*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 20 Oct 2010 13:41:55 +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/Oct/20/t12875821094whrifjyz5kj60e.htm/, Retrieved Wed, 20 Oct 2010 15:41:49 +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/2010/Oct/20/t12875821094whrifjyz5kj60e.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

98,1 98,0 98,3 98,5 98,7 99,3 99,5 99,8 100,3 99,3 99,6 99,3 99,4 99,7 100,0 99,3 100,3 100,8 101,4 101,1 100,6 99,5 99,1 98,8 99,1 98,8 98,5 99,0 99,0 100,6 101,0 101,8 101,8 101,8 101,8 102,4 103,0 103,3 103,6 104,1 104,5 105,6 105,9 106,0 106,3 107,3 107,1 107,3 107,7 108,0 108,9 108,5 109,0 108,9 109,0 108,9 110,3 109,4 108,6 108,0 108,4 108,0 108,0 107,6 107,5 107,9 108,0 107,5 106,8 106,7 107,2 107,8 106,6 106,3 105,7 105,9 106,5 107,2 108,3

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 R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 103.815189873418 0.443083412145813 234.301684575936 Geometric Mean 103.741300831928 Harmonic Mean 103.667334435127 Quadratic Mean 103.888915844969 Winsorized Mean ( 1 / 26 ) 103.805063291139 0.440875978568057 235.451846635629 Winsorized Mean ( 2 / 26 ) 103.8 0.438454990071647 236.740377804888 Winsorized Mean ( 3 / 26 ) 103.807594936709 0.43725328148688 237.408383954744 Winsorized Mean ( 4 / 26 ) 103.802531645570 0.436488803340428 237.812587290152 Winsorized Mean ( 5 / 26 ) 103.815189873418 0.434547852131683 238.903930520310 Winsorized Mean ( 6 / 26 ) 103.822784810127 0.433410534282638 239.548364882200 Winsorized Mean ( 7 / 26 ) 103.796202531646 0.429508157672495 241.662936262066 Winsorized Mean ( 8 / 26 ) 103.806329113924 0.425086973066753 244.200212405998 Winsorized Mean ( 9 / 26 ) 103.794936708861 0.423486474794159 245.096225940419 Winsorized Mean ( 10 / 26 ) 103.794936708861 0.419907482484808 247.185251605075 Winsorized Mean ( 11 / 26 ) 103.753164556962 0.414288906947154 250.43674309676 Winsorized Mean ( 12 / 26 ) 103.783544303797 0.409971580857144 253.148142822029 Winsorized Mean ( 13 / 26 ) 103.783544303797 0.409971580857144 253.148142822029 Winsorized Mean ( 14 / 26 ) 103.783544303797 0.409971580857144 253.148142822029 Winsorized Mean ( 15 / 26 ) 103.783544303797 0.409971580857144 253.148142822029 Winsorized Mean ( 16 / 26 ) 103.783544303797 0.404488089651277 256.579975922833 Winsorized Mean ( 17 / 26 ) 103.783544303797 0.39871763926075 260.293335645293 Winsorized Mean ( 18 / 26 ) 103.760759493671 0.395792614847636 262.159412786453 Winsorized Mean ( 19 / 26 ) 103.760759493671 0.389431203830794 266.441822003443 Winsorized Mean ( 20 / 26 ) 103.760759493671 0.382790356969577 271.064193766818 Winsorized Mean ( 21 / 26 ) 103.787341772152 0.379190818738968 273.707422867742 Winsorized Mean ( 22 / 26 ) 103.787341772152 0.36479428290033 284.509233387599 Winsorized Mean ( 23 / 26 ) 103.874683544304 0.353314478781558 294.000641871588 Winsorized Mean ( 24 / 26 ) 103.844303797468 0.349556898703907 297.074107770449 Winsorized Mean ( 25 / 26 ) 103.939240506329 0.337360055357369 308.095872216481 Winsorized Mean ( 26 / 26 ) 103.906329113924 0.333299292835797 311.750823801221 Trimmed Mean ( 1 / 26 ) 103.806493506494 0.440178526132144 235.828163674051 Trimmed Mean ( 2 / 26 ) 103.808 0.439084879643483 236.418981414909 Trimmed Mean ( 3 / 26 ) 103.812328767123 0.438951745325209 236.500549030079 Trimmed Mean ( 4 / 26 ) 103.814084507042 0.438945580263876 236.507870621760 Trimmed Mean ( 5 / 26 ) 103.817391304348 0.438813581635417 236.586549845221 Trimmed Mean ( 6 / 26 ) 103.817910447761 0.43880581631112 236.591919679918 Trimmed Mean ( 7 / 26 ) 103.816923076923 0.438652707987597 236.672249336390 Trimmed Mean ( 8 / 26 ) 103.820634920635 0.438893541603232 236.550837684667 Trimmed Mean ( 9 / 26 ) 103.822950819672 0.439593661371679 236.179362768130 Trimmed Mean ( 10 / 26 ) 103.827118644068 0.440185063549713 235.871516872452 Trimmed Mean ( 11 / 26 ) 103.831578947368 0.440971514424049 235.460966414083 Trimmed Mean ( 12 / 26 ) 103.841818181818 0.442267579845539 234.794099576742 Trimmed Mean ( 13 / 26 ) 103.849056603774 0.44387970429299 233.957659247304 Trimmed Mean ( 14 / 26 ) 103.856862745098 0.445053465851418 233.358170902934 Trimmed Mean ( 15 / 26 ) 103.865306122449 0.445666502135756 233.056120719637 Trimmed Mean ( 16 / 26 ) 103.874468085106 0.445560567267422 233.132094076812 Trimmed Mean ( 17 / 26 ) 103.884444444444 0.445504543793849 233.183804501252 Trimmed Mean ( 18 / 26 ) 103.895348837209 0.445488688432474 233.216581105083 Trimmed Mean ( 19 / 26 ) 103.909756097561 0.444900713479146 233.557180173934 Trimmed Mean ( 20 / 26 ) 103.925641025641 0.444196615910046 233.963153484913 Trimmed Mean ( 21 / 26 ) 103.925641025641 0.443310988743624 234.430554767375 Trimmed Mean ( 22 / 26 ) 103.96 0.441487173505356 235.476829767375 Trimmed Mean ( 23 / 26 ) 103.978787878788 0.440702726880896 235.938607901760 Trimmed Mean ( 24 / 26 ) 103.990322580645 0.440585017700005 236.027823014745 Trimmed Mean ( 25 / 26 ) 104.006896551724 0.439153098815303 236.835164848665 Trimmed Mean ( 26 / 26 ) 104.014814814815 0.438194420928506 237.371380937288 Median 104.1 Midrange 104.15 Midmean - Weighted Average at Xnp 103.8175 Midmean - Weighted Average at X(n+1)p 103.909756097561 Midmean - Empirical Distribution Function 103.909756097561 Midmean - Empirical Distribution Function - Averaging 103.909756097561 Midmean - Empirical Distribution Function - Interpolation 103.925641025641 Midmean - Closest Observation 103.8175 Midmean - True Basic - Statistics Graphics Toolkit 103.909756097561 Midmean - MS Excel (old versions) 103.909756097561 Number of observations 79

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/20/t12875821094whrifjyz5kj60e/1irbl1287582111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t12875821094whrifjyz5kj60e/1irbl1287582111.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t12875821094whrifjyz5kj60e/2s0so1287582111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t12875821094whrifjyz5kj60e/2s0so1287582111.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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