*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: Wed, 21 Oct 2009 06:40:19 -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/21/t1256129186cxaq7tlb58l0syf.htm/, Retrieved Wed, 21 Oct 2009 14:46:26 +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/2009/Oct/21/t1256129186cxaq7tlb58l0syf.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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0.720720721 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 0.67 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 0.860759494 0.894736842 0.901408451 0.897058824 0.892307692 0.884057971 0.87804878 0.83908046 0.831325301 0.772151899 0.773333333 0.794871795 0.855421687 0.916666667 0.963414634 1 1.027777778 1.02739726 0.987654321 0.952941176

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.827945770442623 0.0100903318274119 82.0533739230838 Geometric Mean 0.824353071788939 Harmonic Mean 0.820848031350554 Quadratic Mean 0.831626771200318 Winsorized Mean ( 1 / 20 ) 0.828163687672131 0.01003211991854 82.5512149372966 Winsorized Mean ( 2 / 20 ) 0.827934536983607 0.00959646196031982 86.2749772162921 Winsorized Mean ( 3 / 20 ) 0.828145688245902 0.00925107791801908 89.518831814491 Winsorized Mean ( 4 / 20 ) 0.82704371657377 0.00872168619509504 94.8261262872412 Winsorized Mean ( 5 / 20 ) 0.827314756409836 0.00829760516999785 99.7052450026434 Winsorized Mean ( 6 / 20 ) 0.82380960204918 0.00746212770216722 110.398754206514 Winsorized Mean ( 7 / 20 ) 0.823234621245902 0.00732084697634011 112.450734717782 Winsorized Mean ( 8 / 20 ) 0.822221652459016 0.00702649516526796 117.017322736272 Winsorized Mean ( 9 / 20 ) 0.823519141442623 0.00656777079430773 125.387923426982 Winsorized Mean ( 10 / 20 ) 0.823569276688525 0.00642640720537351 128.153920280664 Winsorized Mean ( 11 / 20 ) 0.824777705131148 0.00608788928525484 135.478433737091 Winsorized Mean ( 12 / 20 ) 0.824793638180328 0.00601961421367827 137.017690653026 Winsorized Mean ( 13 / 20 ) 0.823476841540984 0.00570669118820138 144.300228343094 Winsorized Mean ( 14 / 20 ) 0.822229736 0.00544691134739758 150.953390565617 Winsorized Mean ( 15 / 20 ) 0.822312127311475 0.00541300567304563 151.914144743322 Winsorized Mean ( 16 / 20 ) 0.822051692688525 0.0049975027031943 164.492495854597 Winsorized Mean ( 17 / 20 ) 0.81976747904918 0.00441217117685506 185.796843819079 Winsorized Mean ( 18 / 20 ) 0.820843853377049 0.00416911472603465 196.886847044810 Winsorized Mean ( 19 / 20 ) 0.820451691819672 0.00372493756595519 220.259179460712 Winsorized Mean ( 20 / 20 ) 0.818497816081967 0.00342462086532109 239.003921388894 Trimmed Mean ( 1 / 20 ) 0.827235834220339 0.00948302369146879 87.233340454959 Trimmed Mean ( 2 / 20 ) 0.826242868245614 0.00879667591005215 93.9267146697367 Trimmed Mean ( 3 / 20 ) 0.825304761036364 0.00824372957997259 100.113031732793 Trimmed Mean ( 4 / 20 ) 0.824214845566038 0.00772533528370377 106.689847792714 Trimmed Mean ( 5 / 20 ) 0.823368957666667 0.00729866487130069 112.810900649003 Trimmed Mean ( 6 / 20 ) 0.822386534306122 0.00691211025274171 118.977635517304 Trimmed Mean ( 7 / 20 ) 0.822078707595745 0.00670195886070612 122.662452080336 Trimmed Mean ( 8 / 20 ) 0.821854864 0.00647237022048378 126.978963811277 Trimmed Mean ( 9 / 20 ) 0.821789823023256 0.00625787458407189 131.320916068684 Trimmed Mean ( 10 / 20 ) 0.821503946536585 0.00609966142141049 134.680253506041 Trimmed Mean ( 11 / 20 ) 0.821180907717949 0.00592200606217498 138.666002549878 Trimmed Mean ( 12 / 20 ) 0.820641829972973 0.00576600226351109 142.324229590791 Trimmed Mean ( 13 / 20 ) 0.820038829257143 0.00556269468374621 147.417551362874 Trimmed Mean ( 14 / 20 ) 0.819549974363636 0.00536749440220875 152.687625352043 Trimmed Mean ( 15 / 20 ) 0.81917332583871 0.00516444446119306 158.617898206513 Trimmed Mean ( 16 / 20 ) 0.818733172068966 0.00487062642639045 168.096072331237 Trimmed Mean ( 17 / 20 ) 0.818264584666667 0.00457698736593878 178.777986313894 Trimmed Mean ( 18 / 20 ) 0.81804887512 0.00435328924915729 187.915120797075 Trimmed Mean ( 19 / 20 ) 0.817637054652174 0.00408355525952727 200.226763858420 Trimmed Mean ( 20 / 20 ) 0.817206746714286 0.00383583988033454 213.045062413558 Median 0.815217391 Midrange 0.848888889 Midmean - Weighted Average at Xnp 0.8172198441 Midmean - Weighted Average at X(n+1)p 0.81917332583871 Midmean - Empirical Distribution Function 0.81917332583871 Midmean - Empirical Distribution Function - Averaging 0.81917332583871 Midmean - Empirical Distribution Function - Interpolation 0.81917332583871 Midmean - Closest Observation 0.8177218866875 Midmean - True Basic - Statistics Graphics Toolkit 0.81917332583871 Midmean - MS Excel (old versions) 0.81917332583871 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256129186cxaq7tlb58l0syf/1u24d1256128814.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256129186cxaq7tlb58l0syf/1u24d1256128814.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256129186cxaq7tlb58l0syf/27kht1256128814.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256129186cxaq7tlb58l0syf/27kht1256128814.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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