*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, 27 Oct 2009 10:05:44 -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/27/t1256659615wapfvawro13do3o.htm/, Retrieved Tue, 27 Oct 2009 17:06:57 +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/Oct/27/t1256659615wapfvawro13do3o.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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0.866666667 0.835164835 0.862068966 0.926829268 0.949367089 0.924050633 0.835164835 0.79787234 0.808510638 0.868131868 0.877777778 0.870967742 0.828282828 0.816326531 0.806451613 0.819277108 0.8125 0.776470588 0.730769231 0.720720721 0.743119266 0.77 0.815217391 0.826086957 0.821052632 0.8125 0.821052632 0.824175824 0.842696629 0.788888889 0.742574257 0.72815534 0.745098039 0.802083333 0.836956522 0.849462366 0.861702128 0.872340426 0.891304348 0.911111111 0.877777778 0.811111111 0.704081633 0.66 0.683673469 0.741935484 0.777777778 0.788888889 0.791208791 0.78021978 0.758241758 0.760869565 0.772727273 0.771084337 0.797619048 0.814814815 0.831168831 0.797468354 0.784810127 0.8125

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.8092821365 0.00754457314382606 107.266789130709 Geometric Mean 0.807189478658432 Harmonic Mean 0.805075043922817 Quadratic Mean 0.811354355944081 Winsorized Mean ( 1 / 20 ) 0.809301063966667 0.00731040510812466 110.7053647502 Winsorized Mean ( 2 / 20 ) 0.809888714933333 0.00709998970762287 114.068998447110 Winsorized Mean ( 3 / 20 ) 0.810073693233333 0.00673038680262561 120.360644490345 Winsorized Mean ( 4 / 20 ) 0.809248883633333 0.00630622883137725 128.325328064031 Winsorized Mean ( 5 / 20 ) 0.808339493716667 0.00602398606432521 134.18681336329 Winsorized Mean ( 6 / 20 ) 0.809456119016667 0.00579158347668776 139.764215136479 Winsorized Mean ( 7 / 20 ) 0.8088962848 0.00565302203660002 143.090948445428 Winsorized Mean ( 8 / 20 ) 0.808785928133333 0.00560396176795991 144.323955376977 Winsorized Mean ( 9 / 20 ) 0.808657362983333 0.00546600003988628 147.943168145340 Winsorized Mean ( 10 / 20 ) 0.81060378265 0.00500947978381678 161.813964250074 Winsorized Mean ( 11 / 20 ) 0.810242635416667 0.0047668432999543 169.974673894658 Winsorized Mean ( 12 / 20 ) 0.811995354816667 0.00444619237988874 182.627130236093 Winsorized Mean ( 13 / 20 ) 0.809578346066667 0.00392697896769534 206.158055015454 Winsorized Mean ( 14 / 20 ) 0.808383025833333 0.00359917485274829 224.602321061468 Winsorized Mean ( 15 / 20 ) 0.807883827833333 0.00321691344275079 251.136327479956 Winsorized Mean ( 16 / 20 ) 0.807754628633333 0.00308681507062374 261.678983078864 Winsorized Mean ( 17 / 20 ) 0.8084465292 0.00297420009421944 271.819818300481 Winsorized Mean ( 18 / 20 ) 0.8086248321 0.00257492437193933 314.038284352008 Winsorized Mean ( 19 / 20 ) 0.809002539116667 0.00224069611555128 361.049645912216 Winsorized Mean ( 20 / 20 ) 0.808270582116667 0.00213553178044399 378.486796365363 Trimmed Mean ( 1 / 20 ) 0.809440708637931 0.00694783210679351 116.502629337642 Trimmed Mean ( 2 / 20 ) 0.809590327928571 0.00649649586931015 124.619540166742 Trimmed Mean ( 3 / 20 ) 0.80942455737037 0.00607876906888545 133.155997241853 Trimmed Mean ( 4 / 20 ) 0.809174889730769 0.00574545643918602 140.837355272927 Trimmed Mean ( 5 / 20 ) 0.80915269156 0.00550449891092523 146.998428858621 Trimmed Mean ( 6 / 20 ) 0.809355991020833 0.00530030952141607 152.699759844327 Trimmed Mean ( 7 / 20 ) 0.809334224065217 0.00511469203705884 158.237136899179 Trimmed Mean ( 8 / 20 ) 0.809419536909091 0.00491601556867048 164.649506414805 Trimmed Mean ( 9 / 20 ) 0.809532681333333 0.00466906656522388 173.382124676245 Trimmed Mean ( 10 / 20 ) 0.809678567725 0.00438188105730949 184.778764447374 Trimmed Mean ( 11 / 20 ) 0.809532481157895 0.00413663983199801 195.698082026853 Trimmed Mean ( 12 / 20 ) 0.809424882027778 0.00387611704667119 208.823642909058 Trimmed Mean ( 13 / 20 ) 0.80904687132353 0.00361203510815236 223.986436205315 Trimmed Mean ( 14 / 20 ) 0.8089702163125 0.00341423618816125 236.940320390715 Trimmed Mean ( 15 / 20 ) 0.809054100666667 0.00323638078835528 249.98730173461 Trimmed Mean ( 16 / 20 ) 0.8092212825 0.00310135375819464 260.925178355359 Trimmed Mean ( 17 / 20 ) 0.809432819115385 0.00293744561667739 275.556699507837 Trimmed Mean ( 18 / 20 ) 0.80957786175 0.00272286952865584 297.325249421573 Trimmed Mean ( 19 / 20 ) 0.809722260181818 0.00255352605621289 317.099666248446 Trimmed Mean ( 20 / 20 ) 0.80983590035 0.00242448395129825 334.024030110141 Median 0.8125 Midrange 0.8046835445 Midmean - Weighted Average at Xnp 0.807882267516129 Midmean - Weighted Average at X(n+1)p 0.809054100666667 Midmean - Empirical Distribution Function 0.807882267516129 Midmean - Empirical Distribution Function - Averaging 0.809054100666667 Midmean - Empirical Distribution Function - Interpolation 0.809054100666667 Midmean - Closest Observation 0.807882267516129 Midmean - True Basic - Statistics Graphics Toolkit 0.809054100666667 Midmean - MS Excel (old versions) 0.8089702163125 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/27/t1256659615wapfvawro13do3o/17sqo1256659542.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256659615wapfvawro13do3o/17sqo1256659542.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256659615wapfvawro13do3o/26ged1256659542.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256659615wapfvawro13do3o/26ged1256659542.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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