Q6

*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, 26 Oct 2008 08:37:20 -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/t1225031955lj0p2unnuhmi4am.htm/, Retrieved Sun, 26 Oct 2008 14:39:15 +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/t1225031955lj0p2unnuhmi4am.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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Dataseries X:

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0,1270303444 0,0569870465 0,0633169852 0,0635119623 0,2045665763 -0,0109913259 0,1685929789 0,1269309882 0,0509008871 -0,0693768269 0,1160703878 0,1254129169 0,0473338719 0,0215080570 -0,0346491100 -0,0368851907 0,1611557235 -0,0466820665 0,1640926131 0,0526423607 -0,0548237876 -0,1229696556 0,1276329691 0,1100648580 -0,0082101473 -0,0052354361 -0,0863610486 -0,0726264062 0,0692500240 -0,1223893006 0,0231458112 -0,0196649964 -0,0436416726 -0,1345459108 0,0611386057 0,0605803220 0,0216621101 -0,0438299252 -0,0910528625 -0,0362473076 0,0623850354 -0,1069348012 0,0125712505 -0,0461436081 -0,0622925832 -0,1495016652 -0,0291191179 0,0482231630 0,0070498618 -0,0829172110 -0,1118452484 -0,1035399499 0,0587898972 -0,1181084499 -0,0458456734 -0,0925061338 -0,0780927375 -0,1788156329 -0,0115950399 0,0385950437 0,0062981780

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 1.63934421689216e-12 0.0114291533032055 1.43435316108008e-10 Geometric Mean NaN Harmonic Mean -0.441033210257928 Quadratic Mean 0.0885298408091324 Winsorized Mean ( 1 / 20 ) -0.000109174255737705 0.0111502480331944 -0.00979119526423917 Winsorized Mean ( 2 / 20 ) 0.000233625370491803 0.0110085322912443 0.0212222087659786 Winsorized Mean ( 3 / 20 ) 0.000658512203278688 0.0108607091380996 0.0606325236138233 Winsorized Mean ( 4 / 20 ) -0.00150164513442623 0.0103531978214794 -0.145041673144776 Winsorized Mean ( 5 / 20 ) -0.0012001512 0.0102755126051592 -0.116797209649416 Winsorized Mean ( 6 / 20 ) -0.000593871334426229 0.0101588317603613 -0.0584586248138739 Winsorized Mean ( 7 / 20 ) -0.000204582296721311 0.0100209628740844 -0.0204154330568761 Winsorized Mean ( 8 / 20 ) -0.0009846056147541 0.0096907756435435 -0.101602353719756 Winsorized Mean ( 9 / 20 ) -0.000242727308196720 0.00923404697467304 -0.0262861244763502 Winsorized Mean ( 10 / 20 ) -0.00669544250491803 0.00798724817749392 -0.83826649130349 Winsorized Mean ( 11 / 20 ) -0.00688411014098361 0.00767868172888924 -0.896522395906026 Winsorized Mean ( 12 / 20 ) -0.00624499004262295 0.00755708672571115 -0.82637533077077 Winsorized Mean ( 13 / 20 ) -0.00541543581147541 0.007354970596332 -0.736296051839573 Winsorized Mean ( 14 / 20 ) -0.00444693380491803 0.00710734829761626 -0.625681142770152 Winsorized Mean ( 15 / 20 ) -0.00378513980491803 0.00695956236856628 -0.543876123880156 Winsorized Mean ( 16 / 20 ) -0.00239659714262295 0.00660049540908232 -0.363093524665621 Winsorized Mean ( 17 / 20 ) -0.000817563318032787 0.00621439654152219 -0.131559566978088 Winsorized Mean ( 18 / 20 ) 0.000302873327868852 0.00567639225481724 0.0533566593485184 Winsorized Mean ( 19 / 20 ) -7.18363245901635e-05 0.00557021744171242 -0.0128965027562872 Winsorized Mean ( 20 / 20 ) -0.000852095144262296 0.0054235710870454 -0.157109611100625 Trimmed Mean ( 1 / 20 ) -0.000436456666101695 0.0108689626376279 -0.0401562394363836 Trimmed Mean ( 2 / 20 ) -0.000786706263157895 0.0105229395364677 -0.074761074168632 Trimmed Mean ( 3 / 20 ) -0.00135252653272727 0.0101895014229334 -0.132737263246576 Trimmed Mean ( 4 / 20 ) -0.00212405711698113 0.00984516991276922 -0.215746110610668 Trimmed Mean ( 5 / 20 ) -0.00231017050392157 0.00961676339124625 -0.240223286144736 Trimmed Mean ( 6 / 20 ) -0.00258654265714286 0.00935158639118318 -0.276588650197520 Trimmed Mean ( 7 / 20 ) -0.0030175814893617 0.00904727309514407 -0.333534917939122 Trimmed Mean ( 8 / 20 ) -0.00356232101555556 0.00869401211765162 -0.409744197195551 Trimmed Mean ( 9 / 20 ) -0.00401941589767442 0.0083309015589435 -0.482470698907665 Trimmed Mean ( 10 / 20 ) -0.00464374653170732 0.00798177721831881 -0.58179355357721 Trimmed Mean ( 11 / 20 ) -0.00432284023846154 0.0078597497798603 -0.5499971830577 Trimmed Mean ( 12 / 20 ) -0.00393896440540541 0.00776021353018319 -0.507584538761064 Trimmed Mean ( 13 / 20 ) -0.00360404163428571 0.0076394269900755 -0.471768581461382 Trimmed Mean ( 14 / 20 ) -0.00334647742727273 0.00750909120335182 -0.44565678277805 Trimmed Mean ( 15 / 20 ) -0.00319180498709677 0.00737514831870602 -0.432778413283054 Trimmed Mean ( 16 / 20 ) -0.00310860171379310 0.00720373584024379 -0.431526333382028 Trimmed Mean ( 17 / 20 ) -0.00320913939629630 0.00704112188980021 -0.455771032872626 Trimmed Mean ( 18 / 20 ) -0.003552400904 0.00689356397961537 -0.515321380131473 Trimmed Mean ( 19 / 20 ) -0.00412044855652174 0.00681304458553051 -0.604788139104904 Trimmed Mean ( 20 / 20 ) -0.00473940932380952 0.00667011013060635 -0.71054438847454 Median -0.0082101473 Midrange 0.0128754717 Midmean - Weighted Average at Xnp -0.00531754255333333 Midmean - Weighted Average at X(n+1)p -0.00319180498709677 Midmean - Empirical Distribution Function -0.00319180498709677 Midmean - Empirical Distribution Function - Averaging -0.00319180498709677 Midmean - Empirical Distribution Function - Interpolation -0.00319180498709677 Midmean - Closest Observation -0.005361636275 Midmean - True Basic - Statistics Graphics Toolkit -0.00319180498709677 Midmean - MS Excel (old versions) -0.00319180498709677 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225031955lj0p2unnuhmi4am/1t3311225031835.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225031955lj0p2unnuhmi4am/1t3311225031835.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225031955lj0p2unnuhmi4am/2fhh51225031835.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225031955lj0p2unnuhmi4am/2fhh51225031835.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')

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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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