Paper Model 3

*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: Sun, 29 Nov 2009 07:28:51 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/29/t1259505014676oyk7frgxah73.htm/, Retrieved Sun, 29 Nov 2009 15:30:16 +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/Nov/29/t1259505014676oyk7frgxah73.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:

JSSHWPapEDA

Dataseries X:

» Textbox « » Textfile « » CSV «

0,016260163 0,013157895 0,014767932 0,024213075 0,018621974 0,011389522 0,022535211 0,00422833 0,025287356 0,014644351 0,024444444 0,024657534 0,006349206 0,008823529 0,036809816 0,01863354 0,017241379 0,009779951 0,014184397 0,022277228 0,01814882 0,004282655 0,018072289 0,004524887 0,019672131 0,016304348 0,02189781 0,006289308 0,025125628 0,027303754 0,010899183 0,010443864 0,020637899 0,0056926 0,011961722 0,005208333 0,013927577 0,032163743 0,01754386 0,007389163 0,002673797 0,012323944 0,014925373 0,013100437 0,019736842 0,018134715 0,01750547 0,01010101 0,016393443 0,008016032 0,014124294 0,01369863 0,021885522 0,00877193 0,021857923 0,010050251 0,010683761 0,014778325 0,009569378 0,022727273

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.0154475792833333 0.0009302133706206 16.6064902647307 Geometric Mean 0.0135909671282300 Harmonic Mean 0.0114705263628233 Quadratic Mean 0.0170199948205888 Winsorized Mean ( 1 / 20 ) 0.0153960536166667 0.000897072891864072 17.1625447121409 Winsorized Mean ( 2 / 20 ) 0.0152358648166667 0.000851401995786697 17.8950306577432 Winsorized Mean ( 3 / 20 ) 0.0151471565166667 0.000826139739618994 18.3348600609049 Winsorized Mean ( 4 / 20 ) 0.0151819377166667 0.00081420599027022 18.6463105136675 Winsorized Mean ( 5 / 20 ) 0.0151832854666667 0.00079798483243909 19.0270351633853 Winsorized Mean ( 6 / 20 ) 0.0152216472666667 0.000781917198502463 19.4670833380048 Winsorized Mean ( 7 / 20 ) 0.0152016423166667 0.000775206878423081 19.6097877093012 Winsorized Mean ( 8 / 20 ) 0.0151421963166667 0.000711472370015685 21.2829014236109 Winsorized Mean ( 9 / 20 ) 0.0152074173666667 0.000689270368225313 22.0630656237576 Winsorized Mean ( 10 / 20 ) 0.0152904032 0.000659838547842845 23.1729462456954 Winsorized Mean ( 11 / 20 ) 0.01523030305 0.000645922836253078 23.5791370039635 Winsorized Mean ( 12 / 20 ) 0.01537701525 0.000621116540433329 24.7570532242984 Winsorized Mean ( 13 / 20 ) 0.0154166596166667 0.000612881279170545 25.1543979896582 Winsorized Mean ( 14 / 20 ) 0.01519505735 0.000553857336660916 27.4349662705701 Winsorized Mean ( 15 / 20 ) 0.01498248285 0.000515430102549296 29.0679236154374 Winsorized Mean ( 16 / 20 ) 0.0150566543166667 0.000498211987748856 30.2213810323982 Winsorized Mean ( 17 / 20 ) 0.0148303576833333 0.000442871521623167 33.4868171901833 Winsorized Mean ( 18 / 20 ) 0.0148915144833333 0.000432177074697185 34.4569745948867 Winsorized Mean ( 19 / 20 ) 0.0148969564 0.000386403440292472 38.5528565395907 Winsorized Mean ( 20 / 20 ) 0.0150829880666667 0.00035689807651901 42.2613319011913 Trimmed Mean ( 1 / 20 ) 0.0152995024827586 0.0008595157291794 17.8001425260308 Trimmed Mean ( 2 / 20 ) 0.0151960548392857 0.000812801773900859 18.6958928083482 Trimmed Mean ( 3 / 20 ) 0.0151739381851852 0.000786207719750166 19.3001643255386 Trimmed Mean ( 4 / 20 ) 0.0151842388269231 0.000765335372304154 19.8399804535477 Trimmed Mean ( 5 / 20 ) 0.01518492916 0.000743688505107971 20.4183997139977 Trimmed Mean ( 6 / 20 ) 0.0151853400833333 0.000721747193178059 21.0396939910053 Trimmed Mean ( 7 / 20 ) 0.0151774472173913 0.000698625299782269 21.7247317297577 Trimmed Mean ( 8 / 20 ) 0.0151727338863636 0.000670559799253228 22.6269661606031 Trimmed Mean ( 9 / 20 ) 0.0151781870238095 0.000652468890618066 23.2626984091634 Trimmed Mean ( 10 / 20 ) 0.0151733153 0.000634307182687177 23.9210838441397 Trimmed Mean ( 11 / 20 ) 0.0151548277368421 0.000617549671872632 24.5402571276368 Trimmed Mean ( 12 / 20 ) 0.0151433920833333 0.000598042428512094 25.321601547585 Trimmed Mean ( 13 / 20 ) 0.0151090357352941 0.000577411165108582 26.1668576021609 Trimmed Mean ( 14 / 20 ) 0.01506466690625 0.000549990176714807 27.3907926796694 Trimmed Mean ( 15 / 20 ) 0.0150460397 0.00052942561468423 28.4195537251707 Trimmed Mean ( 16 / 20 ) 0.01505511925 0.00051098299248575 29.4630535093981 Trimmed Mean ( 17 / 20 ) 0.0150548978461538 0.000488031937659389 30.8481816135998 Trimmed Mean ( 18 / 20 ) 0.0150879184583333 0.000471803079049544 31.9792708617507 Trimmed Mean ( 19 / 20 ) 0.0151176766363636 0.000448227970532213 33.7276511736056 Trimmed Mean ( 20 / 20 ) 0.0151525272 0.000428302593934166 35.3780887965603 Median 0.0147731285 Midrange 0.0197418065 Midmean - Weighted Average at Xnp 0.0148848852258065 Midmean - Weighted Average at X(n+1)p 0.0150460397 Midmean - Empirical Distribution Function 0.0148848852258065 Midmean - Empirical Distribution Function - Averaging 0.0150460397 Midmean - Empirical Distribution Function - Interpolation 0.0150460397 Midmean - Closest Observation 0.0148848852258065 Midmean - True Basic - Statistics Graphics Toolkit 0.0150460397 Midmean - MS Excel (old versions) 0.01506466690625 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/29/t1259505014676oyk7frgxah73/1dgdp1259504930.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/29/t1259505014676oyk7frgxah73/1dgdp1259504930.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/29/t1259505014676oyk7frgxah73/2r1s41259504930.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/29/t1259505014676oyk7frgxah73/2r1s41259504930.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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