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RES CT 3

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

Title produced by software: Central Tendency

Date of computation: Tue, 25 Dec 2007 06:08:01 -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/25/t11985869237o7gt4xddc98lka.htm/, Retrieved Tue, 25 Dec 2007 13:48:45 +0100

User-defined keywords:

Klaas Van Pelt

Dataseries X:

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-0.353141785873333 0.297625082914028 0.0983082341451053 0.139925359720014 -0.0260304190043681 0.236131684625029 0.326810904705451 0.304522961026926 -0.266095559362935 0.229299123788872 0.145396077248178 -0.0120680227813118 0.0167707279435498 0.172565326493242 0.520764957896424 -0.564296215677455 -0.230921780543540 -0.0138191802015432 -1.15680622087539 0.92598803735128 -0.122893896996954 0.224532165198467 1.02007953756655 0.0835680378141303 -0.181444838820578 -0.642504638141853 0.030745797949004 0.99709309689737 -0.385288502061857 -1.04501192852996 0.704231993309034 -0.819403681428793 0.2680213794147 0.337241677254852 0.122000761135222 -0.0448107190759029 -0.389854299691109 -0.542850143364294 -0.321942764154399 0.658530922531208 0.185960548979588 0.140541899053088 0.471770768598889 0.448479867256107 -0.910965941432168 1.44104675420351 0.254841993686707 0.537656369415728 -0.451661850154859 1.83929812376325 0.409184982330585 0.883348997545513 0.47688364584094 0.531002300298511 0.125164005321047 -0.234002081775168 -0.701515355453374 -0.796145550167739 -0.712624468610088 -0.288086134808876 0.870649053749649 1.19817509632766 0.049331213192933 -1.48117575003464 1.38706787975937 0.850000050848651 0.305738416961904 0.125360765731568

Text written by user:

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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.113180806628990 0.0762727947729628 1.48389484043281 Geometric Mean NaN Harmonic Mean -3.7084954122801 Quadratic Mean 0.634495880912751 Winsorized Mean ( 1 / 22 ) 0.112094308976042 0.0731206887590024 1.53300400855758 Winsorized Mean ( 2 / 22 ) 0.113794762443727 0.0718737241246553 1.58325958240824 Winsorized Mean ( 3 / 22 ) 0.11137505084076 0.0684088040672864 1.62808065948956 Winsorized Mean ( 4 / 22 ) 0.106284856796187 0.0648872102652909 1.63799393380672 Winsorized Mean ( 5 / 22 ) 0.10630483404559 0.0641729217875344 1.65653722916882 Winsorized Mean ( 6 / 22 ) 0.107400365399551 0.0613892163027408 1.74949888380895 Winsorized Mean ( 7 / 22 ) 0.104154637656266 0.0603010257106972 1.72724487566701 Winsorized Mean ( 8 / 22 ) 0.109602963952226 0.0586553625744963 1.86859238680901 Winsorized Mean ( 9 / 22 ) 0.117221122423852 0.0561963614566178 2.08592014474717 Winsorized Mean ( 10 / 22 ) 0.0989384775376089 0.0516490785753383 1.91559036998679 Winsorized Mean ( 11 / 22 ) 0.106296704695663 0.0477049558260633 2.22821094485929 Winsorized Mean ( 12 / 22 ) 0.0958731159924168 0.0423011961118439 2.26643983633298 Winsorized Mean ( 13 / 22 ) 0.0954738876197176 0.0419540540310568 2.27567728136695 Winsorized Mean ( 14 / 22 ) 0.099984641046337 0.0405086755416442 2.46822784772486 Winsorized Mean ( 15 / 22 ) 0.0971870770015098 0.0378907449188401 2.56492917227358 Winsorized Mean ( 16 / 22 ) 0.103950312790562 0.0364120738784941 2.85483087663287 Winsorized Mean ( 17 / 22 ) 0.103625231316352 0.0346611830716561 2.98966227154233 Winsorized Mean ( 18 / 22 ) 0.101718976432828 0.0317911813180952 3.19959725356072 Winsorized Mean ( 19 / 22 ) 0.082477843005799 0.0288731119322683 2.85656229918268 Winsorized Mean ( 20 / 22 ) 0.0939620104097876 0.0261427541470672 3.59418942171128 Winsorized Mean ( 21 / 22 ) 0.105536238875694 0.0224812454969434 4.69441245548617 Winsorized Mean ( 22 / 22 ) 0.130405207753541 0.0187354095797312 6.96036065817419 Trimmed Mean ( 1 / 22 ) 0.111184431470344 0.0699366877042609 1.58978692185862 Trimmed Mean ( 2 / 22 ) 0.110217686620541 0.0660811301001761 1.66791467478622 Trimmed Mean ( 3 / 22 ) 0.108256064394923 0.0622201985912611 1.73988619204001 Trimmed Mean ( 4 / 22 ) 0.107077780626495 0.0592195884380136 1.80814800390881 Trimmed Mean ( 5 / 22 ) 0.107310189335379 0.0569508919577911 1.88425827316122 Trimmed Mean ( 6 / 22 ) 0.107554347048613 0.0543997490421396 1.97711108860628 Trimmed Mean ( 7 / 22 ) 0.107586664184836 0.0521119905286769 2.06452801156447 Trimmed Mean ( 8 / 22 ) 0.108227811997865 0.0495672943247476 2.18345208210871 Trimmed Mean ( 9 / 22 ) 0.107994036165624 0.0468207825209914 2.30654060762881 Trimmed Mean ( 10 / 22 ) 0.106541624439792 0.0440029744993165 2.42123687437190 Trimmed Mean ( 11 / 22 ) 0.107665567894897 0.0416403104281314 2.58560915583761 Trimmed Mean ( 12 / 22 ) 0.107857887517930 0.0396396530375619 2.72095942453698 Trimmed Mean ( 13 / 22 ) 0.109474880501531 0.0384087496346801 2.85025890045334 Trimmed Mean ( 14 / 22 ) 0.111305779570691 0.0368446089844095 3.02095157578655 Trimmed Mean ( 15 / 22 ) 0.112752842389593 0.035121121433617 3.21039983312348 Trimmed Mean ( 16 / 22 ) 0.114712975808834 0.0334830159420096 3.42600487385930 Trimmed Mean ( 17 / 22 ) 0.116058308686118 0.0316340855151275 3.66877394418808 Trimmed Mean ( 18 / 22 ) 0.117612443357338 0.029549365456712 3.98020199552620 Trimmed Mean ( 19 / 22 ) 0.119613842895980 0.0274890195660704 4.35133172387199 Trimmed Mean ( 20 / 22 ) 0.124360549648861 0.0253688196332166 4.90210232272806 Trimmed Mean ( 21 / 22 ) 0.128335743241662 0.0232587545502404 5.51773926520652 Trimmed Mean ( 22 / 22 ) 0.131411866846595 0.0215695344835692 6.09247579945217 Median 0.132643062725791 Midrange 0.179061186864305 Midmean - Weighted Average at Xnp 0.104511324586261 Midmean - Weighted Average at X(n+1)p 0.116058308686118 Midmean - Empirical Distribution Function 0.104511324586261 Midmean - Empirical Distribution Function - Averaging 0.116058308686118 Midmean - Empirical Distribution Function - Interpolation 0.116058308686118 Midmean - Closest Observation 0.104511324586261 Midmean - True Basic - Statistics Graphics Toolkit 0.116058308686118 Midmean - MS Excel (old versions) 0.114712975808834 Number of observations 68

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t11985869237o7gt4xddc98lka/164jj1198588071.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t11985869237o7gt4xddc98lka/164jj1198588071.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t11985869237o7gt4xddc98lka/2wong1198588071.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t11985869237o7gt4xddc98lka/2wong1198588071.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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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