*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 26 Oct 2008 09:32:39 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/26/t122503524960da6mqocm4y17m.htm/, Retrieved Sun, 26 Oct 2008 15:34:09 +0000

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/2008/Oct/26/t122503524960da6mqocm4y17m.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

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Dataseries X:

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6,7500 6,7700 6,8200 6,8800 6,8100 6,8700 6,9100 6,9800 7,0400 6,9900 7,0800 7,1300 7,1000 7,0200 7,0300 7,1200 7,1100 7,0900 7,0200 7,0300 7,0600 7,0500 7,1100 7,0600 7,0500 7,1100 7,0900 7,1300 7,0300 7,0600 7,1100 7,0800 7,1300 7,0000 7,0200 6,9600 6,9800 7,0200 7,0200 7,0600 7,0200 6,9400 6,9700 6,9700 6,9400 6,9300 7,0000 6,9700 6,9700 6,9800 6,9200 7,0000 6,9400 6,9700 6,9300 6,9200 6,8400 6,8600 6,8600 6,8400 6,6200 6,6900 6,6200 6,6800 6,6700 6,6900 6,6900 6,6200 6,6500 6,6600 6,6300 6,6200 6,6500 6,6800 6,6600 6,6700 6,7100 6,6800 6,6300 6,6900

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 6.90825 0.0185756876288894 371.897403639373 Geometric Mean 6.90626057407835 Harmonic Mean 6.90425506595014 Quadratic Mean 6.91022268092715 Winsorized Mean ( 1 / 26 ) 6.90825 0.0185756876288894 371.897403639373 Winsorized Mean ( 2 / 26 ) 6.90825 0.0185756876288894 371.897403639373 Winsorized Mean ( 3 / 26 ) 6.907875 0.0185201684025342 372.992018747235 Winsorized Mean ( 4 / 26 ) 6.907875 0.018351951013793 376.410932810804 Winsorized Mean ( 5 / 26 ) 6.907875 0.018351951013793 376.410932810804 Winsorized Mean ( 6 / 26 ) 6.909375 0.0180718885744011 382.327224493136 Winsorized Mean ( 7 / 26 ) 6.909375 0.0180718885744011 382.327224493136 Winsorized Mean ( 8 / 26 ) 6.909375 0.0177538939836386 389.175186376998 Winsorized Mean ( 9 / 26 ) 6.90825 0.0176039184001169 392.426836059075 Winsorized Mean ( 10 / 26 ) 6.9095 0.0173833362662878 397.478360549228 Winsorized Mean ( 11 / 26 ) 6.908125 0.0172060242522676 401.494552065947 Winsorized Mean ( 12 / 26 ) 6.909625 0.0169459712455703 407.744407202755 Winsorized Mean ( 13 / 26 ) 6.906375 0.0165480158185701 417.353661956844 Winsorized Mean ( 14 / 26 ) 6.906375 0.0165480158185701 417.353661956844 Winsorized Mean ( 15 / 26 ) 6.90825 0.0162260290578854 425.751117254581 Winsorized Mean ( 16 / 26 ) 6.90825 0.0162260290578854 425.751117254581 Winsorized Mean ( 17 / 26 ) 6.906125 0.0159791138895810 432.196994634542 Winsorized Mean ( 18 / 26 ) 6.906125 0.0159791138895810 432.196994634542 Winsorized Mean ( 19 / 26 ) 6.9085 0.0149038054778476 463.539329620782 Winsorized Mean ( 20 / 26 ) 6.916 0.0129697798698905 533.239582273525 Winsorized Mean ( 21 / 26 ) 6.92125 0.0121298029766837 570.598715684355 Winsorized Mean ( 22 / 26 ) 6.93225 0.0104426932240755 663.837369464975 Winsorized Mean ( 23 / 26 ) 6.93225 0.0096832345652457 715.902310668037 Winsorized Mean ( 24 / 26 ) 6.93825 0.00881916605317178 786.72404603434 Winsorized Mean ( 25 / 26 ) 6.93825 0.00881916605317178 786.72404603434 Winsorized Mean ( 26 / 26 ) 6.94475 0.0079196419015067 876.902022385478 Trimmed Mean ( 1 / 26 ) 6.90910256410256 0.0184679487612931 374.113154276415 Trimmed Mean ( 2 / 26 ) 6.91 0.0183341307641566 376.892697498870 Trimmed Mean ( 3 / 26 ) 6.91094594594595 0.0181698442547357 380.352514256951 Trimmed Mean ( 4 / 26 ) 6.91208333333333 0.0179929319064890 384.155476675847 Trimmed Mean ( 5 / 26 ) 6.91328571428571 0.0178337403586275 387.652033463705 Trimmed Mean ( 6 / 26 ) 6.91455882352941 0.0176362547406961 392.065034509503 Trimmed Mean ( 7 / 26 ) 6.91560606060606 0.0174667566874477 395.92960412484 Trimmed Mean ( 8 / 26 ) 6.91671875 0.0172545926246279 400.862477629729 Trimmed Mean ( 9 / 26 ) 6.91790322580645 0.0170607789865663 405.485777129734 Trimmed Mean ( 10 / 26 ) 6.91933333333333 0.0168457050246577 410.747625178361 Trimmed Mean ( 11 / 26 ) 6.92068965517241 0.0166197683824668 416.41312296948 Trimmed Mean ( 12 / 26 ) 6.92232142857143 0.0163643401338044 423.012560969185 Trimmed Mean ( 13 / 26 ) 6.92388888888889 0.0160915807308343 430.280219495248 Trimmed Mean ( 14 / 26 ) 6.92596153846154 0.0158096225146635 438.085193497674 Trimmed Mean ( 15 / 26 ) 6.9282 0.0154409738510687 448.689316284315 Trimmed Mean ( 16 / 26 ) 6.93041666666667 0.0150323479021587 461.033546574013 Trimmed Mean ( 17 / 26 ) 6.93282608695652 0.0144952534076006 478.282503382886 Trimmed Mean ( 18 / 26 ) 6.93568181818182 0.0138299768147638 501.496272269799 Trimmed Mean ( 19 / 26 ) 6.93880952380952 0.0129333248662777 536.506242250341 Trimmed Mean ( 20 / 26 ) 6.942 0.0120106790089657 577.985640513574 Trimmed Mean ( 21 / 26 ) 6.94473684210526 0.0113193451028289 613.528148405835 Trimmed Mean ( 22 / 26 ) 6.94722222222222 0.0106205185590008 654.13211074656 Trimmed Mean ( 23 / 26 ) 6.94882352941177 0.0101833871377635 682.368590666964 Trimmed Mean ( 24 / 26 ) 6.950625 0.00976474794448656 711.807927814922 Trimmed Mean ( 25 / 26 ) 6.952 0.00943702661140507 736.67271337332 Trimmed Mean ( 26 / 26 ) 6.95357142857143 0.00892671938463582 778.9615791597 Median 6.97 Midrange 6.875 Midmean - Weighted Average at Xnp 6.93634146341463 Midmean - Weighted Average at X(n+1)p 6.942 Midmean - Empirical Distribution Function 6.93634146341463 Midmean - Empirical Distribution Function - Averaging 6.942 Midmean - Empirical Distribution Function - Interpolation 6.942 Midmean - Closest Observation 6.93634146341463 Midmean - True Basic - Statistics Graphics Toolkit 6.942 Midmean - MS Excel (old versions) 6.93880952380952 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503524960da6mqocm4y17m/1tf9p1225035153.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503524960da6mqocm4y17m/1tf9p1225035153.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503524960da6mqocm4y17m/2nrx11225035153.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503524960da6mqocm4y17m/2nrx11225035153.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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