BDM 17

*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: Wed, 21 Oct 2009 02:48:30 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114935x68gwt99lq7urx0.htm/, Retrieved Wed, 21 Oct 2009 10:48:55 +0200

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/Oct/21/t1256114935x68gwt99lq7urx0.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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0.12999193035676 0.17280058484801 0.02744658130086 0.13656792592222 0.17208401915196 0.23063105723864 0.10352709998142 -0.01170364225406 0.31153382892662 0.46447789978114 0.06917419850729 -0.06767770832384 0.01728190328937 0.13732771663096 0.23840189245513 0.25536952847765 0.22599948322053 0.26945206172352 0.06729380694487 -0.11721317240875 0.28115845461335 0.35064301671549 0.03419863991989 -0.04301317852539 -0.03629085622191 -0.10402750265604 0.06262822639100 0.04949470945548 -0.01257583204966 0.21584027401686 -0.07658873514831 -0.12019539261274 0.09552729827240 0.16956607208243 0.10721272792897 0.04833750824532 -0.04016169685164 -0.04957485360216 0.08941440970949 0.07266396944194 0.01914284268138 0.04319471561136 -0.21797880209304 -0.25855021861266 -0.17034098503775 -0.15215984843556 -0.07253771618185 -0.23786957100764 -0.19784068948076 -0.21613758711707 -0.05841199281214 -0.24961690877621 -0.23020713801112 -0.07302293271969 -0.41787370306736 -0.3587137 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 7.0416668635015e-12 0.0247520249275623 2.84488516964135e-10 Geometric Mean NaN Harmonic Mean -8.5131220863282 Quadratic Mean 0.190123911023483 Winsorized Mean ( 1 / 20 ) -0.000911248159573168 0.0239469999182009 -0.0380527065054431 Winsorized Mean ( 2 / 20 ) -0.0019617720000835 0.0235739518761361 -0.0832177825080486 Winsorized Mean ( 3 / 20 ) 0.00114796022487200 0.0221965981420322 0.0517178451187162 Winsorized Mean ( 4 / 20 ) 0.000500974724552668 0.0220058813400851 0.0227654924068008 Winsorized Mean ( 5 / 20 ) -0.000196191253106496 0.0216731794740547 -0.00905225988375908 Winsorized Mean ( 6 / 20 ) -0.0017714390616135 0.0213176740819788 -0.0830972016365992 Winsorized Mean ( 7 / 20 ) -0.00130751376387083 0.0208790883517355 -0.0626231251979999 Winsorized Mean ( 8 / 20 ) -0.000903399233416165 0.0205685846023189 -0.0439213125687956 Winsorized Mean ( 9 / 20 ) -0.000836074469429663 0.0199881341772433 -0.0418285399735581 Winsorized Mean ( 10 / 20 ) -0.007739306838488 0.018688711936946 -0.414116653121933 Winsorized Mean ( 11 / 20 ) -0.00753312113716933 0.0186029485485685 -0.404942319627551 Winsorized Mean ( 12 / 20 ) -0.00437733102381333 0.0178357591083037 -0.245424430619014 Winsorized Mean ( 13 / 20 ) -0.005404038742313 0.0156342353808476 -0.345654175639003 Winsorized Mean ( 14 / 20 ) -0.00133905803384133 0.0148621055390478 -0.0900988107185194 Winsorized Mean ( 15 / 20 ) 0.00500805703049866 0.0132729591603812 0.377312773284749 Winsorized Mean ( 16 / 20 ) -0.00027113822918133 0.0122054672066568 -0.0222144899978472 Winsorized Mean ( 17 / 20 ) 0.00242054028228067 0.0114514728407984 0.211373708511708 Winsorized Mean ( 18 / 20 ) 0.00825223002189367 0.00983793461886702 0.83881732717228 Winsorized Mean ( 19 / 20 ) 0.00744565274603517 0.00938447724824155 0.79340090546123 Winsorized Mean ( 20 / 20 ) 0.00202391150279850 0.00855577284836733 0.236555076749696 Trimmed Mean ( 1 / 20 ) -0.000803520625711724 0.0231935391505887 -0.0346441576033181 Trimmed Mean ( 2 / 20 ) -0.000688098268003035 0.0222647541606014 -0.0309052713108623 Trimmed Mean ( 3 / 20 ) 1.94982498194450e-05 0.0213658616195174 0.000912588978000006 Trimmed Mean ( 4 / 20 ) -0.00041452558673923 0.020919618440652 -0.0198151600095011 Trimmed Mean ( 5 / 20 ) -0.0006891756801268 0.0204256691306225 -0.0337406660080269 Trimmed Mean ( 6 / 20 ) -0.000812421786881874 0.0199069337950736 -0.0408109955679326 Trimmed Mean ( 7 / 20 ) -0.000603939770635869 0.0193479715365536 -0.0312146298900049 Trimmed Mean ( 8 / 20 ) -0.000466879901823863 0.0187495828730630 -0.0249008153933183 Trimmed Mean ( 9 / 20 ) -0.00038893002118238 0.0180504326417613 -0.0215468531365035 Trimmed Mean ( 10 / 20 ) -0.000314405946474500 0.0172881019555384 -0.0181862617008559 Trimmed Mean ( 11 / 20 ) 0.000857946825948684 0.0166302693011968 0.0515894728106982 Trimmed Mean ( 12 / 20 ) 0.00212932075975444 0.0157456966983014 0.135231917682255 Trimmed Mean ( 13 / 20 ) 0.00308618131616147 0.0147569064409578 0.209134707772882 Trimmed Mean ( 14 / 20 ) 0.00431073228613375 0.014063078596403 0.306528350572991 Trimmed Mean ( 15 / 20 ) 0.00511784518898733 0.0133129211858135 0.384426912587825 Trimmed Mean ( 16 / 20 ) 0.00513352921162857 0.0127499619115627 0.402630944879377 Trimmed Mean ( 17 / 20 ) 0.00591304855405308 0.0122469361074834 0.48281860068168 Trimmed Mean ( 18 / 20 ) 0.00642665271166667 0.0117237279396739 0.548174842058425 Trimmed Mean ( 19 / 20 ) 0.006150050088905 0.0114942030351012 0.535056677711699 Trimmed Mean ( 20 / 20 ) 0.0059454812483055 0.0112197857680032 0.529910407492889 Median 0.018212372985375 Midrange 0.02330209835689 Midmean - Weighted Average at Xnp 4.43712010987148e-05 Midmean - Weighted Average at X(n+1)p 0.00511784518898734 Midmean - Empirical Distribution Function 4.43712010987148e-05 Midmean - Empirical Distribution Function - Averaging 0.00511784518898734 Midmean - Empirical Distribution Function - Interpolation 0.00511784518898734 Midmean - Closest Observation 4.43712010987148e-05 Midmean - True Basic - Statistics Graphics Toolkit 0.00511784518898734 Midmean - MS Excel (old versions) 0.00431073228613375 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114935x68gwt99lq7urx0/1ag0s1256114905.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114935x68gwt99lq7urx0/1ag0s1256114905.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114935x68gwt99lq7urx0/22n6r1256114905.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114935x68gwt99lq7urx0/22n6r1256114905.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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