Central Tendency Jenever

*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: Mon, 20 Dec 2010 12:30:52 +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/20/t129284837076tbf464wijjhbo.htm/, Retrieved Mon, 20 Dec 2010 13:32:50 +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/20/t129284837076tbf464wijjhbo.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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11,04 11,02 11,03 11,17 11,19 11,15 11,13 11,06 11,01 11,03 10,99 10,94 11,00 11,06 11,06 11,05 11,04 11,15 11,20 11,16 11,30 11,23 11,25 11,25 11,12 11,14 11,17 11,25 11,27 11,34 11,39 11,44 11,46 11,49 11,51 11,48 11,49 11,52 11,56 11,58 11,58 11,58 11,60 11,62 11,62 11,64 11,67 11,66 11,72 11,82 11,90 12,04 12,08 12,15 12,19 12,22 12,23 12,25 12,26 12,27 12,34 12,38 12,42 12,43 12,48 12,50 12,50 12,49 12,46 12,45 12,45 12,38 12,42

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 11.6235616438356 0.0611241624629456 190.163123312847 Geometric Mean 11.6121339774314 Harmonic Mean 11.6008588063740 Quadratic Mean 11.6351273753705 Winsorized Mean ( 1 / 24 ) 11.6242465753425 0.0610215290651191 190.494187107925 Winsorized Mean ( 2 / 24 ) 11.6242465753425 0.0609279204005111 190.786859274536 Winsorized Mean ( 3 / 24 ) 11.6242465753425 0.0607891150384842 191.222500409546 Winsorized Mean ( 4 / 24 ) 11.6236986301370 0.0605003575122194 192.126114755426 Winsorized Mean ( 5 / 24 ) 11.6236986301370 0.0602750882005517 192.844157962271 Winsorized Mean ( 6 / 24 ) 11.6236986301370 0.0602750882005517 192.844157962271 Winsorized Mean ( 7 / 24 ) 11.6227397260274 0.059782157899487 194.418203263404 Winsorized Mean ( 8 / 24 ) 11.6216438356164 0.0595774101212157 195.067959684235 Winsorized Mean ( 9 / 24 ) 11.6228767123288 0.0594112666864351 195.634218231246 Winsorized Mean ( 10 / 24 ) 11.6187671232877 0.0582200286445165 199.566496166298 Winsorized Mean ( 11 / 24 ) 11.6187671232877 0.0582200286445165 199.566496166298 Winsorized Mean ( 12 / 24 ) 11.6121917808219 0.0570402160511261 203.579028705181 Winsorized Mean ( 13 / 24 ) 11.6104109589041 0.0534663859593644 217.153464753130 Winsorized Mean ( 14 / 24 ) 11.6104109589041 0.0528954046581403 219.497535446443 Winsorized Mean ( 15 / 24 ) 11.6104109589041 0.0522876361419136 222.048878388619 Winsorized Mean ( 16 / 24 ) 11.6082191780822 0.0512731153891643 226.399724104445 Winsorized Mean ( 17 / 24 ) 11.6058904109589 0.050881811458589 228.095071269319 Winsorized Mean ( 18 / 24 ) 11.6009589041096 0.0493420038904838 235.113250160214 Winsorized Mean ( 19 / 24 ) 11.5931506849315 0.0473043823901698 245.075616658736 Winsorized Mean ( 20 / 24 ) 11.5739726027397 0.0442107945858905 261.79064889355 Winsorized Mean ( 21 / 24 ) 11.5682191780822 0.0416631699289604 277.660562021735 Winsorized Mean ( 22 / 24 ) 11.5290410958904 0.0348191480934834 331.112095704839 Winsorized Mean ( 23 / 24 ) 11.5132876712329 0.0299123877929347 384.900321262628 Winsorized Mean ( 24 / 24 ) 11.4869863013699 0.0245109587297261 468.646960244717 Trimmed Mean ( 1 / 24 ) 11.6208450704225 0.0608480465402259 190.981399258892 Trimmed Mean ( 2 / 24 ) 11.6172463768116 0.0605980017825082 191.710057016516 Trimmed Mean ( 3 / 24 ) 11.6134328358209 0.0603133504038934 192.551611841335 Trimmed Mean ( 4 / 24 ) 11.6093846153846 0.0599875295226004 193.529967107760 Trimmed Mean ( 5 / 24 ) 11.6052380952381 0.0596494526494181 194.557327515583 Trimmed Mean ( 6 / 24 ) 11.6008196721311 0.0592578394352488 195.768522489035 Trimmed Mean ( 7 / 24 ) 11.5961016949153 0.0587314848644785 197.442678687130 Trimmed Mean ( 8 / 24 ) 11.5912280701754 0.0581616181043496 199.293424907458 Trimmed Mean ( 9 / 24 ) 11.5861818181818 0.0574593933086668 201.641213925491 Trimmed Mean ( 10 / 24 ) 11.5805660377358 0.0565752226010766 204.693247420214 Trimmed Mean ( 11 / 24 ) 11.5750980392157 0.0556941032884055 207.833457328065 Trimmed Mean ( 12 / 24 ) 11.5691836734694 0.0545340784164587 212.145946340550 Trimmed Mean ( 13 / 24 ) 11.5636170212766 0.0532908046002427 216.99085063587 Trimmed Mean ( 14 / 24 ) 11.5577777777778 0.0524287769783286 220.447213227102 Trimmed Mean ( 15 / 24 ) 11.5513953488372 0.0513640960684935 224.892409932291 Trimmed Mean ( 16 / 24 ) 11.5443902439024 0.0500329754438691 230.735632679968 Trimmed Mean ( 17 / 24 ) 11.5369230769231 0.048441505616749 238.161942533308 Trimmed Mean ( 18 / 24 ) 11.5289189189189 0.0463288671510438 248.849575391769 Trimmed Mean ( 19 / 24 ) 11.5205714285714 0.0438042683487606 263.001115253130 Trimmed Mean ( 20 / 24 ) 11.5121212121212 0.0408474563758666 281.832021709992 Trimmed Mean ( 21 / 24 ) 11.5048387096774 0.0376853725587361 305.286585444952 Trimmed Mean ( 22 / 24 ) 11.4972413793103 0.0339076424233591 339.075221914864 Trimmed Mean ( 23 / 24 ) 11.4933333333333 0.0311827624235678 368.579703658542 Trimmed Mean ( 24 / 24 ) 11.4908 0.0290512191367821 395.535896304309 Median 11.51 Midrange 11.72 Midmean - Weighted Average at Xnp 11.5105555555556 Midmean - Weighted Average at X(n+1)p 11.5289189189189 Midmean - Empirical Distribution Function 11.5289189189189 Midmean - Empirical Distribution Function - Averaging 11.5289189189189 Midmean - Empirical Distribution Function - Interpolation 11.5289189189189 Midmean - Closest Observation 11.5094871794872 Midmean - True Basic - Statistics Graphics Toolkit 11.5289189189189 Midmean - MS Excel (old versions) 11.5289189189189 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t129284837076tbf464wijjhbo/1c0a91292848248.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t129284837076tbf464wijjhbo/1c0a91292848248.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t129284837076tbf464wijjhbo/2c0a91292848248.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t129284837076tbf464wijjhbo/2c0a91292848248.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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