -0.99 3.16 4.27 -2.97 -7.49 0.33 -2.57 4.07 5.31 -8.09 5.29 7.38 -6.12 -3.38 -8.61 2.58 10.02 7.08 -2.75 3.42 -1.6 0.65 2.86 -3.52 5.65 4.31 -4.39 -5.85 -5.47 -2.3 -0.14 8.08 -7.43 0.02 -2.47 -2.11 7.87 4.66 3.6 -3.64 7.26 -7.62 13.83 1.28 -0.32 -2.9 4.92 11.99 10.06 -2.22 3.97 0.56 3.34 -2.86 4.38 1.43 -0.49 -1.23

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.86695652173913 0.639836746026987 1.35496519561032 Geometric Mean NaN Harmonic Mean 1.37761650352215 Quadratic Mean 5.34698099838605 Winsorized Mean ( 1 / 23 ) 0.856811594202899 0.628539474465498 1.36317865306951 Winsorized Mean ( 2 / 23 ) 0.828985507246377 0.614699697435749 1.34860243254476 Winsorized Mean ( 3 / 23 ) 0.829855072463768 0.605966163383706 1.36947427531245 Winsorized Mean ( 4 / 23 ) 0.835072463768116 0.603910516820888 1.38277516371815 Winsorized Mean ( 5 / 23 ) 0.801739130434783 0.594760117580773 1.34800418981675 Winsorized Mean ( 6 / 23 ) 0.792173913043478 0.54712173593142 1.44789333162734 Winsorized Mean ( 7 / 23 ) 0.798260869565217 0.537941474223506 1.48391768959155 Winsorized Mean ( 8 / 23 ) 0.785507246376812 0.519232971586226 1.51282235405262 Winsorized Mean ( 9 / 23 ) 0.91072463768116 0.492629145302416 1.84870230753822 Winsorized Mean ( 10 / 23 ) 0.993333333333333 0.471204206662296 2.10807399273759 Winsorized Mean ( 11 / 23 ) 0.784492753623189 0.427553037657183 1.83484312945568 Winsorized Mean ( 12 / 23 ) 0.749710144927536 0.414228602957188 1.80989468031743 Winsorized Mean ( 13 / 23 ) 0.749710144927536 0.413067144593523 1.81498372538267 Winsorized Mean ( 14 / 23 ) 0.753768115942029 0.389739300227617 1.93403158342464 Winsorized Mean ( 15 / 23 ) 0.712463768115942 0.378828195375067 1.88070417359128 Winsorized Mean ( 16 / 23 ) 0.656811594202899 0.367714856073823 1.78619814607391 Winsorized Mean ( 17 / 23 ) 0.666666666666667 0.361362078615513 1.84487168443592 Winsorized Mean ( 18 / 23 ) 0.674492753623188 0.357286146234659 1.88782229798575 Winsorized Mean ( 19 / 23 ) 0.649710144927536 0.345026035997849 1.88307570194959 Winsorized Mean ( 20 / 23 ) 0.649710144927536 0.336849399503779 1.92878522533999 Winsorized Mean ( 21 / 23 ) 0.601014492753623 0.315426688705102 1.90540152204914 Winsorized Mean ( 22 / 23 ) 0.613768115942029 0.310181869309178 1.97873627271956 Winsorized Mean ( 23 / 23 ) 0.590434782608696 0.296811518234152 1.98925832164945 Trimmed Mean ( 1 / 23 ) 0.831940298507463 0.608997152936124 1.36608241023209 Trimmed Mean ( 2 / 23 ) 0.805538461538462 0.5855476164196 1.37570103429679 Trimmed Mean ( 3 / 23 ) 0.792698412698413 0.566383104544645 1.39957990684718 Trimmed Mean ( 4 / 23 ) 0.778688524590164 0.547307541611079 1.42276227785567 Trimmed Mean ( 5 / 23 ) 0.762203389830509 0.524821534209594 1.45230967128364 Trimmed Mean ( 6 / 23 ) 0.752631578947368 0.500338577490333 1.50424455120475 Trimmed Mean ( 7 / 23 ) 0.744363636363636 0.484838809246891 1.53528063795031 Trimmed Mean ( 8 / 23 ) 0.73433962264151 0.468100065393739 1.56876633209573 Trimmed Mean ( 9 / 23 ) 0.725686274509804 0.45210871978111 1.60511452833988 Trimmed Mean ( 10 / 23 ) 0.696734693877551 0.438533656252573 1.58878271700147 Trimmed Mean ( 11 / 23 ) 0.696734693877551 0.426175699412734 1.63485317167930 Trimmed Mean ( 12 / 23 ) 0.634888888888889 0.420603297131395 1.50947197327974 Trimmed Mean ( 13 / 23 ) 0.61953488372093 0.415834156594330 1.48986049822098 Trimmed Mean ( 14 / 23 ) 0.602682926829268 0.409214301360344 1.47278070396313 Trimmed Mean ( 15 / 23 ) 0.583589743589744 0.405104822605429 1.44058947468556 Trimmed Mean ( 16 / 23 ) 0.567567567567568 0.401245135134720 1.41451576073814 Trimmed Mean ( 17 / 23 ) 0.556571428571429 0.397641987295135 1.39967972788129 Trimmed Mean ( 18 / 23 ) 0.543030303030303 0.393043313609097 1.38160422586498 Trimmed Mean ( 19 / 23 ) 0.526774193548387 0.386391741462307 1.36331638858222 Trimmed Mean ( 20 / 23 ) 0.511379310344828 0.379097230771738 1.34893971476341 Trimmed Mean ( 21 / 23 ) 0.493703703703704 0.369486495189848 1.33618876503194 Trimmed Mean ( 22 / 23 ) 0.493703703703704 0.360851529949184 1.36816297764687 Trimmed Mean ( 23 / 23 ) 0.461304347826087 0.347480658515865 1.32756841717861 Median 0.09 Midrange 2.04 Midmean - Weighted Average at Xnp 0.446176470588235 Midmean - Weighted Average at X(n+1)p 0.556571428571428 Midmean - Empirical Distribution Function 0.556571428571428 Midmean - Empirical Distribution Function - Averaging 0.556571428571428 Midmean - Empirical Distribution Function - Interpolation 0.556571428571428 Midmean - Closest Observation 0.461666666666667 Midmean - True Basic - Statistics Graphics Toolkit 0.556571428571428 Midmean - MS Excel (old versions) 0.556571428571428 Number of observations 69

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t12303796251720xoanjzzxsxk/13d6u1230379558.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t12303796251720xoanjzzxsxk/13d6u1230379558.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t12303796251720xoanjzzxsxk/2lab91230379558.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t12303796251720xoanjzzxsxk/2lab91230379558.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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