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PAPER-RESUDUAL-CENTR.TEND.

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

Title produced by software: Central Tendency

Date of computation: Sat, 22 Dec 2007 06:09:02 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/22/t1198328982mqvagla5ijoyom9.htm/, Retrieved Sat, 22 Dec 2007 14:09:43 +0100

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Dataseries X:

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Output produced by software:

Summary of compuational 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 5.74327911617711e-14 45.685260664713 1.25714049402660e-15 Geometric Mean NaN Harmonic Mean 5.4578568929996 Quadratic Mean 498.367356473445 Winsorized Mean ( 1 / 40 ) -1.07044118788411 45.4131698301751 -0.0235711621075357 Winsorized Mean ( 2 / 40 ) -2.29879415523333 44.9537151420427 -0.0511369115537994 Winsorized Mean ( 3 / 40 ) -2.64034995871085 44.4887812836035 -0.0593486690920878 Winsorized Mean ( 4 / 40 ) -4.72811312428125 44.0724761971277 -0.107280405646674 Winsorized Mean ( 5 / 40 ) -4.70073054487242 43.0368401465545 -0.109225736110386 Winsorized Mean ( 6 / 40 ) -2.16168783518952 42.4503831775368 -0.0509226931156044 Winsorized Mean ( 7 / 40 ) -2.59857765978668 41.9814893231863 -0.0618981770699471 Winsorized Mean ( 8 / 40 ) -3.53817604544268 41.6701836204214 -0.0849090581810808 Winsorized Mean ( 9 / 40 ) -5.2642725574924 40.5784775167794 -0.129730657226250 Winsorized Mean ( 10 / 40 ) -6.49822675270457 40.2406314099834 -0.161484214462212 Winsorized Mean ( 11 / 40 ) -9.33263392585056 39.4068511953426 -0.236827699822755 Winsorized Mean ( 12 / 40 ) -2.58469728000855 38.381618811807 -0.0673420600804216 Winsorized Mean ( 13 / 40 ) -2.33984736509474 37.4127250573281 -0.0625414845218933 Winsorized Mean ( 14 / 40 ) 0.468525083756458 36.6143233850357 0.0127962240030890 Winsorized Mean ( 15 / 40 ) -4.07227145127066 35.1757866784823 -0.115769164979663 Winsorized Mean ( 16 / 40 ) -10.3032143297527 33.6206526173929 -0.306454917666367 Winsorized Mean ( 17 / 40 ) -1.68337708383053 32.4052195258196 -0.0519477142405796 Winsorized Mean ( 18 / 40 ) -3.36346450879434 31.7869590752379 -0.105812717121925 Winsorized Mean ( 19 / 40 ) -5.43676152806635 31.4661667699081 -0.172781183288765 Winsorized Mean ( 20 / 40 ) -3.21646889350617 30.8550499692547 -0.104244488234866 Winsorized Mean ( 21 / 40 ) -9.09337650972428 29.6573237567675 -0.306614871399151 Winsorized Mean ( 22 / 40 ) -20.5284378752453 28.2164924669055 -0.727533299871436 Winsorized Mean ( 23 / 40 ) -22.7577463101038 27.8333205959273 -0.81764395418324 Winsorized Mean ( 24 / 40 ) -17.0401236839442 26.5702003046565 -0.64132462264343 Winsorized Mean ( 25 / 40 ) -17.5410266188119 26.5052075372506 -0.661795482799356 Winsorized Mean ( 26 / 40 ) -17.7301622663515 26.4321043314074 -0.670781336364657 Winsorized Mean ( 27 / 40 ) -21.8233215047008 25.8462923382268 -0.844350176772705 Winsorized Mean ( 28 / 40 ) -19.077185682415 25.2217996358002 -0.756376862788829 Winsorized Mean ( 29 / 40 ) -19.1137735260231 24.4188783615633 -0.782745761005521 Winsorized Mean ( 30 / 40 ) -17.7367433152219 23.8759106327090 -0.74287190918378 Winsorized Mean ( 31 / 40 ) -12.4301826934017 23.2432382505687 -0.534787044705252 Winsorized Mean ( 32 / 40 ) -8.64104297605933 22.7746387361053 -0.379415150167034 Winsorized Mean ( 33 / 40 ) -2.68802997071634 21.7673404953186 -0.123489131402821 Winsorized Mean ( 34 / 40 ) -5.6619593450246 21.3856147317487 -0.264755510470267 Winsorized Mean ( 35 / 40 ) 3.86678001195432 20.1286014383982 0.192103759607356 Winsorized Mean ( 36 / 40 ) 4.71951567560501 19.7598816848498 0.238843316517605 Winsorized Mean ( 37 / 40 ) 5.46470277223399 19.5775933632873 0.279130466693706 Winsorized Mean ( 38 / 40 ) 8.86107658468298 18.8709647178710 0.469561398537905 Winsorized Mean ( 39 / 40 ) 6.08502554138464 18.47213977226 0.329416386861833 Winsorized Mean ( 40 / 40 ) 17.1059269029020 16.5881092988657 1.03121619195454 Trimmed Mean ( 1 / 40 ) -2.18783081320215 44.2654249361503 -0.0494252752878332 Trimmed Mean ( 2 / 40 ) -3.34375111525529 42.9889400673035 -0.0777816598878761 Trimmed Mean ( 3 / 40 ) -3.89372846263527 41.839576522634 -0.0930632856795018 Trimmed Mean ( 4 / 40 ) -4.34136364260827 40.7519871321113 -0.106531336215195 Trimmed Mean ( 5 / 40 ) -4.23588651124291 39.6748087087171 -0.106765140125609 Trimmed Mean ( 6 / 40 ) -4.13258783710302 38.7568712229547 -0.106628520484270 Trimmed Mean ( 7 / 40 ) -4.50445576199236 37.8704344921651 -0.118943862736095 Trimmed Mean ( 8 / 40 ) -4.81861149312517 36.9778544262923 -0.130310737815523 Trimmed Mean ( 9 / 40 ) -5.00691082366671 36.0366171329019 -0.138939534895892 Trimmed Mean ( 10 / 40 ) -4.97259592582328 35.1798367137342 -0.141347896702488 Trimmed Mean ( 11 / 40 ) -4.78578398783782 34.2717324735813 -0.139642312845637 Trimmed Mean ( 12 / 40 ) -4.26909649488183 33.3839251928607 -0.127878806048690 Trimmed Mean ( 13 / 40 ) -4.44828790071941 32.5427546216284 -0.136690576825448 Trimmed Mean ( 14 / 40 ) -4.65983711834061 31.7370770559165 -0.146826284920020 Trimmed Mean ( 15 / 40 ) -5.14825256615938 30.9388941657277 -0.166400665084608 Trimmed Mean ( 16 / 40 ) -5.24606903114927 30.2387151879049 -0.173488489790321 Trimmed Mean ( 17 / 40 ) -4.80503891789897 29.6559821240273 -0.162025958128897 Trimmed Mean ( 18 / 40 ) -5.06736344177027 29.1518001988474 -0.173826775952266 Trimmed Mean ( 19 / 40 ) -5.2058918103049 28.6516999573604 -0.181695739451841 Trimmed Mean ( 20 / 40 ) -5.18766525363952 28.1141798171778 -0.184521308726561 Trimmed Mean ( 21 / 40 ) -5.33929574288054 27.5705256169926 -0.193659555753618 Trimmed Mean ( 22 / 40 ) -5.05703403108778 27.0949504706627 -0.186641198571790 Trimmed Mean ( 23 / 40 ) -3.91663571333661 26.7192831426724 -0.146584610538502 Trimmed Mean ( 24 / 40 ) -2.55133784400566 26.3200193463142 -0.0969352571681503 Trimmed Mean ( 25 / 40 ) -1.51642456972434 26.0103445592238 -0.0583008258991548 Trimmed Mean ( 26 / 40 ) -0.385276189788742 25.6426759146739 -0.0150248043952491 Trimmed Mean ( 27 / 40 ) 0.827652906474388 25.2068215207845 0.0328344811658201 Trimmed Mean ( 28 / 40 ) 2.40063724058377 24.7557484077138 0.0969729212402136 Trimmed Mean ( 29 / 40 ) 3.88527937811825 24.2971250362129 0.159906959046700 Trimmed Mean ( 30 / 40 ) 5.47142095771421 23.8506272493636 0.229403650499808 Trimmed Mean ( 31 / 40 ) 7.07198401102015 23.3804572797262 0.302474152939363 Trimmed Mean ( 32 / 40 ) 8.42006005049631 22.8992100517588 0.367700895859052 Trimmed Mean ( 33 / 40 ) 9.6048588717849 22.3756145750690 0.42925564522758 Trimmed Mean ( 34 / 40 ) 10.4645014481836 21.8895506570712 0.478059217026601 Trimmed Mean ( 35 / 40 ) 11.6028398571159 21.3333003256358 0.543883959819055 Trimmed Mean ( 36 / 40 ) 12.1554155603418 20.8565588605513 0.582810215319502 Trimmed Mean ( 37 / 40 ) 12.6942488853227 20.3060343135428 0.625146628303314 Trimmed Mean ( 38 / 40 ) 13.2271392622088 19.6224105584978 0.67408329994811 Trimmed Mean ( 39 / 40 ) 13.5554146514965 18.8794130611586 0.717999792026618 Trimmed Mean ( 40 / 40 ) 14.1300599676589 17.9812981423767 0.785819792084892 Median 1.12985447106037 Midrange 129.08201797893 Midmean - Weighted Average at Xnp -0.700690032600609 Midmean - Weighted Average at X(n+1)p 5.4714209577142 Midmean - Empirical Distribution Function -0.700690032600609 Midmean - Empirical Distribution Function - Averaging 5.4714209577142 Midmean - Empirical Distribution Function - Interpolation 5.4714209577142 Midmean - Closest Observation -0.700690032600609 Midmean - True Basic - Statistics Graphics Toolkit 5.4714209577142 Midmean - MS Excel (old versions) 3.88527937811822 Number of observations 120

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/22/t1198328982mqvagla5ijoyom9/1mute1198328936.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/22/t1198328982mqvagla5ijoyom9/1mute1198328936.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/22/t1198328982mqvagla5ijoyom9/2lcq91198328936.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/22/t1198328982mqvagla5ijoyom9/2lcq91198328936.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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